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physics
light and optics
Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions
One round face of a 3.25-m, solid, cylindrical plastic pipe is covered with a thin black coating that completely blocks light. The opposite face is covered with a fluorescent coating that glows when it is struck by lighL Two straight, thin, parallel scratches, 0.225 mm apart, are made in the center
A uniform thin film of material of refractive index 1.40 coats a glass plate of refractive index 1.55. This film has the proper thickness to cancel normally incident light of wavelength 525 nm that strikes the film surface from air, but it is somewhat greater than the minimum thickness to achieve
A uniform thin film of material of refractive index 1.40 coats a glass plate of refractive index 1.55. This film has the proper thickness to cancel normally incident light of wavelength 525 nm that strikes the film surface from air, but it is somewhat greater than the minimum thickness to achieve
A uniform thin film of material of refractive index 1.40 coats a glass plate of refractive index 1.55. This film has the proper thickness to cancel normally incident light of wavelength 525 nm that strikes the film surface from air, but it is somewhat greater than the minimum thickness to achieve
Let the two sources S, and Sz shown in Fig. 35.3 be located at y = d and y = -d, respectively. (a) Rewrite Eq. (35.1) in terms of the x- and y-coordinates of a point P in Fig. 35.3 at which constructive interference occurs. (b) Your expression in part (a) is the
Let the two sources S, and Sz shown in Fig. 35.3 be located at y = d and y = -d, respectively. (a) Rewrite Eq. (35.1) in terms of the x- and y-coordinates of a point P in Fig. 35.3 at which constructive interference occurs. (b) Your expression in part (a) is the equation for the antinodal curves
A thin uniform film of refractive index 1.750 is placed on a sbeet of glass of refractive index 1.50. At room temperature (20.0oC), this film is just thick enough for light with wavelength 582.4 nm reflected off the top of the film to be cancelled by light reflected from the top of the glass. After
Red light with wavelength 700 nm is passed through a two slit apparatus. At the same time, monochromatic visible light with another wavelength passes through the same apparatus. As a result, most of the pattern that appears on the screen is a mixture of two colors; however, the center of the third
Consider a two-slit interference pattern, for which the intensity distribution is given by Eq. (35.14). Let θm be the angular position of the mth bright fringe, where the intensity is 10, Assume that θm is small, so that sin θm ≡ θm. Let θm+ and θm– be the two
White light reflects at normal incidence from the top and bottom surfaces of a glass plate (n = 1.52). There is air ahove and below the plate. Constructive interference is observed for light whose wavelength in air is 477.0 nm. What is the thickness of the plate if the next longer wavelength for
White light reflects at normal incidence from the top and bottom surfaces of a glass plate (n = 1.52). There is air ahove and below the plate. Constructive interference is observed for light whose wavelength in air is 477.0 nm. What is the thickness of the plate if the next longer wavelength for
Reflective Coatings and Herring. Herring and related fish have a brilliant silvery appearance that camouflages them while they are swimming in a sunlit ocean. The silveriness is due to platelets attached to the surfaces of these fish. Each platelet is made up of several alternating layers of
Two thin parallel slits are made in an opaque sheet of film. When a monochromatic beam of ligbt is shone through them at normal incidence, the first bright fringes in the transmitted light occur in air at ± 18.0" with the original direction of the light beam on a distant screen when the apparatus
An oil tanker spills a large amount of oil (n = 1.45) intothe sea (n = 1.33). (a) If you look down onto the oil spill from overhead, what predominant wavelength of light do you see at a point where the oil is 380 DIn thick? What color is the light? (b) In the water under the slick, what
An oil tanker spills a large amount of oil (n = 1.45) intothe sea (n = 1.33). (a) If you look down onto the oil spill from overhead, what predominant wavelength of light do you see at a point where the oil is 380 DIn thick? What color is the light? (b) In the water under the slick, what visible
After a laser beam passes through two thin parallel slits, the first completely dark fringes occur at ± 15.0° with the original direction of the heam, as viewed on a screen far from the slits. (a) What is the ratio of the distance between the slits to the wavelength of the light illuminating the
The index of refraction of a glass rod is 1.48 at T = 20.0°C and varies linearly with temperature, with a coefficient of 2.50 x l0-5/Co. The coefficient oflinear expansion of the glass is 5.00 x l0-6/Co. At 20.0oC the length of the rod is 3.00 cm. A Michelson interferometer has this glass rod in
Figure 35.25 shows an interferometer known as Fresnel's biprism. The magnitude of the prism angle A is extremely small.(a) If S0 is a very narrow source slit, show that the separation of the two virtual coherent sources S1, and S2 is given by d = 2aA (n ?? 1), where n is the index of refraction of
Monochromatic light from a distant source is incident on a slit 0.750mm wide. On a screen 2.00 m away, the distance from the central maximum of the diffraction pattern to the first minimum is measured to be 1.35mm. Calculate the wavelength of the light.
Parallel rays of green mercury light with a wavelength of 546 run pass through a slit covering a lens with a focal length of 60.0 cm. In the focal plane of the lens the distance from the central maximum to the first minimum is to.2mm. What is the width of the slit?
Light of wavelength 585 urn falls on a slit 0.0666mm wide(a) On a very large distant screen, how many totally dark fringes (indicating complete cancellation) will there be, including both sides of the central bright spot? Solve this problem without calculating all the angles!(b) At what angle will
Light of wavelength 633 run from a distant source is incident on a slit 0.750mm wide, and the resulting diffraction pattern is observed on a screen 3.50 m away. What is the distance between the two dark fringes on either side of the central bright fringe?
Diffraction occurs for all types of waves, including sound waves. High-frequency sound from a distant source with wavelength 9.00 cm passes through a narrow slit 12.0 cm wide. A microphone is placed 40.0 cm directly in front of the center of the slit, corresponding to point 0 in Fig. 36.5a. The
Tsunami! On December 26, 2004, a violent magnitude-9.1 earthquake occurred off the coast of Sumatra. This quake triggered a huge tsunami (similar to a tidal wave) that killed more than 150,000 people. Scientists observing the wave on the open ocean measured the time between crests to be 1.0 h and
A series of parallel linear water wave fronts are traveling directly toward the shore at 15.0 cm/s on an otherwise placid lake. A long concrete barrier that runs parallel to the shore at a distance of 3.20 m away has a hole in it. You count the wave crests and observe that 75.0 of them pass by each
A series of parallel linear water wave fronts are traveling directly toward the shore at 15.0 cm/s on an otherwise placid lake. A long concrete barrier that runs parallel to the shore at a distance of 3.20 m away has a hole in it. You count the wave crests and observe that 75.0 of them pass by each
Doorway Diffraction Sound of frequency 1250Hz leaves a room through a 1.0 D-m-wide doorway (see Exercise 36.5). At which angles relative to the centerline perpendicular to the doorway will someone outside the room hear no sound? Use 344 m/s for the speed of sound in air and assume that the source
Light waves, for which the electric field is given by Ey(x, t) = Emax sin [(1.20 x 107 m-1)x - wt], pass through a slit and produce the first dark bands at ±28.6° from the center of the diffraction pattern. (a) What is the frequency of this light? (b) How wide is the slit? (c) At which angles
Parallel rays of light with wavelength 620 nm pass through a slit covering a lens with a focal length of 40.0 cm. The diffraction pattern is observed in the focal plane of the lens, and the distance from the center of the central maximum to the first minimum is 36.5 cm. What is the width of the
Monochromatic electromagnetic radiation with wavelength A from a distant source passes through a slit. The diffraction pattern is observed on a screen 2.50 m from the slit. If the width of the central maximum is 6.00 mm, what is the slit width a if the wavelength is (a) 500 nm (visible light); (b)
Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.350 mm wide. The diffraction pattern is observed on a screen 3.00 m away. Define the width of a bright fringe as the distance between the minima on either side. (a) What is the width of the central bright fringe? (b)
Monochromatic light of wavelength λ = 620 nm from a distant source passes through a slit 0.450 mm wide. The diffraction pattern is observed on a screen 3.00 m from the slit. In terms of the intensity 10 at the peak of the central maximum, what is the intensity of the light at the screen the
A slit 0.240 mm wide is illuminated by parallel light rays of wavelength 540 nm. The diffraction pattern is observed on a screen that is 3.00 m from the slit. The intensity at the center of the central maximum (θ = 0o) is 6.00 x 10-6 W/m2. (a) What is the distance on the screen from the
Laser light of wavelength 6328 nm falls normally on a slit that is 0.0250 mm wide the transmitted light is viewed on a distant screen where the intensity at the center of the central bright fringe is 8.50 W/m2. (a) Find the maximum number of totally dark fringes on the screen, assuming the screen
A single-slit diffraction pattern is formed by monochromatic electromagnetic radiation from a distant source passing through a slit 0.105 mm wide. At the point in the pattern 3.250 from the center of the central maximum, the total phase difference between wavelets from the top and bottom of the
A single-slit diffraction pattern is formed by monochromatic electromagnetic radiation from a distant source passing through a slit 0.105 mm wide. At the point in the pattern 3.250 from the center of the central maximum, the total phase difference between wavelets from the top and bottom of the
Public Radio station KXPR-FM in Sacramento broadcasts at 88.9MHz. The radio waves pass between two tall skyscrapers that are 15.0 m apart along their closest walls. (a) At what horizontal angles, relative to the original direction of the waves, will a distant antenna not receive any signal from
Diffraction and Interference Combined. Consider the interference pattern produced by two parallel slits of width a and separation d, in which d = 3a. The slits are illuminated by normally incident light of wavelength λ. (a) First we ignore diffraction effects due to the slit width. At what
Number of Fringes in a Diffraction Maximum In Fig. 36.12c the central diffraction maximum contains exactly seven interference fringes, and in this case d/a = 4. (a) What must the ratio d/a be if the central maximum contains exactly five fringes? (b) In the case considered in part (a), bow many
An interference pattern is produced by eight parallel and equally spaced, narrow slits. There is an interference minimum when the phase difference Φ between light from adjacent slits is π/4. The phasor diagram is given in Fig. 36.14b. For which pairs of slits is there totally destructive
An interference pattern is produced by light of wavelength 580 nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of 0.530 mm. (a) If the slits are very narrow, what would be the angular positions of the first-order and second-order,
Monochromatic light illuminates a pair of thin parallel slits at normal incidence, producing an interference pattern on a distant screen. The width of each slit is 1/7 the center-to-center distance between the slits. (a) Which interference rnaxima are missing in the pattern on the screen? (b) Does
An interference pattern is produced by four parallel and equally spaced, narrow slits. By drawing appropriate phasor diagrams, show that there is an interference minimum when the phase difference Φ from adjacent slits is (a) π/2; (b) π; (c) 3π/2 in each case, for which
A diffraction experiment involving two thin parallel slits yields the pattern of closely spaced bright and dark fringes shown in Fig. 36.33. Only the central portion of the pattern is shown in the figure. The bright spots are equally spaced at 1.53mm center to center (except for the missing spots)
Laser light of wavelength 500.0 nm illuminates two identical slits, producing an interference pattern on a screen 90.0cm from the slits. The bright bands are 1.00 cm apart, and the third bright bands on either side of the central maximum are missing in the pattern. Find the width and the separation
Monochromatic light is at normal incidence on a plane transmission grating. The first-order maximum in the interference pattern is at an angle of 8.94°. What is the angular position of the fourth-order maximum?
If a diffraction grating produces its third-order bright band at an angle of 78.4° for light of wavelength 681 nm, find (a) The number of slits per centimeter for the grating and (b) The angular location of the first-order and second-order bright bands. (c) Will there be a fourth-order bright
If a diffraction grating produces a third-order bright spot for red light (of wavelength 700 nm) at 65.0o from the central maximum, at what angle will the second-order bright spot be for violet light (of wavelength 400 nm)?
Visible light passes through a diffraction grating that bas 900 slits/cm, and the interference pattern is observed on a screen that is 2.50 m from the grating. (a) Is the angular position of the first-order spectrum small enough for sin θ ≈ θ to be a good approximation? (b) In
The wavelength range of the visible spectrum is approximately 400-700 nm. White light falls at normal incidence on a diffraction grating that bas 350slits/mm, find the angular width of the visible spectrum in (a) The first order and (b) The third order.
Measuring Wavelengths with a CD A laser beam of wavelength λ = 632.8 nm shines at normal incidence on the reflective side of a compact disc. The tracks of tiny pits in which information is coded onto the CD are 1.60µm apart. For what angles of reflection (measured from the normal) will the
(a) What is the wavelength of light that is deviated in the first order through an angle of 13.5° by a transmission grating having 5000 slits/cm? (b) What is the second-order deviation of this wavelength? Assume normal incidence.
Plane monochromatic waves with wavelength 520nm are incident normally on a plane transmission grating having 350slits/rom. Find the angles of deviation in the first, second, and third orders.
Identifying Isotopes by Spectra Different isotopes of the same element emit light at slightly different wavelengths. A wavelength in the emission spectrum of a hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27 nm. (a) What minimum number of slits is required to
A typical laboratory diffraction grating bas 5.00 x 103 lines/cm and these lines are contained in a 3.50-cm width of grating. (a) What is the chromatic resolving power of such a grating in the first order? (b) Could this grating resolve the lines of the sodium doublet (see Section 36.5) in the
The light from an iron arc includes many different wavelengths. Two of these are at λ = 587.9782 nm and λ = 587.8002nm. You wish to resolve these spectral lines in first order using a grating 1.20 cm in length. What minimum number of slits per centimeter must the grating have?
X rays of wavelength 0.0850 nm are scattered from the atoms of a crystal. The second-order maximum in the Bragg reflection occurs when the angle 0 in Fig. 36.23 is 21.5°. What is the spacing between adjacent atomic planes in the crystal?
If the planes of a crystal are 3.50 A (1 A = 10-10 m = 1 Angstrom unit) apart, (a) What wavelength of electromagnetic waves is needed so that the first strong interference maximum in the Bragg reflection occurs when the waves strike the planes at an angle of 15.00, and in what part of the
Due to blurring caused by atmospheric distortion, the best resolution that can be obtained by a normal, earth-based, visible-light telescope is about 0.3 arc second (there are 60 arc minutes in a degree and 60 arc seconds in an arc minute). (a) Using Rayleigh's criterion, calculate the diameter of
If you can read the bottom row of your doctor's eye chart, your eye bas a resolving power of 1 arc minute, equal to 1/60 degree. If this resolving power is diffraction limited, to what effective diameter of your eye's optical system does this correspond? Use Rayleigh's criterion and assume). = 550
Two satellites at an altitude of 1200km are separated by 28 km. If they broadcast 3-m microwaves, what minimum receiving-dish diameter is needed to resolve (by Rayleigh's criterion) the two transmissions?
The Very Long Baseline Array can resolve (by Rayleigh's criterion) signals from sources separated by 1.0 x 10-8 rad. If the effective diameter of the receiver is 8000 km, what is the wavelength of these signals?
Monochromatic light with wavelength 620 nm passes through a circular aperture with diameter 7.4 ",m. The resulting diffraction pattern is observed on a screen that is 4.5 m from the aperture. What is the diameter of the Airy disk on the screen?
Photography A wildlife photographer uses a moderate telephoto lens of focal length 135mm and maximum aperture f/4.00 to photograph a bear that is U.s m away. Assume the wavelength is 550nm. (a) What is the width of the smallest feature on the bear that this lens can resolve if it is opened to its
Observing Jupiter you are asked to design a space telescope for earth orbit. When Jupiter is 5.93 x 108km away (its closest approach to the earth), the telescope is to resolve, by Rayleigh's criterion, features on Jupiter that are 250km apart. What minimum-diameter mirror is required? Assume a
A converging lens 7.20 cm in diameter bas a focal length of 300mm. If the resolution is diffraction limited, how far away can an object be if points on it 4.00mm apart are to be resolved (according to Rayleigh's criterion)? Use λ = 550nm.
Hubble versus Arecibo the Hubble Space Telescope bas an aperture of 2.4 m and focuses visible light (400-700 nm). The Arecibo radio telescope in Puerto Rico is 305 m (1000 ft) in diameter (it is built in a mountain valley) and focuses radio waves of wavelength 75 cm. (a) Under optimal viewing
Searching for Star-spots the Hale Telescope on Palomar Mountain in California bas a mirror 200 in. (5.08 m) in diameter and it focuses visible light. Given that a large sunspot is about 10,000 mi in diameter, what is the most distant star on which this telescope could resolve a sunspot to see
Searching for Planets the Keck Telescopes, on Mauna Kea, Hawaii have a 10.0·m-diameter mirror. Could these telescopes resolve Jupiter-sized planets about our nearest star, Alpha Centauri, which are 4.28 light-years away?
Suppose the entire apparatus (slit, screen, and space in between) in Exercise 36.4 is immersed in water (n = 1.33). Then what is the distance between the two dark fringes?
Consider a single-slit diffraction pattern. The center of the central maximum, where the intensity is I0, is located at θ = 0. (a) Let θ+ and θ_ be the two angles on either side of θ = 0 for which I = ½ I0. ∆θ = | θ+ – θ_| is called the full width at
A loudspeaker having a diaphragm that vibrates at 1250 Hz is traveling at 80.0 mi. directly toward a pair of holes in a very large wall in a region for which the speed of sound is 344m/s. You observe that the sound coming through the openings first cancels at ± 12.7° with respect to the original
Measuring Refractive Index a thin alit illuminated by light of frequency f produces its first dark band at ± 38.2° in air. When the entire apparatus (alit, screen, and space in between) is immersed in an unknown transparent liquid, the slit's first dark bands occur instead at ± 17.4°. Find the
Grating Design your boss asks you to design a diffraction grating that will disperse the first-order visible spectrum through an angular range of 15.0° (see Example 36.4 in Section 36.5). (a) What must the number of slits per centimeter be for this grating? (b) At what angles will the first-order
A slit 0.360mm wide is illuminated by parallel rays of light that have a wavelength of 540nm. The diffraction pattern is observed on a screen that is 1.20 m from the alit. The intensity at the center of the central maximum (θ = 0o) is I0, (a) What is the distance on the screen from the
The intensity of light in the Fraunhofer diffraction pattern of a single slit is I = I0 (sin γ/γ) 2 where γ = π a sin θ/λ (a) Show that the equation for the values of -y at which I is a maximum is tan-y = -y. (b) Determine the three smallest positive values of -y
Angular Width of a Principal Maximum consider N evenly spaced narrow slits. Use the small-angle approximation sin θ = θ (for θ in radians) to prove the following: For an intensity maximum that occurs at an angle θ, the intensity minima immediately adjacent to Ibis maximum are at
The Expanding Universe a cosmologist who is studying the light from a galaxy bas identified the spectrum of hydrogen but finds that the wavelengths are somewhat shifted from those found in the laboratory. In the lab, the Ha line bas a wavelength of 656.3 nm. The cosmologist is using a
Phasor Diagram for Eight Slits an interference pattern is produced by eight equally spaced, narrow slits. Figure 36.14 shows phasor diagrams for the cases in which the phase difference Φ between light from adjacent slits is Φ = π, Φ = π/4, and Φ = π/2. Each of
The Expanding Universe a cosmologist who is studying the light from a galaxy bas identified the spectrum of hydrogen but finds that the wavelengths are somewhat shifted from those found in the laboratory. In the lab, the Ha line bas a wavelength of 656.3 nm. The cosmologist is using a transmission
At the end of Section 36.4, the following statements were made about an array of N slits. Explain using phasor diagrams, why each statement is true. (a) A minimum occurs whenever Φ is an integral multiple of 2π,/N, except when Φ is an integral multiple of 2π (which gives a
In Eq. (36.12), consider the case in which d = a. In a sketch, show that in this case the two slits reduce to a single slit with width 2a. Then show that Eq. (36.12) reduces to Eq. (36.5) with slit width 2a.
What is the longest wavelength that can be observed in the third order for a transmission grating having 6500 slits/cm? Assume normal incidence.
(a) Figure 36.16 shows plane waves of light incident normally on a diffraction grating. If instead the light strikes the grating at an angle of incidence θ' (measured from the normal), show that the condition for an intensity maximum is not Eq. (36.13), but rather d(sin θ + sin θ’)
A diffraction grating bas 650slits/mm what is the highest order that contains the entire visible spectrum? (The wavelength range of the visible spectrum is approximately 400-700mm.)
Quasars, an abbreviation for quasi-stellar radio sources, are distant objects that look like stars through a telescope but that emit far more electromagnetic radiation than an entire normal galaxy of stars. An example is the bright object below and to the left of center in Fig. 36.34; the other
Phased-Array Radar in one common type of radar installation, a rotating antenna sweeps a radio beam around the sky. But in a phased-array radar system, the antennas remain stationary and the beam is swept electronically. To see how this is done, consider an array of N antennas that are arranged
Underwater Photography an underwater camera has a lens of focal length 35.0mm and a maximum aperture of f/2.80. The film it uses has an emulsion that is sensitive to light of frequency 6.00 x 1014 Hz. If the photographer takes a picture of an object 2.75 m in front of the camera with the lens wide
An astronaut in orbit can just resolve two point sources on the earth that are 75.0 m apart. Assume that the resolution is diffraction limited, and use Rayleigh's criterion. What is the astronaut's altitude above the earth? Treat her eye as a circular aperture with a diameter of 4.00mm (the
Observing Planets beyond Our Solar System NASA is considering a project called Planet Imager that would give astronomers the ability to see details on planets orbiting other stars. Using the same principle as the Very Large Array (see Section 36.7), Planet Imager will use an array of infrared
It is possible to calculate the intensity in the single-slit Fraunbofer diffraction pattern without using the phasor method of Section 36.3. Let y' represent the position of a point within the slit of width a in Fig. 36.5a, with y' = 0 at the center of the slit so that the slit extends from y' = ??
It is possible to calculate the intensity in the single-slit Fraunbofer diffraction pattern without using the phasor method of Section 36.3. Let y' represent the position of a point within the slit of width a in Fig. 36.5a, with y' = 0 at the center of the slit so that the slit extends from y' = ??
It is possible to calculate the intensity in the single-slit Fraunbofer diffraction pattern without using the phasor method of Section 36.3. Let y' represent the position of a point within the slit of width a in Fig. 36.5a, with y' = 0 at the center of the slit so that the slit extends from y' = ??
A moth at about eye level is 10 cm in front of a plane mirror; you are behind the moth, 30 cm from the mirror. What is the distance between your eyes and the apparent position of the moth's image in the mirror?
You look through a camera toward an image of a hummingbird in a plane mirror. The camera is 4.30 m in front of the mirror. The bird is at camera level, 5.00 m to your right and 3.30 m from the mirror. What is the distance between the camera and the apparent position of the bird's image in the
Figure shows an overhead view of a corridor with a plane mirror M mounted at one end. A burglar B sneaks along the corridor directly toward the center of the mirror. It d = 3.0 m, how far from the mirror will she be when the security guard S can first see her in the mirror?
In Figure an isotropic point source of light S is positioned at distance d from a viewing screen A and the light intensity Ip at point P (level with S) is measured. Then a plane mirror M is placed behind S at distance d. By how much is Ip multiplied by the presence of the mirror?
Figure shows a small light bulb suspended at distance d1 = 250 cm above the surface of the water in a swimming pool where the water depth is d2 = 200 cm. The bottom of the pool is a large mirror. How far below the mirror surface is the image of the bulb? Construct a diagram of two rays like that of
An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure gives i versus object distance p out to px = 40 cm. What is the image distance when the object is on the central axis and 70 cm from the
A concave shaving mirror has a radius of curvature of 35.0 cm. It is positioned so that the (upright) image of a man's face is 2.50 times the size of the face. How far is the mirror from the face?
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