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vertex : point where the mirror’s surface intersects with the optical axis
https://openstax.org/books/university-physics-volume-3/pages/2-key-terms
virtual image : image that cannot be projected on a screen because the rays do not physically go through the image, they only appear to originate from the image
https://openstax.org/books/university-physics-volume-3/pages/2-key-terms
A plane mirror always forms a virtual image (behind the mirror).
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Spherical mirrors may be concave (converging) or convex (diverging).
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The focal length of a spherical mirror is one-half of its radius of curvature:f=R/2f=R/2.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The mirror equation and ray tracing allow you to give a complete description of an image formed by a spherical mirror.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
This section explains how a single refracting interface forms images.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
When an object is observed through a plane interface between two media, then it appears at an apparent distancehihithat differs from the actual distancehoho:hi=(n2/n1)hohi=(n2/n1)ho.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
An image is formed by the refraction of light at a spherical interface between two media of indices of refractionn1n1andn2n2.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Image distance depends on the radius of curvature of the interface, location of the object, and the indices of refraction of the media.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
For a converging lens, the focal point is where the converging light rays cross; for a diverging lens, the focal point is the point from which the diverging light rays appear to originate.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The distance from the center of a thin lens to its focal point is called the focal lengthf.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Ray tracing is a geometric technique to determine the paths taken by light rays through thin lenses.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
A real image can be projected onto a screen.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
A virtual image cannot be projected onto a screen.
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A converging lens forms either real or virtual images, depending on the object location; a diverging lens forms only virtual images.
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Image formation by the eye is adequately described by the thin-lens equation.
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The eye produces a real image on the retina by adjusting its focal length in a process called accommodation.
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Nearsightedness, or myopia, is the inability to see far objects and is corrected with a diverging lens to reduce the optical power of the eye.
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Farsightedness, or hyperopia, is the inability to see near objects and is corrected with a converging lens to increase the optical power of the eye.
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In myopia and hyperopia, the corrective lenses produce images at distances that fall between the person’s near and far points so that images can be seen clearly.
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Cameras use combinations of lenses to create an image for recording.
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Digital photography is based on charge-coupled devices (CCDs) that break an image into tiny “pixels” that can be converted into electronic signals.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Angular magnification accounts for magnification of an image created by a magnifier. It is equal to the ratio of the angle subtended by the image to that subtended by the object when the object is observed by the unaided eye.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Angular magnification is greater for magnifying lenses with smaller focal lengths.
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Simple magnifiers can produce as great as tenfold (10×10×) magnification.
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Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece. For a two-element system with an objective and an eyepiece, this isM=mobjMeye.M=mobjMeye.2.41wheremobjmobjis the linear magnification of the obje...
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The microscope is a multiple-element system that contains more than a single lens or mirror. It allows us to see detail that we could not to see with the unaided eye. Both the eyepiece and objective contribute to the magnification. The magnification of a compound microscope with the image at infinity isMnet=−(16cm)(2...
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Simple telescopes can be made with two lenses. They are used for viewing objects at large distances.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
The angular magnificationMfor a telescope is given byM=−fobjfeye,M=−fobjfeye,2.43wherefobjfobjandfeyefeyeare the focal lengths of the objective lens and the eyepiece, respectively.
https://openstax.org/books/university-physics-volume-3/pages/2-summary
Δ l = m λ , Δ l = m λ , for m = 0, ±1, ±2, ±3…
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
Δ l = ( m + 1 2 ) λ , Δ l = ( m + 1 2 ) λ , for m = 0, ±1, ±2, ±3…
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
Δ l = d sin θ Δ l = d sin θ
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
d sin θ = m λ , for m = 0 , ± 1 , ± 2 , ± 3 ,… d sin θ = m λ , for m = 0 , ± 1 , ± 2 , ± 3 ,…
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
d sin θ = ( m + 1 2 ) λ , for m = 0, ± 1 , ± 2 , ± 3 , … d sin θ = ( m + 1 2 ) λ , for m = 0, ± 1 , ± 2 , ± 3 , …
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
y m = m λ D d y m = m λ D d
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
Δ d = m λ 0 2 Δ d = m λ 0 2
https://openstax.org/books/university-physics-volume-3/pages/3-key-equations
coherent waves : waves are in phase or have a definite phase relationship
https://openstax.org/books/university-physics-volume-3/pages/3-key-terms
fringes : bright and dark patterns of interference
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incoherent : waves have random phase relationships
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interferometer : instrument that uses interference of waves to make measurements
https://openstax.org/books/university-physics-volume-3/pages/3-key-terms
monochromatic : light composed of one wavelength only
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Newton’s rings : circular interference pattern created by interference between the light reflected off two surfaces as a result of a slight gap between them
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order : integermused in the equations for constructive and destructive interference for a double slit
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principal maximum : brightest interference fringes seen with multiple slits
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secondary maximum : bright interference fringes of intensity lower than the principal maxima
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thin-film interference : interference between light reflected from different surfaces of a thin film
https://openstax.org/books/university-physics-volume-3/pages/3-key-terms
Young’s double-slit experiment gave definitive proof of the wave character of light.
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An interference pattern is obtained by the superposition of light from two slits.
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In double-slit diffraction, constructive interference occurs whendsinθ=mλ(form=0,±1,±2,±3…)dsinθ=mλ(form=0,±1,±2,±3…), wheredis the distance between the slits,θθis the angle relative to the incident direction, andmis the order of the interference.
https://openstax.org/books/university-physics-volume-3/pages/3-summary
Destructive interference occurs whendsinθ=(m+12)λform=0,±1,±2,±3,…dsinθ=(m+12)λform=0,±1,±2,±3,….
https://openstax.org/books/university-physics-volume-3/pages/3-summary
Interference from multiple slits (N>2N>2) produces principal as well as secondary maxima.
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As the number of slits is increased, the intensity of the principal maxima increases and the width decreases.
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When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a180°180°phase change (or aλ/2λ/2shift) occurs.
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Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change.
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When the mirror in one arm of the interferometer moves a distance ofλ/2λ/2each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe.
https://openstax.org/books/university-physics-volume-3/pages/3-summary
a sin θ = m λ for m = ± 1 , ± 2 , ± 3 , .. . a sin θ = m λ for m = ± 1 , ± 2 , ± 3 , .. .
https://openstax.org/books/university-physics-volume-3/pages/4-key-equations
β = ϕ 2 = π a sin θ λ β = ϕ 2 = π a sin θ λ
https://openstax.org/books/university-physics-volume-3/pages/4-key-equations
E = N Δ E 0 sin β β E = N Δ E 0 sin β β
https://openstax.org/books/university-physics-volume-3/pages/4-key-equations
I = I 0 ( sin β β ) 2 I = I 0 ( sin β β ) 2
https://openstax.org/books/university-physics-volume-3/pages/4-key-equations
θ = 1.22 λ D θ = 1.22 λ D
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m λ = 2 d sin θ , m = 1 , 2 , 3 .. . m λ = 2 d sin θ , m = 1 , 2 , 3 .. .
https://openstax.org/books/university-physics-volume-3/pages/4-key-equations
Bragg planes : families of planes within crystals that can give rise to X-ray diffraction
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
destructive interference for a single slit : occurs when the width of the slit is comparable to the wavelength of light illuminating it
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
diffraction : bending of a wave around the edges of an opening or an obstacle
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
diffraction grating : large number of evenly spaced parallel slits
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
diffraction limit : fundamental limit to resolution due to diffraction
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
hologram : three-dimensional image recorded on film by lasers; the word hologram meansentire picture(from the Greek wordholo, as in holistic)
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
holography : process of producing holograms with the use of lasers
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
missing order : interference maximum that is not seen because it coincides with a diffraction minimum
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
Rayleigh criterion : two images are just-resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
resolution : ability, or limit thereof, to distinguish small details in images
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
two-slit diffraction pattern : diffraction pattern of two slits of widthDthat are separated by a distancedis the interference pattern of two point sources separated bydmultiplied by the diffraction pattern of a slit of widthD
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
width of the central peak : angle between the minimum form=1m=1andm=−1m=−1
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
X-ray diffraction : technique that provides the detailed information about crystallographic structure of natural and manufactured materials
https://openstax.org/books/university-physics-volume-3/pages/4-key-terms
Diffraction can send a wave around the edges of an opening or other obstacle.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
A single slit produces an interference pattern characterized by a broad central maximum with narrower and dimmer maxima to the sides.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
The intensity pattern for diffraction due to a single slit can be calculated using phasors asI=I0(sinββ)2,I=I0(sinββ)2,whereβ=ϕ2=πasinθλβ=ϕ2=πasinθλ,ais the slit width,λλis the wavelength, andθθis the angle from the central peak.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
With real slits with finite widths, the effects of interference and diffraction operate simultaneously to form a complicated intensity pattern.
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Relative intensities of interference fringes within a diffraction pattern can be determined.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
Missing orders occur when an interference maximum and a diffraction minimum are located together.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a double slit.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
Constructive interference occurs whendsinθ=mλform=0,±1,±2,...,dsinθ=mλform=0,±1,±2,...,wheredis the distance between the slits,θθis the angle relative to the incident direction, andmis the order of the interference.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
Diffraction limits resolution.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
The Rayleigh criterion states that two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
X-rays are relatively short-wavelength EM radiation and can exhibit wave characteristics such as interference when interacting with correspondingly small objects.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
Holography is a technique based on wave interference to record and form three-dimensional images.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
Lasers offer a practical way to produce sharp holographic images because of their monochromatic and coherent light for pronounced interference patterns.
https://openstax.org/books/university-physics-volume-3/pages/4-summary
Δ t = Δ τ 1 − v 2 c 2 = γ τ Δ t = Δ τ 1 − v 2 c 2 = γ τ
https://openstax.org/books/university-physics-volume-3/pages/5-key-equations
γ = 1 1 − v 2 c 2 γ = 1 1 − v 2 c 2
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L = L 0 1 − v 2 c 2 = L 0 γ L = L 0 1 − v 2 c 2 = L 0 γ
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x = x ′ + v t , y = y ′ , z = z ′ , t = t ′ x = x ′ + v t , y = y ′ , z = z ′ , t = t ′
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t = t ′ + v x ′ / c 2 1 − v 2 / c 2 t = t ′ + v x ′ / c 2 1 − v 2 / c 2
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x = x ′ + v t ′ 1 − v 2 / c 2 x = x ′ + v t ′ 1 − v 2 / c 2
https://openstax.org/books/university-physics-volume-3/pages/5-key-equations
y = y ′ y = y ′
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