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<image>A d.c. electromagnet is to be constructed by winding a coil of $N$ turns tightly on an iron yoke shaped like a doughnut with a small slab sliced out to form the gap as in Fig. 2.34. The radii for the doughnut are $a$ and $b$ and the width of the gap is $W$. The permeability $\mu$ for the iron can be assumed cons...
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301
<image>A d.c. electromagnet is to be constructed by winding a coil of $N$ turns tightly on an iron yoke shaped like a doughnut with a small slab sliced out to form the gap as in Fig. 2.34. The radii for the doughnut are $a$ and $b$ and the width of the gap is $W$. The permeability $\mu$ for the iron can be assumed cons...
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302
<image>A d.c. electromagnet is to be constructed by winding a coil of $N$ turns tightly on an iron yoke shaped like a doughnut with a small slab sliced out to form the gap as in Fig. 2.34. The radii for the doughnut are $a$ and $b$ and the width of the gap is $W$. The permeability $\mu$ for the iron can be assumed cons...
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303
<image>A uniform sheet of surface current of strength $\lambda$ (ampères per meter in the $y$ direction) flows eastward (in $x$ direction) on a horizontal plane ($z=0$), as shown in Fig. 2.50. What are the magnitude and direction of the force on: The same segment but oriented so as to carry a current in the westward di...
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304
<image>A circular wire of radius $R$ carries a current $i$ electromagnetic units. A sphere of radius $a$ ($a \ll R$) made of paramagnetic material with permeability $\mu$ is placed with its center at the center of the circuit. Determine the magnetic dipole moment of the sphere resulting from the magnetic field of the c...
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305
<image>A circular wire of radius $R$ carries a current $i$ electromagnetic units. A sphere of radius $a$ ($a \ll R$) made of paramagnetic material with permeability $\mu$ is placed with its center at the center of the circuit. Determine the force per unit area on the sphere.
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306
<image>In Fig. 2.56 an iron needle 1 cm long and 0.1 cm in diameter is placed in a uniform magnetic field of $H_{0}=1000 \mathrm{Gs}$ with its long axis along the field direction. Give an approximate formula for $\mathbf{H}(\mathbf{r})$ valid for distances $r \gg 1 \mathrm{~cm}$. Here $r$ is measured from the center of...
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307
<image>A long solenoid of radius $b$ and length $l$ is wound so that the axial magnetic field is $$\mathbf{B}=\begin{cases} B_{0}\,\mathbf{e}_{z}, & r<b,\\ 0, & r>b, \end{cases}$$ A particle of charge $q$ is emitted with velocity $v$ perpendicular to a central rod of radius $a$ (see Fig. 2.59). The electric force on th...
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308
<image><image>Figure 2.75 shows two long parallel wires carrying equal and opposite steady currents $I$ and separated by a distance $2a$. Consult the diagram 2.76 which gives specific dimensions and which represents two long pipes of circular cross section carrying equal and opposite charges $q$ (per cm). Given that th...
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309
<image>A Hall probe with dimensions as shown in Fig. 2.81 has conductivity $\sigma$ and carries charge density $\rho$. The probe is placed in an unknown magnetic field $B$ oriented along the $+y$ direction. An external potential $V_{\text {ext }}$ is applied to two ends producing an electric field in the $+z$ direction...
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310
<image>A model for an electron consists of a shell of charge distributed uniformly on the surface of a sphere of radius $a$. The electron moves with velocity $v\ll c$. Use the value of $a$ to calculate the energy in the field of the moving charge and compare it with the rest-mass energy and kinetic energy.
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311
<image><image><image><image>Any linear dc network (a load $R$ is connected between the two arbitrary points A and B of the network) is equivalent to a series circuit consisting of a battery of emf $V$ and a resistance $r$, as shown in Fig. 3.4. Calculate $V$ and $r$ of the circuit in Fig. 3.5. (Hint: Use mathematical i...
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312
<image><image><image><image>Any linear dc network (a load $R$ is connected between the two arbitrary points A and B of the network) is equivalent to a series circuit consisting of a battery of emf $V$ and a resistance $r$, as shown in Fig. 3.4. Calculate $V$ and $r$ of the circuit in Fig. 3.7. (Hint: Use mathematical i...
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313
<image>A square voltage pulse (Fig. 3.15) is applied to terminal A in the circuit shown in Fig. 3.14. What signal appears at B?
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314
<image>As shown in Fig. 3.26, the switch has been in position A for a long time. At $t=0$ it is suddenly moved to position B. Immediately after contact with B: What is the potential of point $B$ (with respect to ground)?
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<image>As shown in Fig. 3.26, the switch has been in position A for a long time. At $t=0$ it is suddenly moved to position B. Immediately after contact with B: What is the time rate of change of the potential difference across $L$ ?
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<image>Switch S is thrown to position A as shown in Fig. 3.30. Now the switch is thrown to position B (open position). What are the magnitude and direction of the currents in $R_{1}, R_{2}$, and $R_{3}$ just after the switch is thrown to position B?
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<image>Switch S is thrown to position A as shown in Fig. 3.30. What are the magnitude and direction of the currents in $R_{1}, R_{2}$, and $R_{3}$ one‐half second after the switch is thrown from A to B?
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318
<image>Switch S is thrown to position A as shown in Fig. 3.30. One second after the switch is thrown from A to B, it is finally thrown from B to C. What are the magnitude and direction of the currents in $R_{2}, R_{3}, R_{4}$, and $R_{5}$ just after the switch is thrown from B to C?
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319
<image>In the electrical circuit shown in Fig. 3.36, $\omega$, $R_{1}$, $R_{2}$ and $L$ are fixed; $C$ and $M$ (the mutual inductance between the identical inductors $L$) can be varied. Find values of $M$ and $C$ which maximize the power dissipated in resistor $R_{2}$. What is the maximum power? You may assume, if need...
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<image>As in Fig. 3.46, $G$ is a ballistic galvanometer (i.e., one whose deflection $\theta$ is proportional to the charge $Q$ which quickly flows through it). The coil $L$ as shown is initially in a magnetic field $B_{0}=0$. Switch $S$ is then closed, current $I=1 \mathrm{amp}$ flows, and $G$ deflects $\theta_{1}=0.5$...
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<image><image>In the circuit shown in Fig. 3.52, the capacitor has circular plates of radius $r_{0}$ separated by a distance $d$. Between the plates there is a vacuum. At $t=0$, when there is a charge $Q_{0}$ on the capacitor, the switch is closed. Find the magnetic field between the plates for $t>0$. You may use ideal...
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<image>In the circuit shown in Fig. 3.52, the capacitor has circular plates of radius $r_{0}$ separated by a distance $d$. Between the plates there is a vacuum. At $t=0$, when there is a charge $Q_{0}$ on the capacitor, the switch is closed. What is the electromagnetic energy density in the vacuum region between the pl...
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<image>The amplifier in the circuit shown in Fig. 3.56 is an operational amplifier with a large gain (say gain $=50,000$). The input signal $V_{\text{in}}$ is sinusoidal with an angular frequency $\omega$ in the middle of the amplifier's bandwidth. Find an expression for the phase angle $\phi$ between the input and out...
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<image>In Fig. 3.66 the 4 basic logic gate symbols are shown. Match them to the negative logic equivalents on the right.
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<image>In Fig. 3.66 the 4 basic logic gate symbols are shown. Name the logic function.
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<image>Refer to Fig. 3.67. Is $Q_{2}$ saturated? Justify your answer.
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<image>Refer to Fig. 3.67. What is the base-emitter voltage of $Q_{1}$ ?
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<image>The square-box in Fig. 3.71 represents an unknown linear lumpedconstant passive network. The source of emf at the left is assumed to have zero internal impedance. It is known that if the input emf $e_{i}(t)$ is a step function, i.e., $e_{i}(t)=\begin{cases}0 & t\leq 0\\ A & t>0\end{cases}$ then the open-circuit ...
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<image>The pions that are produced when protons strike the target at Fermilab are not all moving parallel to the initial proton beam. A focusing device, called a "horn", (actually two of them are used as a pair) is used to deflect the pions so as to cause them to move more closely towards the proton beam direction. Thi...
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<image>The pions that are produced when protons strike the target at Fermilab are not all moving parallel to the initial proton beam. A focusing device, called a "horn", (actually two of them are used as a pair) is used to deflect the pions so as to cause them to move more closely towards the proton beam direction. Thi...
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<image>The pions that are produced when protons strike the target at Fermilab are not all moving parallel to the initial proton beam. A focusing device, called a "horn", (actually two of them are used as a pair) is used to deflect the pions so as to cause them to move more closely towards the proton beam direction. Thi...
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332
<image>The pions that are produced when protons strike the target at Fermilab are not all moving parallel to the initial proton beam. A focusing device, called a "horn", (actually two of them are used as a pair) is used to deflect the pions so as to cause them to move more closely towards the proton beam direction. Thi...
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<image>Consider the situation shown in Fig. 4.28 where a perfectly conducting thin wire connects two small metallic balls. Suppose the charge density is given by $\rho(\mathbf{x}, t)=[\delta(z-a)-\delta(z+a)]\delta(x)\delta(y) Q\cos(\omega_{0}t)$. The current flows between the metallic balls through the thin wire. $a$,...
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334
<image>Consider the situation shown in Fig. 4.28 where a perfectly conducting thin wire connects two small metallic balls. Suppose the charge density is given by $\rho(\mathbf{x}, t)=[\delta(z-a)-\delta(z+a)]\delta(x)\delta(y) Q\cos(\omega_{0}t)$. The current flows between the metallic balls through the thin wire. $a$,...
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335
<image>Two electric dipole oscillators vibrate with the same frequency $\omega$, but their phases differ by $\frac{\pi}{2}$. The amplitudes of the dipole moments are both equal to $\mathbf{P}_{0}$, but the two vectors are at an angle $\psi_{0}$ to each other, (let $\mathbf{P}_{1}$ be along the $x$-axis and $\mathbf{P}_...
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336
<image>Two electric dipole oscillators vibrate with the same frequency $\omega$, but their phases differ by $\frac{\pi}{2}$. The amplitudes of the dipole moments are both equal to $\mathbf{P}_{0}$, but the two vectors are at an angle $\psi_{0}$ to each other, (let $\mathbf{P}_{1}$ be along the $x$-axis and $\mathbf{P}_...
[ -0.01806640625, -0.0036773681640625, -0.004608154296875, -0.005645751953125, 0.0186767578125, 0.0162353515625, -0.00191497802734375, -0.01513671875, -0.0269775390625, 0.0228271484375, -0.05517578125, 0.01953125, -0.01263427734375, 0.0157470703125, -0.004180908203125, 0.01806640625, -...
337
<image><image>A waveguide is formed by two infinite parallel perfectly conducting planes separated by a distance $a$. The gap between the planes is filled with a gas whose index of refraction is $n$ (this is taken to be frequency independent). A uniform charged wire, which extends infinitely along the $y$ direction (Fi...
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338
<image><image>A waveguide is formed by two infinite parallel perfectly conducting planes separated by a distance $a$. The gap between the planes is filled with a gas whose index of refraction is $n$ (this is taken to be frequency independent). Any electromagnetic disturbance (independent of $y$) must be expressible as ...
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339
<image>In a recent classic table-top experiment, a monochromatic neutron beam ($\lambda=1.445 \AA$) was split by Bragg reflection at point $A$ of an interferometer into two beams which were recombined (after another reflection) at point $D$. One beam passes through a region of transverse magnetic field of strength $B$ ...
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340
<image>A particle of charge $q$ moving in one dimension is initially bound to a delta function potential at the origin. From time $t=0$ to $t=\tau$ it is exposed to a constant electric field $\varepsilon_{0}$ in the $x$ direction as shown in Fig. 6.15. The object of this problem is to find the probability that for $t>\...
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341
<image>A particle of charge $q$ moving in one dimension is initially bound to a delta function potential at the origin. From time $t=0$ to $t=\tau$ it is exposed to a constant electric field $\varepsilon_{0}$ in the $x$ direction as shown in Fig. 6.15. The object of this problem is to find the probability that for $t>\...
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342
<image>A point source $Q$ emits coherent light isotropically at two frequencies $w$ and $w+ \Delta w$ with equal power I joules/sec at each frequency. Two detectors $A$ and $B$ each with a (small) sensitive area $s$, capable of responding to individual photons are located at distances $l_{A}$ and $l_{B}$ from $Q$ as sh...
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343
<image>A cylindrical container is initially separated by a clamped piston into two compartments of equal volume. The left compartment is filled with one mole of neon gas at a pressure of 4 atmospheres and the right with argon gas at one atmosphere. The gases may be considered as ideal. The whole system is initially at ...
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344
<image>The elasticity of a rubber band can be described in terms of a onedimensional model of polymer involving $N$ molecules linked together end-to-end. The angle between successive links is equally likely to be $0^{\circ}$ or $180^{\circ}$. Find the relationship between the force and the length, without using the con...
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345
<image>Consider a one-dimensional chain consisting of $n \\gg 1$ segments as illustrated in the figure. Let the length of each segment be $a$ when the long dimension of the segment is parallel to the chain and zero when the segment is vertical (i.e., long dimension normal to the chain direction). Each segment has just ...
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346
<image>Consider a one-dimensional chain consisting of $n \\gg 1$ segments as illustrated in the figure. Let the length of each segment be $a$ when the long dimension of the segment is parallel to the chain and zero when the segment is vertical (i.e., long dimension normal to the chain direction). Each segment has just ...
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347
<image>$D(E)$ is the density of states in a metal, and $E_{\text{F}}$ is the Fermi energy. At the Fermi energy $D\big(E_{\text{F}}\big) \neq 0$. Calculate the temperature dependence of the chemical potential at low temperatures, i.e., $\text{μ} \text{≫} k T$. (Remember: $\text{∫}_{-\text{∞}}^{+\text{∞}} \frac{x e^{x}}{...
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348
<image>At low temperatures, a mixture of ${ }^{3} \text{He}$ and ${ }^{4} \text{He}$ atoms form a liquid which separates into two phases: a concentrated phase (nearly pure ${ }^{3} \text{He}$), and a dilute phase (roughly $6.5 \text{\textperthousand} { }^{3} \text{He}$ for $T \text{\textless}= 0.1 \text{ K}$). The ligh...
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349
<image>At low temperatures, a mixture of ${ }^{3} \text{He}$ and ${ }^{4} \text{He}$ atoms form a liquid which separates into two phases: a concentrated phase (nearly pure ${ }^{3} \text{He}$), and a dilute phase (roughly $6.5 \text{\textperthousand} { }^{3} \text{He}$ for $T \text{\textless}= 0.1 \text{ K}$). The ligh...
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350
<image>A simple molecular beam apparatus is shown in Fig. 2.40. The oven contains $\mathrm{H}_{2}$ molecules at 300 K and at a pressure of 1 mm of mercury. The hole on the oven has a diameter of $100 \mu \mathrm{~m}$ which is much smaller than the molecular mean free path. After the collimating slits, the beam has a di...
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351
<image>A simple molecular beam apparatus is shown in Fig. 2.40. The oven contains $\mathrm{H}_{2}$ molecules at 300 K and at a pressure of 1 mm of mercury. The hole on the oven has a diameter of $100 \mu \mathrm{~m}$ which is much smaller than the molecular mean free path. After the collimating slits, the beam has a di...
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352
<image>The schematic drawing below (Fig. 2.42) shows the experimental set up for the production of a well-collimated beam of sodium atoms for an atomic beam experiment. Sodium is present in the oven $S$, which is kept at the temperature $T=550 \text{ K}$. At this temperature the vapor pressure of sodium is $p=6 \times ...
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353
<image>Consider a one-dimensional solid of length \(L=N a\) made up of \(N\) diatomic molecules, the interatomic spacing within a molecule is \(b\left(b<\frac{a}{2}\right)\). The centers of adjacent molecules are a distance \(a\) apart. We represent the potential energy as a sum of delta functions centered on each atom...
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354
<image>Consider a one-dimensional periodic potential $U(x)$ viewed as an array of identical potential barriers $V(x)$ of width $a$, centered at the points $x= \\pm n a$ where $n$ is an integer. The barrier $V(x)$, schematically drawn in Fig. 1.19, may be characterized by a transmission coefficient $t(k)$ and a reflecti...
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355
<image>Figure 1.22 is an energy versus wave vector diagram for electrons in a one-dimensional solid. Does this material have an even or odd number of conduction electrons per unit cell?
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356
<image>Consider an intrinsic semiconductor whose electronic density of states function $N(E)$ is depicted in Fig. Estimate the density of conduction band electrons at room temperature.
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357
<image>A long thin uniformly magnetized needle of hard steel, length 12 cm, is suspended by a torsionless suspension and makes free, small-angle oscillations about an axis through the center in a horizontal plane in the earth's magnetic field. The period of oscillation is $3-5$ seconds. Estimate the density of magnetiz...
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358
<image>Recently, a "double" quasar was discovered consisting of two indistinguishable images separated by an angle of 6 arc seconds. One interpretation is that we are seeing one quasar imaged as two by an intervening gravitational lens. To analyse this, suppose that the observer, the intervening galaxy, and the quasar ...
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359
<image>Recently, a "double" quasar was discovered consisting of two indistinguishable images separated by an angle of 6 arc seconds. One interpretation is that we are seeing one quasar imaged as two by an intervening gravitational lens. To analyse this, suppose that the observer, the intervening galaxy, and the quasar ...
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360
<image>A photomultiplier tube is to be used to detect light pulses each of which consists of a small but fixed number of photons. The average photoelectric efficiency is $10 \%$. That is, a photon has a $10 \%$ probability of causing the emission of a detectable photoelectron. Assume the photomultiplier gain is $10^{6}...
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361
<image>A photomultiplier tube is to be used to detect light pulses each of which consists of a small but fixed number of photons. The average photoelectric efficiency is $10 \%$. That is, a photon has a $10 \%$ probability of causing the emission of a detectable photoelectron. Assume the photomultiplier gain is $10^{6}...
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362
<image>The cross section for electron impact excitation of a certain atomic level A is $\sigma_{A}=1.4 \times 10^{-20} \mathrm{~cm}^{2}$. The level has a lifetime \tau=2 \times 10^{-8} \mathrm{sec}$, and decays 10 per cent of the time to level B and 90 per cent of the time to level C (Fig. 1.3). Calculate the light int...
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363
<image>Diatomic molecules such as HBr have excitation energies composed of electronic, rotational, and vibrational terms. An infrared absorption spectrum for gaseous HBr is shown in Fig. 1.66. (Infrared absorption involves no electronic transitions.) Use it to determine the moment of inertia $I$ and the vibrational fre...
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364
<image>The single-particle energies for neutrons and protons in the vicinity of ${}_{82}^{208}\text{Pb}_{126}$ are given in Fig. 2.13. Using this figure as a guide, estimate or evaluate the following. The spins and parities of the lowest states of ${}_{83}^{208}\text{Bi}$ (nearly degenerate). What is the energy of the ...
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365
<image>The single-particle energies for neutrons and protons in the vicinity of $_{82}^{208}\text{Pb}_{126}$ are given in Fig. 2.13. Using this figure as a guide, estimate or evaluate the following. The isobaric analog state in $^{208}\text{Bi}$ of the ground state of $^{208}\text{Pb}$ is defined as $\text{with } T_{+...
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366
<image>The simplest model for low-lying states of nuclei with $N$ and $Z$ between 20 and 28 involves only $f_{7/2}$ nucleons. Using this model predict the magnetic dipole moments of ${ }_{20}^{41} \text{Ca}_{21}$ and ${ }_{21}^{41} \text{Sc}_{20}$. Estimate crudely the electric quadrupole moments for these two cases as...
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367
<image>The simplest model for low-lying states of nuclei with $N$ and $Z$ between 20 and 28 involves only $f_{7/2}$ nucleons. What states are expected in ${}_{20}^{42}\text{Ca}$ according to an application of this model? Calculate the magnetic dipole and electric quadrupole moments for these states. Sketch the complete...
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368
<image>The simplest model for low-lying states of nuclei with $N$ and $Z$ between 20 and 28 involves only $f_{7/2}$ nucleons. The first excited state in ${ }_{21}^{43}\text{Ca}_{23}$ is shown below in Fig. 2.14 with a half-life of 34 picoseconds for decay to the ground state. Estimate the lifetime expected for this sta...
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369
<image><image>What is the best neutron magic number between those for $^{40} \text{Ca}$ and $^{208} \text{Pb}$ ?
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370
<image>Figure 2.19 gives the low-lying states of ${}^{18}\text{O}$ with their spin-parity assignments and energies (in MeV) relative to the $0^{+}$ ground state. Given the energies (relative to the ground state) of these ${}^{18}\text{O}$ levels, it is possible within the shell model, ignoring interconfiguration intera...
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371
<image>Suppose a search for solar neutrinos is to be mounted using a large sample of lithium enriched in the isotope $ {}_{3}^{7} \text{Li}$. Detection depends on production, separation, and detection of the electron-capturing isotope $ {}_{4}^{7} \text{Be}$ with a half-life of 53 days. The low-lying levels of these tw...
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372
<image>Consider the following energy level structure (Fig. 2.30): The ground states form an isotriplet as do the excited states (all states have a spin-parity of $0^{+}$). The ground state of $_{21}^{42} \text{Sc}$ can $\beta$-decay to the ground state of $_{20}^{42} \text{Ca}$ with a kinetic end-point energy of 5.4 Me...
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373
<image>In experiments on the reaction $^{21}\text{Ne}(\text{d, }^{3}\text{He}){}^{20}\text{F}$ with 26 MeV deuterons, many states in $^{20}\text{F}$ are excited. The angular distributions are characteristic of the direct reaction mechanism and therefore are easily sorted into those for which the angular momentum of the...
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374
<image>Inelastic neutrino scattering in the quark model. Consider the scattering of neutrinos on free, massless quarks. We will simplify things and discuss only strangeness-conserving reactions, i.e. transitions only between the $u$ and $d$ quarks. The experimental value is $\sigma^{\bar{u} N} / \sigma^{u N} = 0.37 \pm...
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375
<image>According to the Weinberg-Salam model, the Higgs boson $\phi$ couples to every elementary fermion $f$ ( $f$ may be a quark or lepton) in the form $$ \frac{e m_{f}}{m_{W}} \phi \bar{f} f, $$ where $m_{f}$ is the mass of the fermion $f, e$ is the charge of the electron, and $m_{W}$ is the mass of the $W$ boson. As...
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376
<image>High energy neutrino beams at Fermilab are made by first forming a monoenergetic $ \pi^{+}$(or $K^{+}$) beam and then allowing the pions to decay by $$ \pi^{+} \rightarrow \mu^{+}+ u $$ Recall that the mass of the pion is $140 \mathrm{MeV} / c^{2}$ and the mass of the muon is $106 \mathrm{MeV} / c^{2}$. In the...
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377
<image>Consider a $2-\text{cm}$ thick plastic scintillator directly coupled to the surface of a photomultiplier with a gain of $10^{6}$. A $10-\text{GeV}$ particle beam is incident on the scintillator as shown in Fig. 4.8(a). If the beam particle is a muon, estimate the charge collected at the anode of the photomultipl...
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378
<image>The "charmed" particles observed in $e^{+} e^{-}$storage rings have not yet been seen in hadron-hadron interactions. One possible means for detecting such particles is the observation of muons resulting from their leptonic decays. For example, consider a charmed particle $c$ with decay mode $$ c \rightarrow \mu...
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379
<image>A small fish, four feet below the surface of Lake Mendota is viewed through a simple thin converging lens with focal length 30 feet. If the lens is 2 feet above the water surface (Fig. 1.8), where is the image of the fish seen by the observer? Assume the fish lies on the optical axis of the lens and that $n_{\te...
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380
<image>As shown in Fig. 1.29, the image which would be cast by the converging lens alone has a distance of 0.5 cm between top and bottom. Calculate the position and size of the final image. Draw a ray diagram showing image formation for a point on the image not on the axis of the lenses. Using at least 2 rays. (The ray...
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381
<image>A 35 mm camera lens of focal length 50 mm is made into a telephoto lens by placing a negative lens between it and the film, as shown (Fig. 1.43). $\mathrm{L}_{1}=$ camera lens, $f_{1}=50 \mathrm{~mm} ; \mathrm{L}_{2}=$ negative lens, $f_{2}=-100 \mathrm{~mm}$. What is the magnification produced by the lens combi...
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382
<image>A point source $S$ located at the origin of a coordinate system emits a spherical sinusoidal wave in which the electric field $E_{1}$ is given by $E_{1}=$ $A\left(\frac{D}{r}\right) \cos \left(\omega t-\frac{2 \pi r}{\lambda}\right)$, where $r$ is the distance from $S$. In addition, there is a plane wave propaga...
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383
<image>A two-slit diffraction pattern is produced by the arrangement shown in Fig. 2.9. A discharge tube produces light of wavelength $\lambda$ which passes through a small slit $S$ immediately in front of the tube. The centers of the two slits of width $w$ are at distance $D$ apart. Find the condition that a maximum i...
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384
<image>A two-slit diffraction pattern is produced by the arrangement shown in Fig. 2.9. A discharge tube produces light of wavelength $\lambda$ which passes through a small slit $S$ immediately in front of the tube. The centers of the two slits of width $w$ are at distance $D$ apart. How large may $w$ be before the int...
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385
<image>Light of wavelength $\lambda$ and intensity $I_{0}$ is incident perpendicularly onto an opaque circular disk of radius $R$. In each case, find the intensity of the light at a distance $L$ behind the obstacle, on the path passing through the center of the circle. Take $L \gg R$.
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386
<image>A plane wave with wavenumber $k$ is incident on a slit of width $a$. The slit is covered by a transparent wedge whose thickness is proportional to the distance from the top of the slit $(t = \gamma x)$, see Fig.\ 2.36. The index of refraction of the transparent wedge is $n$. The intensity of light at an angle $\...
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387
<image>Shown in Fig. 2.49 is the Fraunhofer diffraction pattern resulting from 3 slits. The slit widths are $w$, slit separation is $d$, the distance between the screen and slits is $f$, and the wavelength of the light is $\\lambda$. Obtain expressions for $x$ in terms of the parameters of this experiment.
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388
<image>Shown in Fig. 2.49 is the Fraunhofer diffraction pattern resulting from 3 slits. The slit widths are $w$, slit separation is $d$, the distance between the screen and slits is $f$, and the wavelength of the light is $\\lambda$. Obtain expressions for $I_{0} / I_{1}$ in terms of the parameters of this experiment.
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389
<image>A plane wave of wavelength $\lambda$ is incident on a system having 3 slits of width a separated by distances $d$. The middle slit is covered by a filter which introduces a $180^{\circ}$ phase change. Calculate the angle $\theta$ for the first interference minimum.
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390
<image>A plane monochromatic wave (wavelength $\lambda$ ) is incident on a set of 5 slits spaced at a distance $d$ (Fig. 2.55). You may assume that the width of the individual slits is much less than $d$. For the resulting interference pattern, which is focused on a screen, compute either analytically or approximately ...
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391
<image>A plane monochromatic wave (wavelength $\lambda$ ) is incident on a set of 5 slits spaced at a distance $d$ (Fig. 2.55). You may assume that the width of the individual slits is much less than $d$. For the resulting interference pattern, which is focused on a screen, compute either analytically or approximately ...
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392
<image>A pinhole camera consists of a box in which an image is formed on the film plane which is a distance $P$ from a pinhole of diameter $d$. The object is at a distance $L$ from the pinhole, and light of wavelength $\nabla$ is used (Fig. 2.66). Using the pinhole from part (a), approximately what is the minimum dista...
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393
<image><image><image><image>Suppose you have been supplied with a number of sheets of two types of optically active material. Sheets of type $P$ are perfect polarizers: they transmit (normally incident) light polarized parallel to some axis $\boldsymbol{n}$ and absorb light polarized perpendicular to $\boldsymbol{n}$. ...
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394
<image><image><image><image>Suppose you have been supplied with a number of sheets of two types of optically active material. Sheets of type $P$ are perfect polarizers: they transmit (normally incident) light polarized parallel to some axis $\boldsymbol{n}$ and absorb light polarized perpendicular to $\boldsymbol{n}$. ...
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395
<image>A beam of light, with $\lambda=5000 \AA$, traveling in the $z$-direction is polarised at $45^{\circ}$ to the $x$-direction. It passes through a Kerr cell, i.e., a substance such that $n_{x}-n_{y}=K E^{2}$, where $n_{x}$ and $n_{y}$ are the refractive indices for light polarized in the $x$ and $y$ directions. $E$...
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396
<image>Given the following arrangement (Fig. 2.82), where the crystal is assumed to have parallel planes of atoms spaced by distance $d$. The $X$-ray tube has anode-cathode potential difference $V$ volts. The angle $\theta$ is variable. What is the angle $\theta_{m}$ below which no $X$-ray intensity will be recorded by...
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397
<image>A special light source directs 1 watt of light into a flat black ( $100 \\%$ absorbing) disc, which is mounted on an axle parallel to the beam (Fig. 2.84). The target starts to spin as it absorbs light. The target is changed from the black surface to a mirror surface. What happens to the torque? Why?
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398
<image>A ruby laser emits light with a wavelength of $6943 \AA$, which to a very good approximation is a plane wave. What are the amplitudes of the electric and magnetic field vectors of this plane wave propagating through water, if the time-averaged power of the beam in the water is 100 milliwatts $/ \mathrm{cm}^{2}$ ...
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399
<image>An undulator consists of a linear periodic array of magnets of alternating polarity. Each repeat unit in the array of magnets has length $d$ and there are $N$ such units. An electron of speed $v(v \text{sim} c)$, passing through this undulator, travels a path with only small deflections, as shown in Fig. 3.5. Th...
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