index int64 0 999 | image stringlengths 4.4k 871k | question stringlengths 189 2.04k | answer stringclasses 4
values | category stringclasses 6
values | subfield stringclasses 26
values | reasoning_type stringclasses 20
values | embedding listlengths 4.1k 4.1k |
|---|---|---|---|---|---|---|---|
0 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEEAToDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a refracted light beam in linseed oil making an angle of \( \phi = 20.0^{\circ} \) with the normal line \( NN' \). The index of refraction of linseed oil is 1.48. Determine the angles\( \theta' \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.000812530517578125,
0.01318359375,
0.00015926361083984375,
-0.0155029296875,
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0.01251220703125,
-0.0162353515625,
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0.0137939453125,
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0.02734375,
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0.0087890625,
0.017822265625,
0.01770019531... |
1 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADIARoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A ray of light travels into another medium, making an angle of \( \theta_1 = 45.0^{\circ} \) with the normal as in figure. Find the angle of refraction \( \theta_2 \) if the second medium is water.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 22.7^{\circ... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.00127410888671875,
0.00762939453125,
-0.0087890625,
0.005279541015625,
-0.003692626953125,
0.02587890625,
-0.0255126953125,
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-0.0234375,
0.0172119140625,
-0.01806640625,
0.0301513671875,
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0.016357421875,
0.020751953125,
0.012451171875,
-0.0307617... |
2 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFSAWgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The two mirrors illustrated in figure meet at a right angle. The beam of light in the vertical plane indicated by the dashed lines strikes mirror 1 as shown. Determine the distance the reflected light beam travels before striking mirror 2.Please directly answer the question and provide the correct OPTION LETTER ONLY, e... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01318359375,
0.0147705078125,
-0.00897216796875,
-0.0213623046875,
0.001678466796875,
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0.001220703125,
0.00109100341796875,
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0.005218505859375,
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0.03515625,
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0.01483154296875,
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3 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFIATYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | When the light ray illustrated in figure passes through the glass block of index of refraction \( n = 1.50 \), it is shifted laterally by the distance \( d \). Find the time interval required for the light to pass through the glass block.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.01202392578125,
-0.018798828125,
-0.0137939453125,
-0.00836181640625,
0.01806640625,
0.02294921875,
0.01446533203125,
0.001861572265625,
-0.017333984375,
0.0174560546875,
-0.030029296875,
0.0283203125,
0.0019378662109375,
0.003326416015625,
0.0020599365234375,
0.01007080078125,
-0.... |
4 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEcASwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A narrow beam of ultrasonic waves reflects off the liver tumor illustrated in figure. The speed of the wave is \( 10.0\% \) less in the liver than in the surrounding medium. Determine the depth of the tumor.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 8... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0294189453125,
0.004547119140625,
-0.015625,
-0.033203125,
-0.0133056640625,
0.0096435546875,
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0.005218505859375,
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0.029296875,
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0.00738525390625,
-0.0... |
5 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEIAQgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A person looking into an empty container as shown in figure. When the container is completely filled with a fluid of index of refraction \( n \) and viewed from the same angle, the person can see the center of a coin at the middle of the container’s bottom For what range of values of \( n \) will the center of the coin... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0157470703125,
-0.00872802734375,
-0.02392578125,
-0.0093994140625,
-0.025390625,
0.015625,
0.008056640625,
0.000926971435546875,
-0.034423828125,
0.0174560546875,
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0.0205078125,
-0.0054931640625,
0,
0.00848388671875,
-0.0111083984375,
-0.0225830078125,
0.0346679687... |
6 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAECAXoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A laser beam is incident on a prism perpendicular to one of its faces as shown in figure. The transmitted beam that exits the hypotenuse of the prism makes an angle of \( \theta = 15.0^\circ \) with the direction of the incident beam. Find the index of refraction of the prism.Please directly answer the question and pro... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0126953125,
0.0150146484375,
-0.006744384765625,
-0.0126953125,
0.01123046875,
0.0166015625,
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0.0018157958984375,
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0.0111083984375,
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0.039306640625,
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0.004180908203125,
0.0177001953125,
-0.0028839111328125,
-0.0033416... |
7 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE6AUADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A beam of light both reflects and refracts at the surface between air and glass as shown in figure. If the refractive index of the glass is \( n_g \). Find the angle of incidence \( \theta_1 \) in the air that would result in the reflected ray and the refracted ray being perpendicular to each other.Please directly answ... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
-0.003997802734375,
0.02978515625,
0.0022125244140625,
-0.00469970703125,
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0.000835418701171875,
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0.0150146484375,
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... |
8 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFQAnwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular spread of visible light passing through a prism of apex angle \( 60.0^\circ \) if the angle of incidence is \( 50.0^\circ \)? See figure.Please directly answer the question and provide the correct... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.01214599609375,
0.00110626220703125,
-0.00335693359375,
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0.02783203125,
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0.057373046875,
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0.0174560546875,
0.00244140625,
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9 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADSATYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A triangular glass prism with apex angle \( \Phi = 60.0^\circ \) has an index of refraction \( n = 1.50 \) as shown in figure. What is the smallest angle of incidence \( \theta_1 \) for which a light ray can emerge from the other side?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.,... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
-0.0057373046875,
0.000545501708984375,
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0.0206298828125,
0.02099609375,
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0.0145263671875,
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0.01953125,
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0.000522613525390625,
0.0078125,
0.00469970703125,
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10 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC0ATIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Assume a transparent rod of diameter \( d = 2.00 \, \mu\text{m} \) has an index of refraction of 1.36. Determine the maximum angle \( \theta \) for which the light rays incident on the end of the rod in figure are subject to total internal reflection along the walls of the rod.Please directly answer the question and pr... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.026611328125,
0.0057373046875,
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0.00347900390625,
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0.02099609375,
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0.0242919921875,
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0.033935546875,
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0.0155029296875,
... |
11 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEwAaIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Consider a light ray traveling between air and a diamond cut in the shape shown in figure If the light ray entering the diamond remains vertical as shown in figure, what angle of rotation should the diamond in the water be rotated about an axis perpendicular to the page through \( O \) so that light will first exit the... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
-0.0072021484375,
0.0009307861328125,
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0.034423828125,
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0.006500244140625,
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0.043212890625,
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0.017822265625,
0.00775146484375,
... |
12 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD4AQoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An optical fiber has an index of refraction \( n \) and diameter \( d \). It is surrounded by vacuum. Light is sent into the fiber along its axis as shown in figure. Find the smallest outside radius \( R_{\text{min}} \) permitted for a bend in the fiber if no light is to escape.Please directly answer the question and p... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
-0.00836181640625,
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0.0069580078125,
0.0189208984375,
0.006988525390625,
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0.0230712890625,
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0.01129150390625,
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0.005767822265625,
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0.0076904296875,
-0.02... |
13 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHqAhADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A digital video disc (DVD) records information in a spiral track approximately \( 1\ \mu\text{m} \) wide. The track consists of a series of pits in the information layer that scatter light from a laser beam sharply focused on them. The laser shines in from below through transparent plastic of thickness \( t = 1.20\ \te... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.00677490234375,
0.004119873046875,
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0.00262451171875,
0.040283203125,
0.00726318359375,
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0.0179443359375,
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0.039306640625,
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0.01434326171875,
0.02197265625,
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14 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEYATIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure How many times will the incident beam shown in Figure be reflected by the left of the parallel mirrors?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 7 B: 5 C: 6 D: 4 | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning'] | [
0.0235595703125,
0.01123046875,
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0.005279541015625,
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0.0084228515625,
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0.0167236328125,
0.0012664794921875,
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-0.015625,
-0.0197... |
15 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEEAWQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A thief hides a precious jewel by placing it on the bottom of a public swimming pool. He places a circular raft on the surface of the water directly above and centered over the jewel as shown in figure. The surface of the water is calm.
The raft, of diameter \( d = 4.54\ \text{m} \), prevents the jewel from being seen ... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01336669921875,
-0.01495361328125,
-0.034423828125,
-0.009033203125,
-0.01324462890625,
-0.00274658203125,
-0.004486083984375,
0.016357421875,
-0.038818359375,
0.0015869140625,
-0.033935546875,
0.02197265625,
0.008544921875,
0.015869140625,
0.0152587890625,
0.01129150390625,
-0.031... |
16 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHMAaIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The light beam in figure strikes surface 2 at the critical angle. Determine the angle of incidence \( \theta_1 \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 11.5^{\circ} \) B: \( 27.5^{\circ} \) C: \( 42.5^{\circ} \) D: \( 19.5^{\circ} \) | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
-0.0103759765625,
0.03125,
-0.0107421875,
-0.000667572021484375,
0.00714111328125,
0.02392578125,
-0.0294189453125,
-0.006591796875,
-0.0284423828125,
0.0152587890625,
-0.02490234375,
0.039794921875,
0.006103515625,
0.0164794921875,
0.00069427490234375,
-0.009765625,
-0.0263671875,
... |
17 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFAAowDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light ray traveling in air is incident on one face of a right-angle prism with index of refraction \( n = 1.50 \) as shown in figure, and the ray follows the path shown in the figure. Assuming \( \theta = 60.0^\circ \) and the base of the prism is mirrored. determine the angle \( \phi \) made by the outgoing ray with... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0181884765625,
0.00616455078125,
-0.0118408203125,
-0.006500244140625,
0.00634765625,
0.0098876953125,
-0.00921630859375,
-0.0238037109375,
-0.0263671875,
0.00121307373046875,
-0.023681640625,
0.04541015625,
-0.0098876953125,
0.01177978515625,
0.01104736328125,
0.0172119140625,
-0.... |
18 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEkAlgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A material is surrounded by vacuum and is in the shape of a quarter circle as shown in figure. A light ray parallel to the base of the material is incident from the left and emerges from the material at the angle \( \theta \). Determine an expression for \( \theta \) in terms of \( n \), \( R \), and \( L \).Please dir... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.007232666015625,
0.004791259765625,
-0.004241943359375,
-0.0166015625,
-0.000118255615234375,
0.0087890625,
0.02294921875,
-0.01708984375,
-0.05126953125,
0.02099609375,
-0.0184326171875,
0.036865234375,
-0.0213623046875,
0.00457763671875,
-0.006591796875,
0.0111083984375,
-0.02343... |
19 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFWAgwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure, a light ray is incident normal to one face of a block of flint glass (a prism) that is immersed in water. A substance is dissolved in the water to increase the index of refraction \( n_2 \). At what value of \( n_2 \) does total internal reflection cease at point \( P \)?Please directly answer the q... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00946044921875,
-0.01361083984375,
0.006927490234375,
-0.004058837890625,
-0.002349853515625,
0.028564453125,
-0.00933837890625,
-0.01129150390625,
-0.0277099609375,
-0.0009613037109375,
-0.0235595703125,
0.037109375,
-0.020751953125,
0.01611328125,
0.0169677734375,
-0.00005221366882... |
20 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE2AogDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A transparent cylinder of radius \( R = 2.00 \text{ m} \) as shown in figure. A light ray traveling in air is incident on the left side of the cylinder. The incident light ray and exiting light ray are parallel, and \( d = 2.00 \text{ m} \). Determine the index of refraction of the material.Please directly answer the q... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00970458984375,
-0.0026702880859375,
0.00107574462890625,
-0.01226806640625,
-0.005950927734375,
0.0184326171875,
-0.01214599609375,
-0.0125732421875,
-0.02099609375,
0.00274658203125,
-0.0181884765625,
0.041259765625,
-0.0118408203125,
0.004241943359375,
0.017822265625,
0.0043334960... |
21 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFcAjgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows the path of a light beam through several slabs with different indices of refraction. What the minimum incident angle \( \theta_1 \) be to have total internal reflection at the surface between the medium with \( n = 1.20 \) and the medium with \( n = 1.00 \)?Please directly answer the question and provide t... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
-0.006256103515625,
0.0172119140625,
-0.0274658203125,
-0.01373291015625,
0.0115966796875,
0.0213623046875,
-0.015625,
-0.022216796875,
-0.03271484375,
0.032958984375,
-0.034912109375,
0.039794921875,
-0.0152587890625,
0.0093994140625,
0.021728515625,
0.0157470703125,
-0.007934570312... |
22 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFwAwADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A. H. Pfund's method for measuring the index of refraction of glass is illustrated in figure. One face of a slab of thickness \( t \) is painted white, and a small hole scraped clear at point \( P \) serves as a source of diverging rays when the slab is illuminated from below. Ray \( PBB' \) strikes the clear surface a... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.00131988525390625,
0.006103515625,
-0.0208740234375,
-0.00154876708984375,
-0.009765625,
0.00823974609375,
0.00168609619140625,
-0.0157470703125,
-0.0181884765625,
0.00537109375,
-0.0084228515625,
0.030517578125,
-0.01422119140625,
0.0020294189453125,
0.007232666015625,
-0.0043029785... |
23 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAESAZwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light ray enters a rectangular block of plastic at an angle \( \theta_1 = 45.0^{\circ} \) and emerges at an angle \( \theta_2 = 76.0^{\circ} \) as shown in figure. If the light ray enters the plastic at a point \( L = 50.0 \text{ cm} \) from the bottom edge, what time interval is required for the light ray to travel ... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00848388671875,
0.0036163330078125,
-0.007080078125,
-0.0167236328125,
0.015380859375,
0.021240234375,
0.0191650390625,
-0.0106201171875,
-0.01806640625,
0.0030364990234375,
-0.0283203125,
0.0213623046875,
-0.0034637451171875,
-0.01263427734375,
0.01123046875,
0.00823974609375,
-0.... |
24 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEGAN4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a top view of a square enclosure. The inner surfaces are plane mirrors. A ray of light enters a small hole in the center of one mirror. At what angle \( \theta \) must the ray enter if it exits through the hole after being reflected once by each of the other three mirrors?Please directly answer the questio... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.002410888671875,
0.015869140625,
-0.0174560546875,
-0.00933837890625,
-0.015380859375,
0.01409912109375,
-0.01806640625,
0.00787353515625,
-0.040771484375,
0.0157470703125,
-0.034912109375,
0.0205078125,
-0.0036468505859375,
0.01220703125,
-0.000885009765625,
0.009521484375,
-0.000... |
25 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFqAXIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows an overhead view of a room of square floor area. At the center of the room is a mirror set in a vertical plane and rotating on a vertical shaft about an axis coming out of the page. A bright red laser beam enters from the center point on one wall of the room and strikes the mirror. As the mirror rotates, t... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.005584716796875,
-0.006500244140625,
-0.03564453125,
-0.002044677734375,
-0.000843048095703125,
0.01300048828125,
-0.00762939453125,
-0.0179443359375,
-0.0291748046875,
-0.0030670166015625,
-0.027587890625,
0.006317138671875,
-0.0284423828125,
0.0057373046875,
0.00457763671875,
0.016... |
26 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFyAkYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A periscope as shown in figure is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance from the upper mirror and the centers of the two flat mirrors are separated. What is the dista... | D | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01446533203125,
0.002105712890625,
-0.000762939453125,
-0.013427734375,
0.00982666015625,
0.01275634765625,
-0.00506591796875,
0.026611328125,
-0.013427734375,
0.00160980224609375,
-0.0186767578125,
0.01068115234375,
-0.00531005859375,
0.0020751953125,
-0.004364013671875,
-0.02648925... |
27 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEoAZ4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a thin converging lens of focal length 14.0 cm forms an image of the square \( abcd \), which is \( h_c = h_b = 10.0 \text{ cm} \) high and lies between distances of \( p_d = 20.0 \text{ cm} \) and \( p_a = 30.0 \text{ cm} \) from the lens. Let \( a' \), \( b' \), \( c' \), and \( d' \) represent the respect... | D | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
-0.00032806396484375,
-0.006500244140625,
0.01275634765625,
-0.0185546875,
0.00579833984375,
0.021484375,
-0.01226806640625,
0.0012359619140625,
-0.0286865234375,
-0.002227783203125,
-0.005279541015625,
0.0244140625,
0.0036468505859375,
0.0123291015625,
0.0048828125,
-0.0146484375,
-... |
28 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEQAmIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two rays traveling parallel to the principal axis strike a large plano-convex lens having a refractive index of 1.60 as shown in figure. If the convex face is spherical, a ray near the edge does not pass through the focal point (spherical aberration occurs). Assume this face has a radius of curvature of \( R = 20.0 \te... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.005767822265625,
-0.0130615234375,
0.00023651123046875,
-0.0277099609375,
0.009765625,
0.0185546875,
0.016845703125,
0.017578125,
-0.027587890625,
0.01239013671875,
-0.01611328125,
0.051025390625,
-0.01361083984375,
0.012451171875,
0.015380859375,
0.00341796875,
-0.01495361328125,
... |
29 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFKAboDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A person is to be fitted with bifocals. She can see clearly when the object is between 30 cm and 1.5 m from the eye. The lower portions of the bifocals should enable her to see objects located 25 cm in front of the eye. What power should they have?Please directly answer the question and provide the correct OPTION LETTE... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00860595703125,
0.0001926422119140625,
-0.006134033203125,
-0.0281982421875,
-0.0072021484375,
-0.00970458984375,
0.005889892578125,
-0.020751953125,
-0.0084228515625,
0.0169677734375,
-0.0179443359375,
0.020263671875,
-0.01068115234375,
-0.000701904296875,
-0.0018463134765625,
0.020... |
30 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD2AkoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The lens and mirror in figure are separated and have focal lengths of \( +80.0 \text{ cm} \) and \( -50.0 \text{ cm} \), respectively. An object is placed to the left of the lens as shown. Determine the overall magnification of the image.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0286865234375,
-0.011962890625,
0.0021209716796875,
-0.0203857421875,
-0.0189208984375,
0.007537841796875,
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0.00604248046875,
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0.002716064453125,
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0.0245361328125,
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0.004913330078125,
0.01043701171875,
0.0078125,
... |
31 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFKAxIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two converging lenses having focal lengths of \( f_1 = 10.0 \text{ cm} \) and \( f_2 = 20.0 \text{ cm} \) are placed a distance \( d = 50.0 \text{ cm} \) apart as shown in figure. The image due to light passing through both lenses is to be located between the lenses at the position \( x = 31.0 \text{ cm} \) indicated. ... | D | Optics | Optical Instruments | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00885009765625,
0.00885009765625,
-0.000018715858459472656,
-0.01263427734375,
-0.0113525390625,
0.01226806640625,
0.0001926422119140625,
0.017822265625,
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0.00121307373046875,
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0.0322265625,
0.000461578369140625,
0.006591796875,
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0.0... |
32 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADQARQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The object in figure is midway between the lens and the mirror, which are separated by a distance \( d = 25.0 \text{ cm} \). The magnitude of the mirror's radius of curvature is \( 20.0 \text{ cm} \), and the lens has a focal length of \( -16.7 \text{ cm} \). What is the overall magnification?Please directly answer the... | D | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0220947265625,
-0.0031280517578125,
-0.00909423828125,
-0.01611328125,
-0.00872802734375,
0.01904296875,
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0.0018310546875,
-0.025390625,
0.01031494140625,
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0.0390625,
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0.00836181640625,
-0.0003147125244140625,... |
33 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEcAsoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A parallel beam of light enters a glass hemisphere perpendicular to the flat face as shown in Figure. The magnitude of the radius of the hemisphere is \( R = 6.00 \text{ cm} \), and its index of refraction is \( n = 1.560 \). Assuming paraxial rays, determine the point at which the beam is focused.Please directly answe... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0133056640625,
-0.0159912109375,
-0.006561279296875,
-0.0120849609375,
0.01190185546875,
0.00506591796875,
0.0032806396484375,
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-0.031982421875,
0.00787353515625,
-0.01165771484375,
0.0361328125,
0.0028228759765625,
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0.0070190429... |
34 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD+AooDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An observer to the right of the mirror-lens combination shown in figure (not to scale) sees two real images that are the same size and in the same location. One image is upright, and the other is inverted. Both images are 1.50 times larger than the object. The lens has a focal length of \( 10.0 \text{ cm} \). The lens ... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0086669921875,
-0.000499725341796875,
0.00775146484375,
-0.02294921875,
-0.0034637451171875,
0.007110595703125,
-0.000133514404296875,
0.00469970703125,
-0.0040283203125,
0.003173828125,
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0.024169921875,
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-0.004913330078125,
0.00970458984375,
0.0048828125... |
35 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAC8AiIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of \( 9.00 \text{ cm} \) and \( 11.0 \text{ cm} \). The lens is in front of a con- cave spherical mirror with the radius of curvature \( R = 8.00 \text{ cm} \). Assume the focal points \( F_1 \) and \( F_2 \) of the len... | D | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0155029296875,
-0.0025787353515625,
-0.0009918212890625,
-0.00946044921875,
-0.00732421875,
0.0047607421875,
0.0048828125,
-0.01116943359375,
-0.0201416015625,
-0.0029449462890625,
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0.00830078125,
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0.0087890625,
0.021240234375,
-... |
36 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGYAzADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, material \( a \) is water and material \( b \) is glass with index of refraction 1.52. find the directions of the reflected and refracted rays.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 60.0^\circ B: 49.3^\circ C: 68.0^\circ D: 67.4^\circ | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.00701904296875,
0.01287841796875,
-0.01287841796875,
-0.01324462890625,
-0.004547119140625,
0.0294189453125,
-0.0296630859375,
-0.013427734375,
-0.0274658203125,
0.007415771484375,
-0.0322265625,
0.029296875,
0.001953125,
0.00531005859375,
0.018310546875,
0.0150146484375,
0.0008773... |
37 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGoAtIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Sunlight reflects off the smooth surface of a swimming pool. For what angle of reflection is the reflected light completely polarized?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 60.0^\circ B: 53.1^\circ C: 68.0^\circ D: 67.4^\circ | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0032501220703125,
0.0277099609375,
-0.0120849609375,
-0.00051116943359375,
0.0057373046875,
0.029541015625,
-0.0289306640625,
-0.0035552978515625,
-0.037109375,
0.0029296875,
-0.0167236328125,
0.03466796875,
-0.00173187255859375,
-0.01220703125,
0.0091552734375,
0.008544921875,
-0.... |
38 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIMBNwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A concave mirror forms an image, on a wall 3.00 m in front of the mirror, of a headlamp filament in front of the mirror. What is the focal length of the mirror?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 8.68cm B: 9.68cm C: 9.66cm D: 9.05cm | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0218505859375,
0.0247802734375,
-0.021728515625,
-0.007476806640625,
-0.006072998046875,
0.0035247802734375,
-0.0172119140625,
-0.0140380859375,
-0.0255126953125,
0.004302978515625,
-0.01080322265625,
0.039794921875,
0.01153564453125,
0,
0.0162353515625,
0.0093994140625,
-0.0272216... |
39 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCANqBxwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Santa checks himself for soot. The diameter of the ornament is 7.20 cm. Standard reference texts state that he is a “right jolly old elf,” so we estimate his height to be 1.6 m. How tall is the image of Santa formed by the ornament?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A,... | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0245361328125,
0.0081787109375,
-0.027587890625,
-0.01409912109375,
-0.01416015625,
-0.00095367431640625,
-0.019287109375,
-0.005279541015625,
-0.029541015625,
0.004119873046875,
-0.003021240234375,
0.042236328125,
0.0125732421875,
-0.0184326171875,
0.020263671875,
-0.0079345703125,
... |
40 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFuBLoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A cylindrical glass rod (figure) has index of refraction 1.52. It is surrounded by air. One end is ground to a hemispherical surface. A small object is placed on the axis of the rod to the left of the vertex. Find the lateral magnification.Please directly answer the question and provide the correct OPTION LETTER ONLY, ... | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01287841796875,
-0.00299072265625,
-0.01190185546875,
-0.010009765625,
-0.00653076171875,
-0.00115203857421875,
0.006439208984375,
-0.01190185546875,
-0.00885009765625,
0.0078125,
-0.00555419921875,
0.037841796875,
-0.004730224609375,
-0.005645751953125,
0.022216796875,
0.01080322265... |
41 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHABuwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A cylindrical glass rod (figure) has index of refraction 1.52. It is surrounded by water that has index of refraction of 1.33. One end is ground to a hemispherical surface. A small object is placed on the axis of the rod to the left of the vertex. Find the lateral magnification.Please directly answer the question and p... | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0045166015625,
-0.017333984375,
-0.01019287109375,
-0.00823974609375,
-0.0107421875,
0.01434326171875,
0.003631591796875,
-0.0174560546875,
-0.01153564453125,
0.00787353515625,
-0.004180908203125,
0.0341796875,
0.0040283203125,
-0.0091552734375,
0.01953125,
0.00726318359375,
-0.024... |
42 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAPSA8oDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | If you look straight down into a swimming pool where it is 2.00 m deep, how deep does it appear to be? If you look straight down into a swimming pool where it is 2.00 m deep, how deep does it appear to be?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.856m... | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.018310546875,
-0.00860595703125,
-0.0174560546875,
-0.0252685546875,
-0.009765625,
-0.006317138671875,
0.003143310546875,
-0.00970458984375,
-0.030517578125,
0.017333984375,
-0.0179443359375,
0.050048828125,
0.0003032684326171875,
0.01031494140625,
0.0245361328125,
-0.004058837890625... |
43 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCANqBLIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure Find the magnification of the image produced by the lenses in combination.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -0.856 B: -1.00 C: +0.995 D: -0.814 | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0146484375,
-0.00091552734375,
-0.015380859375,
-0.01300048828125,
-0.003173828125,
0.00174713134765625,
-0.004486083984375,
-0.006134033203125,
-0.03125,
0.0189208984375,
-0.0034637451171875,
0.03564453125,
0.0020751953125,
-0.005828857421875,
0.0211181640625,
0.0035400390625,
-0.... |
44 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGSBSIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure Find the focal length of the contact lens that will permit the wearer to see clearly an object that is 25 cm in front of the eye.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 35cm B: 33cm C: 37cm D: 43cm | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.021240234375,
0.01239013671875,
0.005523681640625,
-0.01141357421875,
0.0006103515625,
0.004669189453125,
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-0.004852294921875,
-0.00946044921875,
-0.005615234375,
0.018798828125,
0.0186767578125,
0.00299072265625,
-0.01116943359375,
-0.0040283203125,
-0.0151977539062... |
45 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF4BOQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The far point of a certain myopic eye is 50 cm in front of the eye. Assume that the lens is worn 2 cm in front of the eye. Find the focal length of the eyeglass lens that will permit the wearer to see clearly an object at infinity.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, ... | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.033447265625,
0.01007080078125,
0.013671875,
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-0.005615234375,
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46 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI+A+wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure Find the wavelength of the light.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 643nm B: 633nm C: 639nm D: 533nm | B | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0159912109375,
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47 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJsBIoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You pass 633\ \mathrm{nm} laser light through a narrow slit and observe the diffraction pattern on a screen. How wide is the slit?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 643nm B: 633nm C: 639nm D: 533nm | B | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0228271484375,
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48 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEyAgwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure How long is the streak of reflected light across the floor?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 6.43m B: 3.75m C: 6.39m D: 5.33m | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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49 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHGAwYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A laser beam is aimed at a 1.0\text{-}\mathrm{cm}\text{-thick} sheet of glass at an angle above the glass. What is its direction in the air on the other side?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 64.0^\circ B: 60.0^\circ C: 50.0^\circ D: 56.0^\circ | B | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01470947265625,
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50 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFyAjgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure What is the prism’s index of refraction?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.64 B: 1.59 C: 0.89 D: 1.24 | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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51 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFiAxwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A lightbulb is set in the bottom of a swimming pool. What is the diameter of the circle of light seen on the water’s surface from above?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 6.4m B: 6.8m C: 8.9m D: 1.24m | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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52 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF2AyIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | To see a flower better, a naturalist holds a magnifying glass 4.0 cm from the flower. What is the magnification?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 6.4 B: 3.0 C: 8.9 D: 1.24 | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02099609375,
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53 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF+AjwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A diverging lens with a focal length is placed some distence from a flower. What is the magnification?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.49 B: 0.33 C: 0.14 D: 0.84 | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.023193359375,
0.000530242919921875,
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54 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADKAsgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | One end of a 4.0-cm-diameter glass rod is shaped like a hemisphere. A small lightbulb is some distance from the end of the rod. How faraway inside is the real image located in the rod?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 14cm B: 18cm C: 96cm D: 74c... | B | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.03125,
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0.004425048828125,
0.0048828125,
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0.006439208984375,
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55 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHWAqwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Based on the figure How faraway is the image of the fish from the edge of the bowl?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 14cm B: 8.6cm C: 8.3cm D: 7.4cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0086669921875,
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56 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGwAugDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | What is the focal length of the glass meniscus lens shown? What is the focal length of the glass meniscus lens shown?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 14cm B: 86cm C: 80cm D: 74cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.031982421875,
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0.00665283203125,
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0.015625,
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0.02294921875,
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0.0228271484375,
-0.001312255859375,
-0.02... |
57 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI2AgADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The objective lens of a microscope uses a planoconvex glass lens with the flat side facing the specimen. What is the radius of the lens’s curved surface?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4mm B: 8.6mm C: 3.8mm D: 7.4mm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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58 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIiAigDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A stamp collector uses a magnifying lens that sits above the stamp. The magnification is 4.0. What is the focal length of the lens?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4cm B: 1.6cm C: 2.7cm D: 2.4cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0115966796875,
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59 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFeA1oDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A 3.0-cm-high object is located 20 cm from a concave mirror. The mirror’s radius of curvature is 80 cm. Determine the height of the image.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4cm B: 5.6cm C: 6.0cm D: 2.4cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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60 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACWAOQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The mirror in figure deflects a horizontal laser beam What is the angle \phi?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 30^\circ B: 90^\circ C: 60^\circ D: 120^\circ | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning'] | [
0.0196533203125,
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-0.016357421875,
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0.0189208984375,
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0.01904296875,
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61 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEMAZQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A light ray leaves point A in Figure, reflects from the mirror, and reaches point B. How far below the top edge does the ray strike the mirror?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4cm B: 5.6cm C: 4.0cm D: 2.4cm | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning'] | [
0.01263427734375,
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0.006011962890625,
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62 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADIAZoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The laser beam in Figure is aimed at the center of a rotating hexagonal mirror. How long is the streak of laser light as the reflected laser beam sweeps across the wall behind the laser?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4m B: 5.6m C: 6.1m D: ... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.027099609375,
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0.00518798828125,
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0.0322265625,
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63 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEGAaADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | At what angle \phi should the laser beam in Figure aimed at the mirrored ceiling in order to hit the midpoint of the far wall? At what angle \phi should the laser beam in Figure aimed at the mirrored ceiling in order to hit the midpoint of the far wall?Please directly answer the question and provide the correct OPTION ... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.03759765625,
0.0185546875,
-0.018310546875,
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0.0252685546875,
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... |
64 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADsAY4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Find the focal length of the glass lens in Figure Find the focal length of the glass lens in FigurePlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 24cm B: 56cm C: 30cm D: 35cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.03564453125,
0.00762939453125,
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0.0040283203125,
0.0028076171875,
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0.017822265625,
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65 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD4AWADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Find the focal length of the planoconvex polystyrene plastic lens in Figure Find the focal length of the planoconvex polystyrene plastic lens in FigurePlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 24cm B: 56cm C: 68cm D: 80cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning'] | [
0.0218505859375,
0.0026397705078125,
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0.017822265625,
0.00811767578125,
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0.023193359375,
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0.0022430419921875,
0.00988769... |
66 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADIAcgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Find the focal length of the glass lens in Figure Find the focal length of the glass lens in FigurePlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -24cm B: -56cm C: -40cm D: -68cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.025146484375,
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0.0033721923828125,
0.0079345703125,
0.0169677734375,
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0.01251220703125,
0.014892578125,
0.004364013671875,
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67 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADYAVoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Find the focal length of the meniscus polystyrene plastic lens Find the focal length of the meniscus polystyrene plastic lensPlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 24cm B: 56cm C: 20cm D: 28cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.030029296875,
0.005859375,
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0.01202392578125,
0.00653076171875,
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0.0089111328125,
0.0140380859375,
0.0186767578125,
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0.00077056884765625,
-0.0250... |
68 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFyAaYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A red ball is at point A. How many images are seen by an observer at point OPlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 4 B: 5 C: 3 D: 1 | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning'] | [
0.02880859375,
0.00060272216796875,
-0.02294921875,
0.00064849853515625,
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0.006011962890625,
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0.00836181640625,
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0.00933837890625,
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0.0014495849609375,
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69 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADYAPgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A laser beam is incident on the left mirror in Figure. Its initial direction is parallel to a line that bisects the mirrors. What is the angle \phi of the reflected laser beam?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 35^\circ B: 90^\circ C: 20^\circ D... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.02099609375,
0.00897216796875,
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0.030517578125,
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0.031494140625,
0.00152587890625,
0.01129150390625,
0.0115966796875,
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70 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFGAhwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The meter stick in Figure lies on the bottom of a 100-cm-long tank with its zero mark against the left edge. You look into the tank at a angle. What mark do you see on the meter stick if the tank is empty?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 24cm B... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning'] | [
0.037353515625,
0.0255126953125,
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0.01373291015625,
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0.0024566650390625,
0.0155029296875,
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0.00506591796875,
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... |
71 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJUAfgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The tank shown in Figure is completely filled with water. What mark do you see on the meter stick if the tank is empty?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 20cm B: 50cm C: 60cm D: 80cm | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.046142578125,
0.01397705078125,
-0.022705078125,
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0.00982666015625,
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0.00787353515625,
0.006500244140625,
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0.00848388671875,
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... |
72 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFyAgoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Shown from above in figure is one corner of a rectangular box filled with water. You can ignore the thin walls of the container. Find the minimum value of x for which the laser beam passes through side B and emerges into the air.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B,... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.01025390625,
0.00653076171875,
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-0.024658203125,
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0.022705078125,
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0.00579833984375,
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0.006591796875,
0.0002155303955078125,
0.05078125,
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0.01458740234375,
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0... |
73 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFoAdwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | \text{White light is incident onto a prism at the angle shown in figure. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is } 2.0\% \text{ larger than the index of refraction of red light.} At what angle \phi does red light emerge from the rear fac... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00494384765625,
0.0091552734375,
-0.00689697265625,
-0.01361083984375,
0.003173828125,
0.0211181640625,
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0.004180908203125,
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0.03857421875,
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0.0244140625,
-0.0007476806640625,... |
74 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACqAYQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | There’s one angle of incidence onto a prism for which the light inside an isosceles prism travels parallel to the base and emerges at an angle. A laboratory measurement finds that \beta = 52.2^\circ for a prism shaped like an equilateral triangle. What is the prism’s index of refraction?Please directly answer the quest... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0120849609375,
0.005767822265625,
0.000812530517578125,
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0.010498046875,
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0.017578125,
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0.043212890625,
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0.0181884765625,
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75 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD0AzoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The normal human eye has maximum visual acuity with a pupil diameter of about 3\ \mathrm{mm}. For larger pupils, acuity decreases due to increasing aberrations; for smaller pupils, acuity decreases due to increasing diffraction. If your pupil diameter is 2.0\ \mathrm{mm}, as it would be in bright light, what is the sma... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01031494140625,
-0.0074462890625,
-0.0174560546875,
-0.0103759765625,
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76 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHqAm4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In the figure, at what distance are are parallel rays from the left focused to a point? In the figure, at what distance are are parallel rays from the left focused to a point?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 14cm B: 26cm C: 15cm D: 19.5cm | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.004730224609375,
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77 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHeA1gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | What is the height of the final image? What is the height of the final image?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.4cm B: 2.6cm C: 2.7cm D: 1.95cm | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0037994384765625,
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78 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIeAkwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The figure shows a simple zoom lens in which the magnitudes of both focal lengths are \( f \). If the spacing \( d < f \), the image of the converging lens falls on the right side of the diverging lens. Our procedure of letting the image of the first lens act as the object of the second lens will continue to work in th... | C | Optics | Optical Instruments | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00970458984375,
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79 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHeAp0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, let a beam of x rays of wavelength 0.125\,\text{nm} be incident on an NaCl crystal at angle \( heta = 45.0^\circ \) to the top face of the crystal and a family of reflecting planes. Let the reflecting planes have separation \( d = 0.252\,\text{nm} \). The crystal is turned through angle \( \phi \) around an... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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80 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFQAYEDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength $0.260 \, \text{nm}$ makes an angle $ heta = 63.8^\circ$ with the top face of the crystal. What is the unit cell size $a_0$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, ... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01141357421875,
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0.0078125,
-0... |
81 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGAAy0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure is a graph of intensity versus angular position $ heta$ for the diffraction of an x-ray beam by a crystal. The horizontal scale is set by $ heta_s = 2.00^\circ$. The beam consists of two wavelengths, and the spacing between the reflecting planes is $0.94 \, \text{nm}$. What is the longer wavelengths in the beam?... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.015869140625,
0.01409912109375,
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82 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHtAl4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Light of wavelength $440 \, \text{nm}$ passes through a double slit, yielding a diffraction pattern whose graph of intensity $I$ versus angular position $ heta$ is shown in figure. Verify the displayed intensities of the $m = 1$ and $m = 2$ interference fringes.Please directly answer the question and provide the correc... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.025634765625,
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0,
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0.03... |
83 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJZA4IDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives \( \alpha \) versus the sine of the angle \( \theta \) in a single-slit diffraction experiment using light of wavelength 610\,\text{nm}. The vertical axis scale is set by \( \alpha_s = 12\,\text{rad} \). What is the slit width?Please directly answer the question and provide the correct OPTION LETTER ONLY, ... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.017822265625,
0.0152587890625,
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0.0181884765625,
0.00003647804260253906,
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0.009033203125,
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0.035400390625,
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0.00775146484375,
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... |
84 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEUAxADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, an oil drop \( n = 1.20 \) floats on the surface of water \( n = 1.33 \) and is viewed from overhead when illuminated by sunlight shining vertically downward and reflected vertically upward. Move from the rim inward to the third blue band and, using a wavelength of 475\,\text{nm} for blue light, determine th... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0133056640625,
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0.007476806640625,
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0.013671875,
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0.043212890625,
0.0174560546875,
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0.016845703125,
... |
85 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAL2AvkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Four laser pistols are pointed toward the center of an array of plastic layers where a clay armadillo is the target. The indexes of refraction of the layers are \( n_1 = 1.55 \), \( n_2 = 1.70 \), \( n_3 = 1.45 \), \( n_4 = 1.60 \), \( n_5 = 1.45 \), \( n_6 = 1.61 \), \( n_7 = 1.59 \), \( n_8 = 1.70 \), and \( n_9 = 1.... | C | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0255126953125,
0.022216796875,
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0.01287841796875,
0.0211181640625,
0.000926971435546875,
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0.0096435546875,
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0.037353515625,
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0.0004558563232421875,
0.0260009765625,
-0.006713867187... |
86 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGkAxADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows an optical fiber in which a central plastic core of index of refraction \( n_1 = 1.58 \) is surrounded by a plastic sheath of index of refraction \( n_2 = 1.53 \). Light can travel along different paths within the central core, leading to different travel times through the fiber. This causes an initially s... | C | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.01171875,
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0.01495361328125,
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0.0030059814453125,
0.0181884765625,
-0.00674438476... |
87 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJSAsEDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, two isotropic point sources \( S_1 \) and \( S_2 \) emit light at wavelength \( \lambda = 400\,\text{nm} \). Source \( S_1 \) is located at \( y = 640\,\text{nm} \); source \( S_2 \) is located at \( y = -640\,\text{nm} \). At point \( P_1 \) (at \( x = 720\,\text{nm} \)), the wave from \( S_2 \) arrives ahe... | C | Optics | Wave Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0159912109375,
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0.041015625,
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0.01226806640625,
0.022705078... |
88 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJUAoADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, the waves along rays 1 and 2 are initially in phase, with the same wavelength \( \lambda \) in air. Ray 2 goes through a material with length \( L \) and index of refraction \( n \). The rays are then reflected by mirrors to a common point \( P \) on a screen. Suppose that we can vary \( L \) from 0 to 2400\... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0255126953125,
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0.006317138671875,
0.0162353515625,
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89 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHCAnoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, the waves along rays 1 and 2 are initially in phase, with the same wavelength \( \lambda \) in air. Ray 2 goes through a material and index of refraction \( n \). The rays are then reflected by mirrors to a common point \( P \) on a screen. Suppose that we can vary \( n \) from \( n = 1.0 \) to \( n = 2.5 \)... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0201416015625,
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0.01483154296875,
0.0167236328125,
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0.0242919921875,
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0.035400390625,
0.00927734375,
0.00347900390625,
-0.00067138671875,
-0.004913330078125,
-0.03686523... |
90 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJOAo8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, two isotropic point sources \( S_1 \) and \( S_2 \) emit light in phase at wavelength \( \lambda \) and at the same amplitude. The sources are separated by distance \( d = 6.00\lambda \) on an \( x \) axis. A viewing screen is at distance \( D = 20.0\lambda \) from \( S_2 \) and parallel to the \( y \) axis.... | C | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.01806640625,
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0.01177978515625,
0.0143432617187... |
91 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFQAVQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | As shown in figure, a ray of light traveling upward follows the path indicated. Find the angle the light makes with the normal in the air.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 82° B: 83° C: 81° D: 84° | A | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0179443359375,
0.01275634765625,
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0.018798828125,
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92 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACSAYgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A laser beam shines along the surface of a block of transparent material.Half of the beam goes straight to a detector, while the other half travels through the block and then hits the detector. The time delay between the arrival of the two light beams at the detector is 6.25 ns. What is the index of refraction of this ... | A | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0186767578125,
0.004302978515625,
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93 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD6AugDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A beam of light passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in figure. If we remove the middle filter, what will be the light intensity at point C?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION... | A | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
0.01214599609375,
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94 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADsAu4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Light passes through two ideal polarizing filters having their polarizing axes oriented as shown in figure.You want to adjust the angle $\varphi$ so that the intensity at point $P$ is equal to $I_0 / 10$. If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the... | A | Optics | Wave Optics | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.01129150390625,
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95 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJcAa4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Fill a transparent drinking glass with water and place it on top of the line you have drawn, making sure the line extends outward from both sides of the glass. You look downward at an angle to see the image of the line through the water. The image of the line beneath the glass will appear shifted away from the line you... | A | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0184326171875,
-0.01519775390625,
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0,
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0... |
96 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFQAPIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A ray of light is incident in air on a block of a transparent solid whose index of refraction is $n$. If $n = 1.38$. What is the largest angle of incidence $\theta_a$ for which total internal reflection will occur at the vertical face.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.,... | A | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
-0.0037078857421875,
0.021484375,
0.00823974609375,
-0.020263671875,
0.0184326171875,
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0.01165771484375,
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0.011474609375,
0.020263671875,
0.00640869140625,
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97 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADYAZQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A ray of light traveling in air is incident on one face of a prism made of glass. Part of the light refracts into the prism and strikes the opposite face at point A.The ray at A is at the critical angle. What is the value of $\theta_a$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.... | A | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0101318359375,
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0.024169921875,
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0.01904296875,
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0.0028533935546875,
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0.0041503906... |
98 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAsoFlADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Optical fibers are constructed with a cylindrical core surrounded by a sheath of cladding material. Common materials used are pure silica ($n_2 = 1.450$) for the cladding and silica doped with germanium ($n_1 = 1.465$) for the core. What is the value of $ heta_i$ for $n_1 = 1.465$ and $n_2 = 1.450$?Please directly answ... | A | Optics | Geometrical Optics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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... |
99 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGIAP4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The prism has a refractive index of 1.66, and the angles $A$ are $25.0^\circ$. Two light rays $m$ and $n$ are parallel. What is the angle between them after they emerge?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 39.1° B: 35.9° C: 37.3° D: 38.2° | A | Optics | Geometrical Optics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
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