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physics
light and optics
College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions
A ray of light impinges from air onto a block of ice (n = 1.309) at a 60.0° angle of incidence. Assuming that this angle remains the same, find the difference θ2, ice - θ2, water in the angles of refraction when the ice turns to water (n = 1.333).
The drawing shows a coin resting on the bottom of a beaker filled with an unknown liquid. A ray of light from the coin travels to the surface of the liquid and is refracted as it enters into the air. A person sees the ray as it skims just above the surface of the liquid. How fast is the light
A beam of light is traveling in air and strikes a material. The angles of incidence and refraction are 63.0° and 47.0°, respectively. Obtain the speed of light in the material.
Review Conceptual Example as background for this problem. A man in a boat is looking straight down at a fish in the water directly beneath him. The fish is looking straight up at the man. They are equidistant from the air–water interface. To the man, the fish appears to be 2.0 m beneath his eyes.
In Figure suppose that the angle of incidence is θ1 = 30.0°, the thickness of the glass pane is 6.00 mm, and the refractive index of the glass is n2 = 1.52. Find the amount (in mm) by which the emergent ray is displaced relative to the incidentray.
A glass is half-full of water, with a layer of vegetable oil (n = 1.47) floating on top. A ray of light traveling downward through the oil is incident on the water at an angle of 71.4°. Determine the critical angle for the oil–water interface and decide whether the ray will penetrate into the
Multiple- Concept Example provides helpful background for this problem. The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of θ1 = 34°, enters the quartz, and travels to point P. This slab is surrounded by a fluid
Light is reflected from a glass coffee table. When the angle of incidence is 56.7°, the reflected light is completely polarized parallel to the surface of the glass. What is the index of refraction of the glass?
When light strikes the surface between two materials from above, the Brewster angle is 65.0°. What is the Brewster angle when the light encounters the same surface from below?
A beam of sunlight encounters a plate of crown glass at a 45.000 angle of incidence. Using the data in Table, find the angle between the violet ray and the red ray in theglass.
This problem relates to Figure which illustrates the dispersion of light by a prism. The prism is made from glass, and its cross section is an equilateral triangle. The indices of refraction for the red and violet light are 1.662 and 1.698, respectively. The angle of incidence for both the red and
An object is located 9.0 cm in front of a converging lens (f = 6.0 cm). Using an accurately drawn ray diagram, determine where the image is located.
The moon’s diameter is 3.48 × 106 m, and its mean distance from the earth is 3.85 × 108 m. The moon is being photographed by a camera whose lens has a focal length of 50.0 mm.(a) Find the diameter of the moon’s image on the slide film.(b) When the slide is projected onto a screen that is 15.0
An object is 18cm in front of a diverging lens that has a focal length of -12 cm. How far in front of the lens, should the object be placed so that the size of its image is reduced by a factor of 2.0?
A converging lens (f = 12.0 cm) is located 30.0cm to the left of a diverging lens (f = -6.00 cm). A postage stamp is placed 36.0 cm to the left of the converging lens.(a) Locate the final image of the stamp relative to the diverging lens.(b) Find the overall magnification.(c) Is the final image
An object is placed 20.0 cm to the left of a diverging lens (f = -8.00 cm). A concave mirror (f = 12.0cm) is placed 30.0 cm to the right of the lens. (a) Find the final image distance, measured relative to the mirror. (b) Is the final image real or virtual? (c) Is the final image upright or
Your friend has a near point of 138cm, and she wears contact lenses that have a focal length of 35.1cm. How close can she hold a magazine and still read it clearly?
A person has far points of 5.0 m from the right eye and 6.5 m from the left eye. Write a prescription for the refractive power of each corrective contact lens.
A jeweler whose near point is 72 cm from his eye uses a magnifying glass as in Figure (b) to examine a watch. The watch is held 4.0 cm from the magnifying glass. Find the angular magnification of the magnifyingglass.
A farsighted person can read printing as close as 25.0 cm when she wears contacts that have a focal length of 45.4 cm. One day, she forgets her contacts and uses a magnifying glass, as in Figure (b). Its maximum angular magnification is 7.50 for a young person with a normal near point of 25.0cm.
A compound microscope has a barrel whose length is 16.0 cm and an eyepiece whose focal length is 1.4 cm. The viewer has a near point located 25 cm from his eyes. What focal length must the objective have so that the angular magnification of the microscope will be -320?
Mars subtends an angle of 8.0 × 10-5 rad at the unaided eye. An astronomical telescope has an eyepiece with a focal length of 0.032m. When Mars is viewed using this telescope, it subtends an angle of 2.8 × 10-3 rad. Find the focal length of the telescope’s objective lens.
A stargazer has an astronomical telescope with an objective whose focal length is 180 cm and an eyepiece whose focal length is 1.20 cm. He wants to increase the angular magnification of a galaxy under view by replacing the telescope’s eyepiece. Once the eyepiece is replaced, the barrel of the
An object is located 30.0 cm to the left of a converging lens whose focal length is 50.0cm.(a) Draw a ray diagram to scale and from it determine the image distance and the magnification.(b) Use the thin-lens and magnification equations to verify your answers to part (a).
A glass block (n = 1.56) is immersed in a liquid. A ray of light within the glass hits a glass–liquid surface at a 75.0° angle of incidence. Some of the light enters the liquid. What is the smallest possible refractive index for the liquid?
A nearsighted patient’s far point is 0.690 m from her eyes. She is able to see distant objects in focus when wearing glasses with a refractive power of -1.50 diopters. What is the distance between her eyes and the glasses?
A microscope for viewing blood cells has an objective with a focal length of 0.50 cm and an eyepiece with a focal length of 2.5cm. The distance between the objective and eyepiece is 14.0cm. If a blood cell subtends an angle of 2.1 × 10-5 rad when viewed with the naked eye at a near point of
A scuba diver, submerged under water, looks up and sees sunlight at an angle of 28.0° from the vertical. At what angle, measured from the vertical, does this sunlight strike the surface of the water?
An office copier uses a lens to place an image of a document onto a rotating drum. The copy is made from this image.(a) What kind of lens is used, converging or diverging? If the document and its copy are to have the same size, but are inverted with respect to one another,(b) How far from the
At age forty, a man requires contact lenses (f = 65.0cm) to read a book held 25.0cm from his eyes. At age forty-five, while wearing these contacts he must now hold a book 29.0 cm from his eyes.(a) By what distance has his near point changed?(b) What focal length lenses does he require at age
The angular magnification of a telescope is 32 800 times as large when you look through the correct end of the telescope as when you look through the wrong end. What is the angular magnification of the telescope?
In a Young’s double-slit experiment, the wavelength of the light used is 520 nm (in vacuum), and the separation between the slits is 1.4 × 10-6 m. Determine the angle that locates(a) The dark fringe for which m = 0,(b) The bright fringe for which m = 1,(c) The dark fringe for which m = 1, and(d)
A sheet that is made of plastic (n = 1.60) covers one slit of a double slit (see the drawing). When the double slit is illuminated by monochromatic light (λvacuum = 586 nm), the center of the screen appears dark rather than bright. What is the minimum thickness of theplastic?
A non-reflective coating of magnesium fluoride (n = 1.38) covers the glass (n = 1.52) of a camera lens. Assuming that the coating prevents reflection of yellow-green light (wavelength in vacuum = 565 nm), determine the minimum nonzero thickness that the coating can have.
Orange light (λvacuum = 611 nm) shines on a soap film (n = 1.33) that has air on either side of it. The light strikes the film perpendicularly. What is the minimum thickness of the film for which constructive interference causes it to look bright in reflected light?
A diffraction pattern forms when light passes through a single slit. The wavelength of the light is 675 nm. Determine the angle that locates the first dark fringe when the width of the slit is (a) 1.8 × 10-4 m and (b) 1.8 × 10-6 m.
Light that has a wavelength of 668 nm passes through a slit 6.73 × 10-6 m wide and falls on a screen that is 1.85 m away. What is the distance on the screen from the center of the central bright fringe to the third dark fringe on either side?
How many dark fringes will be produced on either side of the central maximum if light (λ = 651 nm) is incident on a single slit that is 5.47 × 10-6 m wide?
Late one night on a highway, a car speeds by you and fades into the distance. Under these conditions, the pupils of your eyes have diameters of about 7.0 mm. The taillights of this car are separated by a distance of 1.2 m and emit red light (wavelength = 660 nm in vacuum). How far away from you, is
Consult Multiple-Concept Example to see a model for solving this kind of problem. You are using a microscope to examine a blood sample. Recall from Section that the sample should be placed just outside the focal point of the objective lens of the microscope.(a) If the specimen is being illuminated
A diffraction grating is 1.50 cm wide and contains 2400 lines. When used with light of a certain wavelength, a third-order maximum is formed at an angle of 18.0°. What is the wavelength (in nm)?
The wavelength of the laser beam used in a compact disc player is 780 nm. Suppose that a diffraction grating produces first-order tracking beams that are 1.2 mm apart at a distance of 3.0 mm from the grating. Estimate the spacing between the slits of the grating.
Violet light (wavelength = 410 nm) and red light (wavelength = 660 nm) lie at opposite ends of the visible spectrum.(a) For each wavelength, find the angle θ that locates the first-order maximum produced by a grating with 3300 lines/cm. This grating converts a mixture of all colors between violet
In a Young€™s double-slit experiment, two rays of monochromatic light emerge from the slits and meet at a point on a distant screen, as in Figure (a). The point on the screen where these two rays meet is the eighth-order bright fringe. The difference in the distances that the two rays
A flat observation screen is placed at a distance of 4.5 m from a pair of slits. The separation on the screen between the central bright fringe and the first-order bright fringe is 0.037 m. The light illuminating the slits has a wavelength of 490 nm. Determine the slit separation.
The same diffraction grating is used with two different wavelengths of light, λA and λB. The fourth-order principal maximum of light A exactly overlaps the third-order principal maximum of light B. Find the ratio λA/ λB.
The distance between New York City and London is 3470 mi. (a) If a radio wave from New York City is transmitted directly across the ocean, how long will it take to reach a receiver in London? (b) In fact, due to the curvature of the earth, radio waves cannot be transmitted directly across such
(a) When the Apollo astronauts landed on the moon, it took the radio signal 1.28 s to reach Mission Control on the earth. How far away were the astronauts from the earth? (b) Since the sun is 1.50 x 1011 from the earth, how much time does it take for light to travel from the sun to the earth? (c)
The range of electromagnetic wave frequencies on the FM radio band is 88.0 MHz to 108 MHz(a) What is the range of wavelengths for the FM radio band? (b) What is the range of photon energy for the FM radio band? (c) Explain the relationship between frequency and photon energy.
The individual rods on rooftop antennas are designed to be one-quarter of a wavelength for each television frequency. What is the range of rod lengths needed for television Channels 2 through 6 if their frequencies are between 54.0 MHz and 88.0 MHz?
An illumination of 180 lux on student desks and other work areas is the standard that architects use when designing lighting systems for schools. (a) If a ceiling is 2.50 m above a student work area, what intensity light source must be installed? (b) If the ceiling were twice its original height,
1. Find the distance (in meters) traveled by a radio wave in 5.00 s.2. Find the distance (in meters) traveled by a light wave in 6.40 s.3. A television signal is sent to a communications satellite that is 20,000 mi above a relay station. How long does it take for the signal to reach the
1. How long does it take for a radio wave to travel 3000 mi across the United States?2. How long does it take for a flash of light to travel 100 m?3. How long does it take for a police radar beam to travel to a truck and back if the truck is 115 m from the radar unit?4. How far away (in km) is an
(a) How long does it takes for light to reach the earth from Mars when the separation of the two planets is at its smallest? The earth’s orbital radius is 143 million kilometers. The orbital radius of Mars is 218 million kilometers. (b) How long does it take when the separation is at its maximum?
If it takes 4.31 years for light to reach the earth from Alpha Centauri, the closest star to the earth other than the sun, what is the distance (in miles) to the next nearest neighbor (Barnard’s Star), which is 25% farther away?
How long does it take light to reach the earth from Jupiter when the separation of the two planets is? (a) At its smallest.(b) At its largest? The earth’s orbital radius is 143 million kilometers. The orbital radius of Jupiter is 725 million kilometers. Assume the planetary orbits are circular.
1. Preparing for reentry, astronauts use radar to determine the distance back to the earth. What is their altitude if it takes 0.330 s for the radar wave to travel to the earth and return?2. The distance to the moon can be calculated by reflecting a ray of light off a mirror left by astronauts. The
1. c = 3.00 x 108 m/sλ = 4.55 x 10–5 mf =?2. c = 3.00 x 108 m/sλ = 9.70 x 10–10 mf =?3. c = 3.00 x 108 m/sf = 9.70 x 1011 Hzλ =?4. c = 3.00 x 108 m/sf = 24.2 MHzλ =?5. c = 3.00 x 108 m/sf = 45.6 MHzλ =?6. c = 3.00 x 108 m/sf = 415Hzλ =?7. c = 3.00 x 108
1. Find the wavelength of a radio wave from an AM station broadcasting at a frequency of 1400 kHz2. Find the wavelength of a radio wave from an FM station broadcasting at a frequency of 100 MHz3. Find the frequency of an electromagnetic wave if its wavelength is 85.5 m.4. Find the frequency of an
1. What is the energy of a photon of electromagnetic radiation with frequency 8.95 x 1010 Hz?2. What is the frequency of a photon of electromagnetic radiation with energy 3.96 x 10–22 J?3. What is the energy of a photon of electromagnetic radiation with frequency 4.55 x 108 Hz?4. Find the
1. Find the energy of a photon of electromagnetic radiation with frequency 9.20 x 1016 Hz.2. Find the energy of a red photon.3. Find the energy of a blue photon.4. Find the energy of a yellow photon if the wavelength of its electromagnetic radiation is midway between those of red and blue
1. I = 48.0 cdI = ___ℓm2. I = 342 cdI = ___ℓm3. I = 765 ℓmI = ____cd4. I = 432 ℓmI = ____cd5. I = 75.0 cdI = ___ℓm6. I = 650 ℓmI = ___cd7. I = 900 ℓmr = 7.00 ftE =?8. I = 741 ℓmr = 6.50 mE =?9. I = 893 ℓmr = 3.25 ftE =?10. E = 4.32 luxr = 9.00 mI =?11. E = 10.5 ft-candlesr = 6.00
1. Find the intensity of a light source that produces an illumination of 5.50 ft-candles at 9.85 ft from the source.2. Find the intensity of a light source that produces an illumination of 2.39 lux at 4.50 m from the source.3. Find the intensity of a light source that produces an illumination of
Find the illumination on a surface by three light sources, each with intensity 150 ℓm located at distances of 2.00 m, 2.70 m, and 2.98 m from the surface, respectively.
1. Find the intensity of two identical light sources located 1.40 m and 1.96 m, respectively, from a point where the illumination is 3.54ℓm/m22. Find the intensity of two identical light sources located 0.880 m and 1.12 m from a point where the illumination is 5.86ℓm/m2.3. A desk is 3.35 m
1. Find the distance (in meters) traveled by a radio wave in 21.5 h.2. A radar wave that is bounced off an airplane returns to the radar receiver in 3.78 x 10–5, How far (in miles) is the airplane from the radar receiver?3. How long does it take for a police radar beam to travel to a car and back
1. Find the frequency of a light wave if its wavelength is 5.415 x 10–8m.2. What is the energy of a photon with frequency 1.45 x 1011 Hz?3. What is the frequency of a photon with energy of 4.75 x 10–23J?4. What is the energy of a photon with frequency 8.25 x 10–15 Hz?5. Find the intensity of
What are the maximum and minimum transit times for light traveling from Jupiter to Mars? The orbital radii are 215 million kilometers for Mars and 725 million kilometers for Jupiter. Assume the planetary orbits are circular. Also, make the (nonphysical) assumption that the sun is transparent to the
Find the intensity of two identical light sources located 0.454 m and 0.538 m, respectively, from a point where the illumination is 8.46ℓm/m2
Find the illumination on a surface by three light sources, each with intensity 125 ℓm, located at 1.85 m, 1.92 m, and 2.43 m from the surface, respectively.
1. Which of the following are examples of electromagnetic radiation?(a) Gamma rays(b) Sound waves(c) Radio waves(d) Water waves(e) Visible light2. The particle theory of light explains(a) Diffraction of light around a sharp edge.(b) Refraction of light at a boundary.(c) The photoelectric effect.(d)
1. Does light always travel at the same speed? Explain.2. What name is given to the entire range of waves that are similar to visible light?3. Who proposed the particle theory of light?4. Who developed the wave packet theory of light?5. Who made the first estimate of the speed of light?6. How was
Tamera uses a concave mirror when applying makeup. (a) The mirror has a radius of curvature of 38.0cm. What is the focal length of the mirror?(b) Tamera’s face is located 12.5 cm from the mirror. Where will her image appear? (c) Will the image be upright or inverted? (d) How long will her face
A convex security mirror has a radius of curvature of –1.50 m. (a) A shoplifter picks up a 0.255-mhigh purse 11.5 m from the mirror. How far behind the mirror, is the image of the purse? (b) Is the image real or virtual? (c) How high is the image of the purse? (d) Are convex security mirrors
A fish tank made of crown glass is full of fresh water. (a) What is the angle of refraction when the light travels from the air and enters the crown glass at an incident angle of 30.0°? (b) Determine the angle of refraction when the light leaves the crown glass and enters the water. (c) If the
Diamonds are cut to take advantage of internal reflections of light. The angles of a diamond are cut so that all of the light that enters it reflects out the top. The light or brilliance that emerges from the top of a diamond is one of the qualities that determine its monetary value. (a) What is
A photographer uses a 60.0-mm lens. (a) How far away should the lens be from the film if the object is located 9.20 m from the lens? (b) What will be the height of the image if the object is 2.00 m tall?
Use the formulas 1/f = 1/so + 1/st and M = hi/ho = –si /so for Problems 1–8.1. Given so = 1.65cm and si = 6.00cm find f.2. Given f = 15.0cm and si = 3.00cm find so.3. Given si = 1.45cm and f = 10. 0cm find so.4. Given si = –10.0cm and f = –5.00cm find so5. Given so = 7.35cm and si = 17.0cm
1. An object 30.0 cm tall is located 10.5 cm from a concave mirror with focal length 16.0 cm. (a) Where is the image located? (b) How high is it?2. An object and its image in a concave mirror are the same height, yet inverted, when the object is 20.0 cm from the mirror. What is the focal length of
(a) What is the height of a figurine 7.33 cm in front of a concave mirror that produces an image –2.75 cm high? The image appears to be 5.03 cm in front of the mirror.(b) Find the focal length of the mirror. (c) What distance would an image appear to be from the mirror with double the focal
1. Find the index of refraction of a medium for which the angle of incidence of a light beam is 31.5° and angle of refraction is 25.6°.2. If the index of refraction of a medium is 2.40 and the angle of incidence is 14.6°, what is the angle of refraction?3. If the index of refraction of a liquid
An object 5.00 cm tall is placed 15.0 cm from a converging lens, and a real image is formed 7.50 cm from the lens. (a) What is the focal length of the lens? (b) What is the size of the image?
An object 4.50 cm tall is placed 18.0 cm from a converging lens with a focal length of 26.0 cm. (a) What is the location of the image? (b) What is its size?
What are the size and location of an image produced by a converging lens with a focal length of 19.5 cm of an object 5.76 cm from the lens and 1.45 cm high?
What are the size and location of an image produced by a convex lens with a focal length of 14.5 cm of an object 10.5 cm from the lens and 2.35 cm high?
What is the focal length of a convex lens that produces an inverted image twice as large as the object at a distance of 13.3 cm from the lens?
1. Using 1/f = 1/so+1/st , so = 3.50 cm, and st = 7.25 cm, find f.2. Using 1/f = 1/so+1/st , so = 8.50 cm, and f = 25.0 cm, find st3. Using M = ht/ho = –st/so, ho = 6.50 cm, st = 7.50 cm, and so = 1.40cm, find ht.4. If an object is 3.75 m tall and 7.35 m from a large mirror with an image formed
1. An object 4.50 cm tall is placed 20.0 cm from a converging lens. A real image is formed 12.0 cm from the lens. (a) What is the focal length of the lens? (b) What is the size of the image?2. The focal length of a lens is 4.00 cm. How far from the lens, must the object be to produce an image 7.20
1. Stained glass is an example of(a) A transparent material.(b) A translucent material.(c) An opaque material.(d) None of the above.2. A virtual image may be(a) Larger than the object.(b) Smaller than the object.(c) Erect.(d) All of the above.(e) None of the above.3. A real image may be(a)
1. Explain the difference between real and virtual images.2. Explain the difference between a concave and a convex mirror.3. Explain the effect of spherical aberration.4. For a mirror of given focal length, how does the image distance change if the object distance is decreased?5. For a given object
1. Explain the difference between converging and diverging lenses.2. Give several examples of total internal reflection.3. In your own words, explain the law of refraction.4. How does the speed of light in a high-index-of-refraction material compare to the speed of light in a vacuum?5. In your own
1. How do water waves affect the escape of light from below the surface of the water?2. Explain why a fish under water appears to be at a different depth below the surface than it actually is. Does it appear deeper or shallower?3. Does light always travel in a straight line? Explain.4. Explain how
1. Name the colors of the visible spectrum.2. What property of light determines its color?3. Name the light waves whose wavelengths are(a) slightly longer than visible light and(b) slightly shorter than visible light.4. What is the apparent color of a green dress in a closed room with only a red
1. True or false: For you to see a rainbow, the raindrops must be between the sun and you.2. Name the property of a wave that describes its ability to bend around obstacles in its path.3. When a narrow beam of light passes by a sharp edge, around a fine wire, or through a narrow slit or a pinhole,
Why is the sky blue?
Why is a sunset red?
Why are clouds white?
Why is the ocean blue?
If glass is dispersive, why don’t we normally see a spectrum of colors when sunlight passes through a glass window? Explain. (Are the speeds of each color of light the same in the glass?)
When you see the Sun over a lake or the ocean, you often observe a long swath of light (Fig. 22.22). What causes this effect, sometimes called a €œglitter path€?
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