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physics
modern physics

Physics 5th edition James S. Walker - Solutions

The Fresnel Lens Optical Landing System (FLOLS) used to ensure safe landings on aircraft carriers consists of a series of Fresnel lenses of different colors. Each lens focuses light in a different, specific direction, and hence which light a pilot sees on approach determines whether the plane is
A Cassegrain astronomical telescope uses two mirrors to form the image. The larger (concave) objective mirror has a focal length Æ’1 = +50.0 cm. A small convex secondary mirror is mounted 43.0 cm in front of the primary. As shown in FIGURE 27-31, light is reflected from the secondary
A convex lens (Æ’ = 20.0 cm) is placed 10.0 cm in front of a plane mirror. A matchstick is placed 25.0 cm in front of the lens, as shown in FIGURE 27-32.(a) If you look through the lens toward the mirror, where will you see the image of the matchstick?(b) Is the image real or virtual?
The diameter of a collimated laser beam can be expanded or reduced by using two converging lenses, with focal lengths Æ’1 and Æ’1, mounted a distance Æ’1 + Æ’2 from each other, as shown in FIGURE 27-33. What is the ratio of the two beam diameters, (d1 /
Consider three lenses with focal lengths of 25.0 cm, -15.0 cm, and 11.0 cm positioned on the x axis at x = 0, x = 0.400 m, and x = 0.500 m, respectively. An object is at x = -122 cm. Find (a) The location (b) The orientation and magnification of the final image produced by this lens system.
Because a concave lens cannot form a real image of a real object, it is difficult to measure its focal length precisely. One method uses a second, convex, lens to produce a virtual object for the concave lens. Under the proper conditions, the concave lens will form a real image of the virtual
A person with a near-point distance N uses a magnifying glass with a focal length ƒ. Show that the greatest magnification that can be achieved with this magnifier is M = 1 + N/ƒ.
What happens to the two-slit interference pattern if the separation between the slits is less than the wavelength of light?
Two identical sheets of glass are coated with films of different materials but equal thickness. The colors seen in reflected light from the two films are different. Give a reason that can account for this observation.
Which portion of the soap film in the accompanying photograph is thinnest? Explain.
Two sources emit waves that are coherent, in phase, and have wavelengths of 26.0 m. Do the waves interfere constructively or destructively at an observation point 78.0 m from one source and 143 m from the other source?
Radio waves of frequency 1.427 GHz arrive at two telescopes that are connected by a computer to perform interferometry. One portion of the same wave front travels 1.051 m farther than the other before the two signals are combined.(a) Will the two waves combine constructively or destructively?(b)
Moe, Larry, and Curly stand in a line with a spacing of 1.00 m. Larry is 3.00 m in front of a pair of stereo speakers 0.800 m apart, as shown in FIGURE 28-43. The speakers produce a single-frequency tone, vibrating in phase with each other. What are the two lowest frequencies that allow Larry to
In Figure 28-43 the two speakers emit sound that is 180Â° out of phase and of a single frequency, Æ’.(a) Does Larry hear a sound intensity that is a maximum or a minimum? Does your answer depend on the frequency of the sound? Explain.(b) Find the lowest two frequencies that produce a maximum
Consider a two-slit interference pattern, with monochromatic light of wavelength λ. What is the path difference Δℓ for(a) The fourth bright fringe(b) The third dark fringe above the central bright fringe? Give your answers in terms of the wavelength of the light.
(a) Does the path-length difference Δℓ increase or decrease as you move from one bright fringe of a two-slit experiment to the next bright fringe farther out?(b) What is Δℓ in terms of the wavelength λ of the light?
A two-slit experiment with red light produces a set of bright fringes. (a) Will the spacing between the fringes increase, decrease, or stay the same if the color of the light is changed to blue? (b) Choose the best explanation from among the following: I. The spacing between the fringes will
Laser light with a wavelength λ = 690 nm illuminates a pair of slits at normal incidence. What slit separation will produce first order maxima at angles of ±25° from the incident direction?
Monochromatic light passes through two slits separated by a distance of 0.0374 mm. If the angle to the third maximum above the central fringe is 3.61°, what is the wavelength of the light?
In Young's two-slit experiment, the first dark fringe above the central bright fringe occurs at an angle of 0.44°. What is the ratio of the slit separation, d, to the wavelength of the light, λ?
A two-slit experiment with slits separated by 48.0 × 10-5 m produces a second-order maximum at an angle of 0.0990°.(a) Find the wavelength of the light used in this experiment.(b) If the slit separation is increased but the second-order maximum stays at the same angle, does the wavelength
In an experiment to demonstrate interference, you connect two antennas to a single radio receiver. When the two antennas are adjacent to each other, the received signal is strong. You leave one antenna in place and move the other one directly away from the radio transmission tower. How far should
A two-slit pattern is viewed on a screen 1.00 m from the slits. If the two third-order minima are 22.0 cm apart, what is the width (in cm) of the central bright fringe?
Light from a He-Ne laser (Î» = 632.8 nm) strikes a pair of slits at normal incidence, forming a double-slit interference pattern on a screen located 1.16 m from the slits. FIGURE 28-44 shows the interference pattern observed on the screen. What is the slit separation?In figure 28-44
For a science fair demonstration you would like to create a diffraction pattern similar to that shown in Figure 28-44. If you plan to shine a laser pointer (Î» = 652 nm) through a pair of slits that are separated by 175 Î¼m, how far away from the slits should you place the screen?In figure 28-44
Light with a wavelength of 576 nm passes through two slits and forms an interference pattern on a screen 8.85 m away. If the linear distance on the screen from the central fringe to the first bright fringe above it is 5.36 cm, what is the separation of the slits?
Suppose the interference pattern shown in Figure 28-44 is produced by monochromatic light passing through two slits, with a separation of 135Î¼m, and onto a screen 1.20 m away.(a) What is the wavelength of the light?(b) If the frequency of this light is increased, will the bright spots of the
A physics instructor wants to produce a double-slit interference pattern large enough for her class to see. For the size of the room, she decides that the distance between successive bright fringes on the screen should be at least 2.50 cm. If the slits have a separation d = 0.0175 mm, what is the
When green light (Î» = 505 nm) passes through a pair of double slits, the interference pattern shown in FIGURE 28-45 (a) is observed. When light of a different color passes through the same pair of slits, the pattern shown in FIGURE 28-45 (b) is observed.(a) Is the wavelength of the second color
The interference pattern shown in Figure 28-45 (a) is produced by green light with a wavelength of Î» = 505 nm passing through two slits with a separation of 127 mm. After passing through the slits, the light forms a pattern of bright and dark spots on a screen located 1.25 m from the slits.(a)
FIGURE 28-46 shows four different cases where light of wavelength l reflects from both the top and the bottom of a thin film of thickness d. The indices of refraction of the film and the media above and below it are indicated in the figure. For which of the cases will the two reflected rays undergo
The oil film floating on water in the accompanying photo appears dark near the edges, where it is thinnest. Is the index of refraction of the oil greater than or less than that of the water? Explain.
A theme park creates a new kind of water wave pool with large waves caused by constructive interference. There are two wave generators in phase with each other along either side of a pool that is 24.0 m wide. A swimmer that is 8.0 m from one generator and 16.0 m from the other notices that she is
A soap bubble with walls 418 nm thick floats in air. If this bubble is illuminated perpendicularly with sunlight, what wavelength (and color) will be absent in the reflected light? Assume that the index of refraction of the soap film is 1.33.
A soap film (n = 1.33) is 825 nm thick. White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides?
White light is incident on a soap film (n = 1.30) in air. The reflected light looks bluish because the red light (λ = 670 nm) is absent in the reflection. What is the minimum thickness of the soap film?
A 742-nm-thick soap film (nfilm = 1.33) rests on a glass plate (nglass = 1.52). White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected from the film?
An oil film (n = 1.46) floats on a water puddle. You notice that green light (λ = 538 nm) is absent in the reflection. What is the minimum thickness of the oil film?
A radio broadcast antenna is 36.00 km from your house. Suppose an airplane is flying 2.230 km above the line connecting the broadcast antenna and your radio, and that waves reflected from the airplane travel 88.00 wavelengths farther than waves that travel directly from the antenna to your house.
Monochromatic light with Î» = 648 nm shines down on a plano-convex lens lying on a piece of plate glass, as shown in FIGURE 28-47. When viewing from above, one sees a set of concentric dark and bright fringes, referred to as Newton's rings.(a) If the radius of the twelfth dark ring from the
Light is incident from above on two plates of glass, separated on both ends by small wires of diameter d = 0.600 mm. Considering only interference between light reflected from the bottom surface of the upper plate and light reflected from the upper surface of the lower plate, state whether the
A naval engineer is testing an nonreflective coating for submarines that would help them avoid detection by producing destructive interference for sonar waves that have a frequency of 512 Hz and travel at 1480 m/s. If there is a phase change for waves reflected from both the top and bottom surfaces
A thin layer of magnesium fluoride (n = 1.38) is used to coat a flint-glass lens (n = 1.61).(a) What thickness should the magnesium fluoride film have if the reflection of 565-nm light is to be suppressed? Assume that the light is incident at right angles to the film.(b) If it is desired to
Two sources emit waves that are in phase with each other. What is the longest wavelength that will give constructive interference at an observation point 161 m from one source and 295 m from the other source?
An interferometric hologram is produced by exposing the film twice, once when the object is unstressed and once when it is stressed, causing it to flex slightly. The resulting hologram has light and dark bands that are analogous to the interference fringes of an air wedge. If 22 bright fringes are
White light is incident normally on a thin soap film (n = 1.33) suspended in air.(a) What are the two minimum thicknesses that will constructively reflect yellow (λ = 590 nm) light?(b) What are the two minimum thicknesses that will destructively reflect yellow (λ = 590 nm) light?
Two glass plates are separated by fine wires with diameters d1 = 0.0500 mm and d2 = 0.0520 mm, as indicated in FIGURE 28-48. The wires are parallel and separated by a distance of 7.00 cm. If monochromatic light with Î» = 589 nm is incident from above, what is the distance (in cm)
A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if(a) The wavelength is doubled,(b) The slit width is doubled,(c) The distance from the slit to the screen is
What width single slit will produce first-order diffraction minima at angles of ±28° from the central maximum with 710-nm light?
Diffraction also occurs with sound waves. Consider 1400-Hz sound waves diffracted by a door that is 94 cm wide. What is the angle between the two first-order diffraction minima?
Green light (λ = 546 nm) strikes a single slit at normal incidence. What width slit will produce a central maximum that is 2.75 cm wide on a screen 1.80 m from the slit?
Light with a wavelength of 696 nm passes through a slit 7.64μm wide and falls on a screen 1.95 m away. Find the linear distance on the screen from the central bright fringe to the first bright fringe above it.
A single slit is illuminated with 610-nm light, and the resulting diffraction pattern is viewed on a screen 2.3 m away.(a) If the linear distance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit?(b) If the slit is made wider, will the distance between
How many dark fringes will be produced on either side of the central maximum if green light (λ = 553 nm) is incident on a slit that is 8.00 mm wide?
A person driving at 17 m>s crosses the line connecting two radio transmitters at right angles, as shown in FIGURE 28-41. The transmitters emit identical signals in phase with each other, which the driver receives on the car radio. When the car is at point A, the radio picks up a maximum net
The diffraction pattern shown in FIGURE 28-49 is produced by passing He-Ne laser light (Î» = 632.8 nm) through a single slit and viewing the pattern on a screen 1.50 m behind the slit.(a) What is the width of the slit?(b) If monochromatic yellow light with a wavelength of 591 nm is used with this
A screen is placed 1.50 m behind a single slit. The central maximum in the resulting diffraction pattern on the screen is 1.60 cm wide-that is, the two first-order diffraction minima are separated by 1.60 cm. What is the distance between the two second order minima?
(a) In principle, do your eyes have greater resolution on a dark cloudy day or on a bright sunny day?(b) Choose the best explanation from among the following:I. Your eyes have greater resolution on a cloudy day because your pupils are open wider to allow more light to enter the eye.II. Your eyes
Two point sources of light are separated by 5.5 cm. As viewed through a 12-μm-diameter pinhole, what is the maximum distance from which they can be resolved (a) If red light (λ = 690 nm) is used, (b) If violet light (λ = 420 nm) is used?
A spy camera is said to be able to read the numbers on a car's license plate. If the numbers on the plate are 5.5 cm apart, and the spy satellite is at an altitude of 180 km, what must be the diameter of the camera's aperture? (Assume light with a wavelength of 550 nm.)
As seen from Earth, the red dwarfs Krüger 60A and Krüger 60B form a binary star system with an angular separation of 2.5 arc seconds. What is the smallest diameter telescope that could theoretically resolve these stars using 550-nm light?
A series of optical telescopes produced an image that has a resolution of about 0.00350 arc second. What is the smallest diameter telescope that could theoretically resolve these features using light with a wavelength of 2.30 μm?
Find the minimum aperture diameter of a camera that can resolve detail on the ground the size of a person (2.0 m) from an SR-71 Blackbird airplane flying at an altitude of 24 km. (Assume light with a wavelength of 480 nm.)
The Hubble Space Telescope (HST) orbits Earth at an altitude of 613 km. It has an objective mirror that is 2.4 m in diameter. If the HST were to look down on Earth's surface (rather than up at the stars), what is the minimum separation of two objects on the Earth's surface that could be resolved
A lens that is "optically perfect" is still limited by diffraction effects. Suppose a lens has a diameter of 120 mm and a focal length of 640 mm.(a) Find the angular width (that is, the angle from the bottom to the top) of the central maximum in the diffraction pattern formed by this lens when
Two students in a dorm room listen to a pure tone produced by two loudspeakers that are in phase. Students A and B in FIGURE 28-42 hear a maximum sound. What is the lowest possible frequency of the loudspeakers?In figure 28-42
Early cameras were little more than a box with a pinhole on the side opposite the film.(a) What angular resolution would you expect from a pinhole with a 0.50-mm diameter?(b) What is the greatest distance from the camera at which two point objects 15 cm apart can be resolved? (Assume light with a
A grating has 797 lines per centimeter. Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 645-nm light.
Suppose you want to produce a diffraction pattern with X-rays whose wavelength is 0.030 nm. If you use a diffraction grating, what separation between lines is needed to generate a pattern with the first maximum at an angle of 14°? (For comparison, a typical atom is a few tenths of a nanometer in
A diffraction grating has 2500 lines/cm. What is the angle between the first-order maximum for red light (λ = 680 nm) and the first-order maximum for blue light (λ = 410 nm)?
The yellow light from a helium discharge tube has a wavelength of 587.5 nm. When this light illuminates a certain diffraction grating it produces a first-order principal maximum at an angle of 1.450°. Calculate the number of lines per centimeter on the grating.
A diffraction grating with 365 lines/mm is 1.25 m in front of a screen. What is the wavelength of light whose first-order maxima will be 16.4 cm from the central maximum on the screen?
X-rays with a wavelength of 0.0711 nm create a diffraction pattern when they pass through a protein crystal. If the angular spacing between adjacent bright spots (m = 0 and m = 1) in the diffraction pattern is 28.9°, what is the average spacing between atoms in the crystal?
White light strikes a grating with 7600 lines/cm at normal incidence. How many complete visible spectra will be formed on either side of the central maximum?
White light strikes a diffraction grating (615 lines/mm) at normal incidence. What is the highest-order visible maximum that is formed?
The rows of bumps on a CD form lines that are separated by 1.60 μm. When white light reflects from its surface, at what angle from the specular reflection ray would you expect to see the first-order maximum for 555-nm green light?
If the loudspeakers in Problem 6 are 180Â° out of phase, determine whether a 185-Hz tone heard at location B is a maximum or a minimum.In figure 28-42
A light source emits two distinct wavelengths [λ1 = 430 nm (violet); λ2 = 630 nm (orange)]. The light strikes a diffraction grating with 450 lines/mm at normal incidence. Identify the colors of the first eight interference maxima on either side of the central maximum.
A laser emits two wavelengths (λ1 = 420 nm; λ2 = 630 nm). When these two wavelengths strike a grating with 450 lines/mm, they produce maxima (of different orders) that coincide.(a) What is the order (m) of each of the two overlapping lines?(b) At what angle does this overlap occur?
When blue light with a wavelength of 465 nm illuminates a diffraction grating, it produces a first-order principal maximum but no second-order maximum.(a) Explain the absence of higher-order principal maxima.(b) What is the maximum spacing between lines on this grating?
Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 2.50 m away. If the first order maxima are separated by 1.43 m on the screen, what is the distance between the two second-order maxima?
A diffraction grating with a slit separation d is illuminated by a beam of monochromatic light of wavelength l. The diffracted beam is observed at an angle f relative to the incident direction. If the plane of the grating bisects the angle between the incident and diffracted beams, show that the
(a) If a thin liquid film floating on water has an index of refraction less than that of water, will the film appear bright or dark in reflected light as its thickness goes to zero? (b) Choose the best explanation from among the following: I. The film will appear bright because as the thickness of
If the index of refraction of an eye could be magically reduced, would the eye's resolution increase or decrease? Explain.
When reading the printout from a laser printer, you are actually looking at an array of tiny dots. If the pupil of your eye is 4.3 mm in diameter when reading a page held 28 cm from your eye, what is the minimum separation of adjacent dots that can be resolved? (Assume light with a wavelength of
The headlights of a pickup truck are 1.36 m apart. What is the greatest distance at which these headlights can be resolved as separate points of light on a photograph taken with a camera whose aperture has a diameter of 15.5 mm?
A glass lens (nglass = 1.52) has an antireflection coating of MgF2 (n = 1.38).(a) For 545-nm light, what minimum thickness of MgF2 will cause the reflected rays R2 and R4 in FIGURE 28-50 to interfere destructively, assuming normal incidence?(b) Interference will also occur between the
A microphone is located on the line connecting two speakers that are 0.938 m apart and oscillating in phase. The microphone is 2.83 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphone's location?
A thin film of oil (n = 1.30) floats on water (n = 1.33). When sunlight is incident at right angles to this film, the only colors that are enhanced by reflection are blue (458 nm) and red (687 nm). Estimate the thickness of the oil film.
The yellow light of sodium, with wavelengths of 588.99 nm and 589.59 nm, is normally incident on a grating with 494 lines/cm. Find the linear distance between the first-order maxima for these two wavelengths on a screen 2.55 m from the grating.
A thin soap film (n = 1.33) suspended in air has a uniform thickness. When white light strikes the film at normal incidence, violet light (λV = 420 nm) is constructively reflected. (a) If we would like green light (λG = 560 nm) to be constructively reflected, instead, should the film's thickness
A thin film of oil (n = 1.40) floats on water (n = 1.33). When sunlight is incident at right angles to this film, the only colors that are absent from the reflected light are blue (458 nm) and red (687 nm). Estimate the thickness of the oil film.
Sodium light, with a wavelength of Î» = 589 nm, shines downward onto the system shown in Figure 28-47. When viewed from above, you see a series of concentric circles known as Newton's rings.(a) Do you expect a bright or a dark spot at the center of the pattern? Explain.(b) If the radius
The colossal squid (Mesonychoteuthis hamiltoni) has the largest eyes documented in the animal kingdom, at least 27 cm in diameter. The eyes are large in order to see in dim light, but they also have terrific resolution. If the squid's eyes are free of defects, find the maximum distance at which the
Figure 28-49 shows a single-slit diffraction pattern formed by light passing through a slit of width W = 11.2 mm and illuminating a screen 0.855 m behind the slit.(a) What is the wavelength of the light?(b) If the width of the slit is decreased, will the distance indicated in Figure 28-49 be
Images produced by structures within the eye (like lens fibers or cell fragments) are referred to as entoptic images. These images can sometimes take the form of "halos" around a bright light seen against a dark background. The halo in such a case is actually the bright outer rings of a circular
White light is incident on a soap film (n = 1.33, thickness = 800.0 nm) suspended in air. If the incident light makes a 45° angle with the normal to the film, what visible wavelength(s) will be constructively reflected?
A system like that shown in Figure 28-35 consists of N slits, each transmitting light of intensity I0. The light from each slit has the same phase and the same wavelength. The net intensity I observed at an angle u due to all N slits isIn this expression, Ñ„ = (2Ï€d/Î») sin u, where l is
A microphone is located on the line connecting two speakers that are 0.845 m apart and oscillating 180° out of phase. The microphone is 2.25 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphone's location?
A curved piece of glass with a radius of curvature R rests on a flat plate of glass. Light of wavelength λ is incident normally on this system. Considering only interference between waves reflected from the curved (lower) surface of glass and the top surface of the plate, show that the radius of

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