A secondary rainbow is formed when the incident light undergoes two internal reflections in a spherical drop of water as shown in Fig. 33.19e. (See Challenge Problem 33.60.) a. In terms of the incident angle θ a A and the refractive index n of the drop, what is the angular deflection ∆ of the ray? That is, what is the angle between the ray before it enters the drop and after it exits? b. What is the incident angle θ2 for which the derivative of ∆ with respect to the incident angle θ a A is zero? c. The indexes of refraction for red and violet light in water are given in part (e) of Challenge Problem 33.60. Use the results of parts (a) and (b) to find θ2 and ∆ for violet and red light. Do your results agree with the angles shown in Fig. 33.19e? When you view a secondary rainbow, is red or violet higher above the horizon? Explain.
> A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with inner radius R and outer radius 2R. The insulating shell has a uniform charge density
> Repeat Problem 22.45, but now let the outer shell have charge -2q. The inner shell still has charge +2q. Problem 22.45: A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell wit
> A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d (Fig. P22.45). The inner shell has total charge +2q, and the outer shell has charge +4
> A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated from its surroundings (Fig. P22.44). Fig. P22.44: (a). Derive expressio
> In a follow-up experiment, a charge of +40 pC was placed at the center of an artificial flower at the end of a 30-cmlong stem. Bees were observed to approach no closer than 15 cm from the center of this flower before they flew away. This observation sugg
> After one bee left a flower with a positive charge, that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in Fig. P21.100 best represents the electric field lines between the bee and the flower?
> Two identical metal objects are mounted on insulating stands. Describe how you could place charges of opposite sign but exactly equal magnitude on the two objects.
> If you peel two strips of transparent tape off the same roll and immediately let them hang near each other, they will repel each other. If you then stick the sticky side of one to the shiny side of the other and rip them apart, they will attract each oth
> After a long day of driving you take a late-night swim in a motel swimming pool. When you go to your room, you realize that you have lost your room key in the pool. You borrow a powerful flashlight and walk around the pool, shining the light into it. The
> A series circuit has an impedance of 60.0 Ω and a power factor of 0.720 at 50.0 Hz. The source voltage lags the current. a. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor? b. What
> A circular wire loop has a radius of 7.50 cm. A sinusoidal electromagnetic plane wave traveling in air passes through the loop, with the direction of the magnetic field of the wave perpendicular to the plane of the loop. The intensity of the wave at the
> A ray of light traveling in a block of glass (n = 1.52) is incident on the top surface at an angle of 57.2° with respect to the normal in the glass. If a layer of oil is placed on the top surface of the glass, the ray is totally reflected. What is the ma
> A source of sinusoidal electromagnetic waves radiates uniformly in all directions. At a distance of 10.0 m from this source, the amplitude of the electric field is measured to be 3.50 N/C. What is the electric-field amplitude 20.0 cm from the source?
> Two square reflectors, each 1.50 cm on a side and of mass 4.00 g, are located at opposite ends of a thin, extremely light, 1.00-m rod that can rotate without friction and in vacuum about an axle perpendicular to it through its center (Fig. P32.39). These
> When a solenoid is connected to a 48.0-V dc battery that has negligible internal resistance, the current in the solenoid is 5.50 A. When this solenoid is connected to an ac source that has voltage amplitude 48.0 V and angular frequency 20.0 rad/s, the cu
> A coworker of yours was making measurements of a large solenoid that is connected to an ac voltage source. Unfortunately, she left for vacation before she completed the analysis, and your boss has asked you to finish it. You are given a graph of 1/I2 ver
> A ray of light traveling in air is incident at angle θa on one face of a 90.0° prism made of glass. Part of the light refracts into the prism and strikes the opposite face at point A (Fig. P33.42). If the ray at A is at the critic
> A light ray in air strikes the right angle prism shown in Fig. P33.40. The prism angle at B is 30.0°. This ray consists of two different wavelengths. When it emerges at face AB, it has been split into two different rays that diverge from each
> The sun emits energy in the form of electromagnetic waves at a rate of 3.9 * 1026 W. This energy is produced by nuclear reactions deep in the sun’s interior. a. Find the intensity of electromagnetic radiation and the radiation pressure on an absorbing o
> 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 θa for which total internal reflection will occur at the vertical face (point A shown in
> A 400-Ω resistor and a 6.00-µF capacitor are connected in parallel to an ac generator that supplies an rms voltage of 180 V at an angular frequency of 360 rad/s. Use the results of Problem 31.54. Note that since there is no inductor in this circuit, the
> An L-R-C series circuit has R = 500 Ω, L = 2.00 H, C = 0.500 µF, and V = 100 V. a. For ω = 800 rad/s, calculate VR, VL, VC, and ɸ. Using a single set of axes, graph v, vR, vL, and vC as functions of time. Include two cycles of v on your graph. b. Repea
> A horizontal cylindrical tank 2.20 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam toward the c
> When the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly when entering the earth’s atmosphere, as shown in
> Figure P31.48 shows a low-pass filter (see Problem 31.47); the output voltage is taken across the capacitor in an L-R-C series circuit. Derive an expression for Vout /Vs, the ratio of the output and source voltage amplitudes, as a function of the angular
> A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. a. What is the largest angle with respect to the normal that the ray can make at the i
> A laser beam shines along the surface of a block of transparent material (see Fig. E33.8). 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
> NASA is giving serious consideration to the concept of solar sailing. A solar sail craft uses a large, low mass sail and the energy and momentum of sunlight for propulsion. a. Should the sail be absorbing or reflective? Why? b. The total power output o
> The GPS network consists of 24 satellites, each of which makes two orbits around the earth per day. Each satellite transmits a 50.0-W (or even less) sinusoidal electromagnetic signal at two frequencies, one of which is 1575.42 MHz. Assume that a satellit
> a. Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. b. Compute the reactance of a 2.50-µF capacitor at the same frequencies. c. At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-µF capacit
> A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, the light takes 8.72 ns to travel the length of the tube, but when the tube is filled with a transparent jelly, the light takes 1.82 ns longer to
> Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portions back into place. In one such procedure, a laser beam has a wavelen
> As a physics lab instructor, you conduct an experiment on standing waves of microwaves, similar to the standing waves produced in a microwave oven. A transmitter emits microwaves of frequency f. The waves are reflected by a flat metal reflector, and a re
> The company where you work has obtained and stored five lasers in a supply room. You have been asked to determine the intensity of the electromagnetic radiation produced by each laser. The lasers are marked with specifications, but unfortunately differen
> In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency 110.0 MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standing-wave pattern to occur. a. How far apart are the nod
> A thin beam of white light is directed at a flat sheet of silicate flint glass at an angle of 20.0° to the surface of the sheet. Due to dispersion in the glass, the beam is spread out in a spectrum as shown in Fig. P33.56. The refractive index
> A beam of unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (Fig. P33.55). The refractive index of the plastic wall is 1.61. If the light that has bee
> Light is incident in air at an angle θa (Fig. P33.54) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. a. Prove that θa = θ′ a. b. S
> The incident angle θa shown in Fig. P33.53 is chosen so that the light passes symmetrically through the prism, which has refractive index n and apex angle A. a. Show that the angle of deviation δ (the angle between the initial
> Light is incident normally on the short face of a 30°-60°-90° prism (Fig. P33.50). A drop of liquid is placed on the hypotenuse of the prism. If the index of refraction of the prism is 1.56, find the maximum index that th
> A parallel beam of light in air makes an angle of 47.5° with the surface of a glass plate having a refractive index of 1.66. a. What is the angle between the reflected part of the beam and the surface of the glass? b. What is the angle between the refr
> The prism shown in Fig. P33.49 has a refractive index of 1.66, and the angles A are 25.0°. Two light rays m and n are parallel as they enter the prism. What is the angle between them after they emerge? Figure P33.49 m A A n
> a. At what angular frequency is the voltage amplitude across the resistor in an L-R-C series circuit at maximum value? b. At what angular frequency is the voltage amplitude across the inductor at maximum value? c. At what angular frequency is the volta
> In an L-R-C series circuit the current is given by i = I cos ωt. The voltage amplitudes for the resistor, inductor, and capacitor are VR, VL, and VC. a. Show that the instantaneous power into the resistor is PR = VRIcos2ωt = 1/2VRI(1+cos2ωt). What does
> You are given this table of data recorded for a circuit that has a resistor, an inductor with negligible resistance, and a capacitor, all in series with an ac voltage source: Here f is the frequency of the voltage source, Z is the impedance of the circ
> You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. P33.45a). The glass is a thin-walled, hollow cylinder 16.0 cm high. The diameter of the top and bottom of the glass is 8.0 c
> To vary the angle as well as the intensity of polarized light, ordinary unpolarized light is passed through one polarizer with its transmission axis vertical, and then a second polarizer is placed between the first polarizer and the insect. When the ligh
> Next, unpolarized light is reflected off a smooth horizontal piece of glass, and the reflected light shines on the insect. Which statement is true about the two types of cells? a. When the light is directly above the glass, only type V detects the refle
> First, light with a plane of polarization at 45° to the horizontal shines on the insect. Which statement is true about the two types of cells? a. Both types detect this light. b. Neither type detects this light. c. Only type H detects the light. d. O
> In an L-R-C series ac circuit, the source has a voltage amplitude of 240 V, R = 90.0 Ω, and the reactance of the inductor is 320 Ω. The voltage amplitude across the resistor is 135 V. a. What is the current amplitude in the circuit? b. What is the volt
> Equation (31.9) says that vab = L di/dt (see Fig. 31.8a). Using Faraday’s law, explain why point a is at higher potential than point b when i is in the direction shown in Fig. 31.8a and is increasing in magnitude. When i is counterclock
> A beam of light traveling horizontally is made of an unpolarized component with intensity I0 and a polarized component with intensity Ip. The plane of polarization of the polarized component is oriented at an angle θ with respect to the vert
> Given small samples of three liquids, you are asked to determine their refractive indexes. However, you do not have enough of each liquid to measure the angle of refraction for light refracting from air into the liquid. Instead, for each liquid, you take
> In physics lab, you are studying the properties of four transparent liquids. You shine a ray of light (in air) onto the surface of each liquid—A, B, C, and D—one at a time, at a 60.0° angle of incidence; you
> The ICNIRP also has guidelines for magnetic-field exposure for the general public. In the frequency range of 25 Hz to 3 kHz, this guideline states that the maximum allowed magnetic field amplitude is 5/f T, where f is the frequency in kHz. Which is a mor
> The impedance of an L-R-C parallel circuit was derived in Problem 31.54. a. Show that at the resonance angular frequency v0 = 1/ LC , the impedance Z is a maximum and therefore the current through the ac source is a minimum. b. A 100-Ω resistor, a 0.10
> A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ω. Let the source voltage be given by v = V cos ω t. a. Show that each of the instantaneous voltages vR, vL, and vC at any
> Electromagnetic waves propagate much differently in conductors than they do in dielectrics or in vacuum. If the resistivity of the conductor is sufficiently low (that is, if it is a sufficiently good conductor), the oscillating electric field of the wave
> The electron in a hydrogen atom can be considered to be in a circular orbit with a radius of 0.0529 nm and a kinetic energy of 13.6 eV. If the electron behaved classically, how much energy would it radiate per second (see Challenge Problem 32.51)? What d
> Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by where c is the speed of light. a. Verify that this equation is dimensionally
> An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and variable angular frequency ω. Using the results of Problem 31.49, find an expression for a. the amplitude VL of the voltage across the inductor as a function of ω
> Medical x rays are taken with electromagnetic waves having a wavelength of around 0.10 nm in air. What are the frequency, period, and wave number of such waves?
> An L-R-C series circuit is connected to an ac source of constant voltage amplitude V and variable angular frequency ω. a. Show that the current amplitude, as a function of ω, is b. Show that the average power dissipated in the re
> An electromagnetic wave of wavelength 435 nm is traveling in vacuum in the –z-direction. The electric field has amplitude 2.70 * 10-3 V/m and is parallel to the x-axis. What are a. the frequency and b. the magnetic-field amplitude? c. Write the vector
> The microwaves in a certain microwave oven have a wavelength of 12.2 cm. a. How wide must this oven be so that it will contain five antinodal planes of the electric field along its width in the standing-wave pattern? b. What is the frequency of these m
> Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 1012 W) pulses of light that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell wi
> Three polarizing filters are stacked, with the polarizing axis of the second and third filters at 23.0° and 62.0°, respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 55.0 W/cm2 after it passes throu
> A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is θ, the intensity of the emerging beam is I. If you now want the intensity to be I/2,
> A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in Fig. E33.27. a. What is the light intensity (in terms of I0) at points A, B, and C? b. If w
> a. At what angle above the horizontal is the sun if sunlight reflected from the surface of a calm lake is completely polarized? b. What is the plane of the electric-field vector in the reflected light?
> Unpolarized light with intensity I0 is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0° with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed thr
> A narrow beam of white light strikes one face of a slab of silicate flint glass. The light is traveling parallel to the two adjoining faces, as shown in Fig. E33.23. For the transmitted light inside the glass, through what angle ∆Î
> Equation (31.14) was derived by using the relationship i = dq/dt between the current and the charge on the capacitor. In Fig. 31.9a the positive counterclockwise current increases the charge on the capacitor. When the charge on the left plate is positive
> The indexes of refraction for violet light (λ = 400 nm) and red light (λ = 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 53.5° to the normal. Calculate the angular sepa
> At the very end of Wagner’s series of operas Ring of the Nibelung, Brünnhilde takes the golden ring from the finger of the dead Siegfried and throws it into the Rhine, where it sinks to the bottom of the river. Assuming that the ring is small enough comp
> A beam of light is traveling inside a solid glass cube that has index of refraction 1.62. It strikes the surface of the cube from the inside. a. If the cube is in air, at what minimum angle with the normal inside the glass will this light not enter the
> The critical angle for total internal reflection at a liquid– air interface is 42.5°. a. If a ray of light traveling in the liquid has an angle of incidence at the interface of 35.0°, what angle does the refracted ray in the air make with the normal? b
> A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of I) of scattered light in the middle of a. the red part
> Three polarizing filters are stacked with the polarizing axes of the second and third at 45.0° and 90.0°, respectively, with that of the first. a. If unpolarized light of intensity I0 is incident on the stack, find the intensity and state of polarizatio
> Unpolarized light of intensity 20.0 W/cm2 is incident on two polarizing filters. The axis of the first filter is at an angle of 25.0° counterclockwise from the vertical (viewed in the direction the light is traveling), and the axis of the second filter i
> In an L-R-C series circuit, R = 400 Ω, L = 0.350 H, and C = 0.0120 µF. a. What is the resonance angular frequency of the circuit? b. The capacitor can withstand a peak voltage of 670 V. If the voltage source operates at the resonance frequency, what ma
> In an L-R-C series circuit, R = 150 Ω, L = 0.750 H, and C = 0.0180 µF. The source has voltage amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. a. What is the power factor? b. What is the average power delivered by th
> An L-R-C series circuit consists of a source with voltage amplitude 120 V and angular frequency 50.0 rad/s, a resistor with R = 400 Ω, an inductor with L = 3.00 H, and a capacitor with capacitance C. a. For what value of C will the current amplitude in
> Give several examples of electromagnetic waves that are encountered in everyday life. How are they all alike? How do they differ?
> A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of θa = 36.2°, the ray refracted into the water makes an an
> Light of original intensity I0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle f so that the intensity at point P is equal to I0/10. a. If the original light is unpo
> You have a 200-Ω resistor, a 0.400-H inductor, a 5.00-µF capacitor, and a variable frequency ac source with an amplitude of 3.00 V. You connect all four elements together to form a series circuit. a. At what frequency will the current in the circuit be
> In an L-R-C series circuit the source is operated at its resonant angular frequency. At this frequency, the reactance XC of the capacitor is 200 Ω and the voltage amplitude across the capacitor is 600 V. The circuit has R = 300 Ω. What is the voltage amp
> A series ac circuit contains a 250-Ω resistor, a 15-mH inductor, a 3.5-µF capacitor, and an ac power source of voltage amplitude 45 V operating at an angular frequency of 360 rad/s. a. What is the power factor of this circuit? b. Find the average power
> For a certain sinusoidal wave of intensity I, the amplitude of the magnetic field is B. What would be the amplitude (in terms of B) in a similar wave of twice the intensity?
> Is polarization a property of all electromagnetic waves, or is it unique to visible light? Can sound waves be polarized? What fundamental distinction in wave properties is involved? Explain.
> A light source radiates a sinusoidal electromagnetic wave uniformly in all directions. This wave exerts an average pressure p on a perfectly reflecting surface a distance R away from it. What average pressure (in terms of p) would this wave exert on a pe
> If a light beam carries momentum, should a person holding a flashlight feel a recoil analogous to the recoil of a rifle when it is fired? Why is this recoil not actually observed?
> By measuring the electric and magnetic fields at a point in space where there is an electromagnetic wave, can you determine the direction from which the wave came? Explain.
> In an ac circuit, why is the average power for an inductor and a capacitor zero, but not for a resistor?
> When hot air rises from a radiator or heating duct, objects behind it appear to shimmer or waver. What causes this?
> In Fig. 33.31, since the light that is scattered out of the incident beam is polarized, why is the transmitted beam not also partially polarized? From Fig. 33.31 33.31 When the sunbathing observer on the left looks up, he sees blue, polarized sunli
> When unpolarized light is incident on two crossed polarizers, no light is transmitted. A student asserted that if a third polarizer is inserted between the other two, some transmission will occur. Does this make sense? How can adding a third filter incre
> Public television station KQED in San Francisco broadcasts a sinusoidal radio signal at a power of 777 kW. Assume that the wave spreads out uniformly into a hemisphere above the ground. At a home 5.00 km away from the antenna, a. what average pressure d
> When a sheet of plastic food wrap is placed between two crossed polarizers, no light is transmitted. When the sheet is stretched in one direction, some light passes through the crossed polarizers. What is happening?
