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physics
light and optics
College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions
Two hunters, one with a bow and arrow and the other with a laser gun, see a fish under water. They both aim directly for the location where they see the fish. Does the arrow or the laser beam have a better chance of hitting the fish? Explain.
Explain why the pencil in Fig. 22.23 appears almost severed. Also, compare this figure with Fig. 22.13b and explain the difference.
The photos in Fig. 22.24 were taken with a camera on a tripod at a fixed angle. There is a penny in the container, but only its tip is seen initially. However, when water is added, more of the coin is seen. Why? Use a diagram to explain.
The index of refraction in a certain precious transparent stone is 2.35. What is the speed of light in that stone?
The indices of refraction for zircon and fused quartz can be found in Table 22.1. (a) The speed of light in fused quartz is (1) greater than, (2) less than, (3) the same as the speed of light in zircon. Explain. (b) Compute the ratio of the speed of light in fused quartz to that in zircon.
A beam of light traveling in air is incident on a trans-parent plastic material at an angle of incidence of 50o. The angle of refraction is 35o. What is the index of refraction of the plastic?
A beam of light enters water from air. (a) Will the angle of refraction be (1) greater than, (2) equal to, or (3) less than the angle of incidence? Explain. (b) If the angle of incidence is 50o, find the angle of refraction.
Light passes from a crown glass container into water. (a) Will the angle of refraction be (1) greater than, (2) equal to, or (3) less than the angle of incidence? Explain. (b) If the angle of refraction is 20o, what is the angle of incidence?
The critical angle for a certain type of glass in air is 41.8o. What is the index of refraction of the glass?
(a) For total internal reflection to occur, should the light be directed from (1) air to water or (2) water to air? Explain. (b) What is the critical angle of water in air?
What is the critical angle of a diamond in water?
A beam of light in air is incident on the surface of a slab of fused quartz. Part of the beam is transmitted into the quartz at an angle of refraction of 30o relative to a normal to the surface, and part is reflected. What is the angle of reflection?
A beam of light is incident from air onto a flat piece of polystyrene at an angle of relative to a normal to the surface. What angle does the refracted ray make with the plane of the surface?
The laser used in cornea surgery to treat corneal disease is the excimer laser, which emits ultraviolet light at a wavelength of 193 nm in air. The index of refraction of the cornea is 1.376. What are the wavelength and frequency of the light in the cornea?
Light passes from material A, which has an index of refraction of 4/3, into material B, which has an index of refraction of 5/4. (a) The speed of light in material A is (1) greater than, (2) the same as, (3) less than the speed of light in material B. Explain. (b) Find the ratio of the speed of
In Exercise 22, In exercise Light passes from material A, which has an index of refraction of 4/3, into material B, which has an index of refraction of 5/4. (a) The wavelength of light in material A is (1) greater than, (2) the same as, (3) less than the wave-length of light in material B.
The critical angle between two materials is 43o. If the angle of incidence is 35o, what is the angle of refraction? (Consider that light can travel to the interface from either material.)
(a) An object immersed in water appears closer to the surface than it actually is. What is the cause of this illusion?(b) Using Fig. 22.26, show that the apparent depth for small angles of refraction is d€™ = d/n, where n is the index of refraction of the water.
A person looks over the edge of a pool and sees a bottle cap on the bottom directly below, where the depth is 3.2 m. How far below the water surface does the bottle cap appear to be?
What percentage of the actual depth is the apparent depth of an object submerged in oil if the observer is looking almost straight downward?
Alight ray in air is incident on a glass plate 10.0 cm thick at an angle of incidence of 40o. The glass has an index of refraction of 1.65. The emerging ray on the other side of the plate is parallel to the incident ray, but is later-ally displaced. What is the perpendicular distance between the
To a submerged diver looking upward through the water, the altitude of the Sun (the angle between the Sun and the horizon) appears to be 45o. (a) The actual altitude of the Sun is (1) greater than, (2) the same as, (3) less than 45o. Explain. (b) What is the Sun’s actual altitude?
A beam of light is incident on a plane mirror at an angle relative to the surface of the mirror. (a) Will the angle between the reflected ray and the normal be (1) α, (2) 90o – α, or (3) 2α? (b) If α = 33o, what is the angle between the reflected ray and the normal?
At what angle to the surface must a diver submerged in a lake look toward the surface to see the setting Sun just along the horizon?
A submerged diver shines a light toward the surface of a body of water at angles of incidence of 40o and 50o. Can a person on the shore see a beam of light emerging from the surface in either case? Justify your answer mathematically.
Light in air is incident on a transparent material. It is found that the angle of reflection is twice the angle of refraction. What is the range of the index of refraction of the material?
A beam of light is to undergo total internal reflection through a 45o €“ 90o €“ 45o prism (Fig. 22.27).(a) Will this arrangement depend on (1) the index of refraction of the prism, (2) the index of refraction of the surrounding medium, or (3) the indices of refraction of both?
A 45o – 90o – 45o prism (Fig. 22.27) is made of a material with an index of refraction of 1.85. Can the prism be used to deflect a beam of light by 90o. (a) In air? (b) What about in water?
A coin lies on the bottom of a pool under 1.5 m of water and 0.90 m from the side wall (Fig. 22.28). If a light beam is incident on the water surface at the wall, at what angle relative to the wall must the beam be directed so that it will illuminate the coin?
A flint glass plate 3.5 cm thick is placed over a news-paper. How far beneath the top surface of the plate would the print appear to be if you were looking almost vertically downward through the plate?
Yellow- green light of wavelength 550 nm in air is incident on the surface of a flat piece of crown glass at an angle of 40o. (a) What is the angle of refraction of the light? (b) What is the speed of the light in the glass? (c) What is the wavelength of the light in the glass?
Alight beam traveling upward in a plastic material with an index of refraction of 1.60 is incident on an upper horizontal air interface. (a) At certain angles of incidence, the light is not transmitted into air. The cause of this is (1) reflection, (2) refraction, (3) total internal reflection.
A 15-cm-deep opaque container is empty except for a single coin resting on its bottom surface. When looking into the container at a viewing angle of 50o relative to the vertical side of the container, you see nothing on the bottom. When the container is filled with water, you see the coin (from the
Two upright plane mirrors touch along one edge, where their planes make an angle of α. A beam of light is directed onto one of the mirrors at an angle of incidence of β(β < α) and is reflected onto the other mirror. (a) Will the angle of reflection of the beam from the second mirror be (1) α,
An outdoor circular fish pond has a diameter of 4.00 m and a uniform full depth of 1.50 m. A fish halfway down in the pond and 0.50 m from the near side can just see the full height of a 1.80-m-tall person. How far away from the edge of the pond is the person?
For total internal reflection to occur inside an optic fiber as shown in Fig. 22.29, the angle u must be greater than the critical angle for the fiber€“air interface. At the end of the fiber, the incident light undergoes a refraction to enter the fiber. If total internal reflection is to
Two glass prisms are placed together (Fig. 22.30).(a) If a beam of light strikes the face of one of the prisms at normal incidence as shown, at what angle does the beam emerge from the other prism? (b) At what angle of incidence would the beam be refracted along the inter-face of the prisms?
White light is incident from air onto a transparent material at an angle of incidence of 40o. The angles of refraction for the red and blue colors are and 27.95o, respectively. What are the indices of refraction for the two colors?
The index of refraction of crown glass is 1.515 for red light and 1.523 for blue light. (a) If light of both colors is incident on crown glass from air, the blue color will be refracted (1) more, (2) less, or (3) the same amount as the red color. Explain. (b) Find the angle separating rays of the
A beam of light with red and blue components of wavelengths 670 nm and 425 nm, respectively, strikes a slab of fused quartz at an incident angle of 30o. On refraction, the different components are separated by an angle of 0.001 31 rad. If the index of refraction of the red light is 1.4925, what is
White light passes through a piece of crown glass and strikes an interface with air at an angle of 41.15o. Assume the indices of refraction of crown glass are the same as given in Exercise 44. Which color(s) of light will be refracted out into the air? In exercise The index of refraction of crown
A beam of red light is incident on an equilateral prism as shown in Fig. 22.31.(a) If the index of refraction of red light of the prism is 1.400, at what angle θ does the beam emerge from the other face of the prism? (b) Suppose the incident beam were white light. What would be the
The angle of incidence and angle of refraction along a particular interface between two media are 30o and 40o, respectively. What is the critical angle for the same interface?
Light passes from medium A into medium B at an angle of incidence of 30o. The index of refraction of A is 1.5 times that of B. (a) What is the angle of refraction? (b) What is the ratio of the speed of light in B to the speed of light in A? (c) What is the ratio of the frequency of light in B to
Two identical plane mirrors of width w are placed a distance d apart with their mirrored surfaces parallel and facing each other. (a) A beam of light is incident at one end of one mirror so that the light just strikes the far end of the other mirror after reflection. Will the angle of incidence be
The critical angle between two materials is 43o. If the angle of incidence is twice the angle of refraction, what are the angles of incidence and refraction?
The critical angle for a glass– air interface is 41.11° for red light and 41.04° for blue light. (a) During the time the blue light travels 1.000 m, the red light will travel (1) more than, (2) less than, (3) exactly 1.000 m. Explain. (b) Calculate the difference in distance traveled by the
In Exercise 47, if the angle of incidence is too small, light will not emerge from the other side of the prism. How could this happen? Calculate the minimum angle of incidence for the red light so that it does not emerge from the other side of the prism. In exercise If the index of refraction of
An optic fiber of index of refraction of 1.6 is surrounded by a layer called the cladding layer. The index of refraction of the cladding is 1.3. If the angle of incidence inside the fiber is 40°, will there be light leaking into air? What if the angle of incidence is 50°?
Two people stand 5.0 m apart and 3.0 m away from a large plane mirror in a dark room. At what angle of incidence should one of them shine a flashlight on the mirror so that the reflected beam directly strikes the other person?
A beam of light is incident on a plane mirror at an angle of incidence of 35o. If the mirror rotates through a small angle of θ, through what angle will the reflected ray rotate?
Two plane mirrors, M1 and M2, are placed together as illustrated in Fig. 22.25.(a) If the angle α between the mirrors 70o is and the angle of incidence, θi1 of a light ray incident on M1 is 35o, what is the angle of reflection, θr2, from M2? (b) If a = 115o
How can you quickly determine the focal length of a converging lens? Will the same method work for a diverging lens?
How would you use a converging lens as a magnifying glass? Can you do the same with a diverging lens?
When you open your eyes underwater, everything is blurry. However, when you wear goggles, you can see clearly. Explain.
What is the cause of spherical aberration?
Day€“night rearview mirrors are common in cars. At night, when you tilt the mirror backward, the intensity and glare of headlights behind you are reduced (Fig. 23.22). The mirror is wedge shaped and is silvered on the back. The unsilvered front surface reflects about 5% of incident light;
When you stand in front of a plane mirror, there is a right–left reversal. (a) Why is there not a top–bottom reversal of your body? (b) Could you create an apparent top–bottom reversal by positioning your body differently?
How can the focal length be quickly determined experimentally for a concave mirror? Can you do the same thing for a convex mirror?
(a) If you look into a shiny spoon, you see an upright image on one side and an inverted image on the other (Fig. 23.24). (Try it.) Why?(b) Could you see upright images on both sides? Explain.
(a) What is the purpose of using two mirrors on a car or truck, such as the one shown in Fig. 23.25?(b) Some side rearview mirrors have the warning €œOBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR.€ Explain why. (c) Could a TV satellite dish be considered a converging mirror?
(a) A10-cm-tall mirror bears the following advertisement: €œFull-view mini mirror. See your full body in 10 cm.€ How can this be?(b) A popular novelty item consists of a concave mirror with a ball suspended at or slightly inside the center of curvature (Fig. 23.26). When the
Draw ray diagrams that show how three images of an object are formed in two plane mirrors at right angles, as shown in Fig. 23.27a. Figure 23.27b shows a similar situation from a different point of view that gives four images. Explain the extra image in this case.
An object is 100 cm in front of a concave mirror that has a radius of 80 cm. (a) Use a ray diagram to determine whether the image is (1) real or virtual, (2) upright or inverted, and (3) magnified or reduced. (b) Calculate the image distance and lateral magnification.
A candle with a flame 1.5 cm tall is placed 5.0 cm from the front of a concave mirror. A virtual image is formed 10 cm behind the mirror. (a) Find the focal length and radius of curvature of the mirror. (b) How tall is the image of the flame?
An object is placed 50 cm in front of a convex mirror and its image is found to be 20 cm behind the mirror. What is the focal length of the mirror? What is the lateral magnification?
An object 3.0 cm tall is placed 20 cm from the front of a concave mirror with a radius of curvature of 30 cm. Where is the image formed, and how tall is it?
If the object in Exercise 14 is moved to a position 10 cm from the front of the mirror, what will be the characteristics of the image?
An object 3.0 cm tall is placed at different locations in front of a concave mirror whose radius of curvature is 30 cm. Determine the location of the image and its characteristics when the object distance is 40 cm, 30 cm, 15 cm, and 5.0 cm, using (a) A ray diagram and (b) The mirror equation.
Use the mirror equation and the magnification factor to show that when do = R = 2f for a concave mirror, the image is real, inverted, and the same size as the object.
An object is 120 cm in front of a convex mirror that has a focal length of 50 cm. (a) Use a ray diagram to determine whether the image is (1) real or virtual, (2) upright or inverted, and (3) magnified or reduced. (b) Calculate the image distance and image height.
A bottle 6.0 cm tall is located 75 cm from the concave surface of a mirror with a radius of curvature of 50 cm. Where is the image located, and what are its characteristics?
A man stands 2.0 m away from a plane mirror. (a) What is the distance between the mirror and the man’s image? (b) What are the image characteristics?
A virtual image of magnification +2.0 is produced when an object is placed 7.0 cm in front of a spherical mirror. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) Find the radius of curvature of the mirror.
A virtual image of magnification + 0.50 is produced when an object is placed 5.0 cm in front of a spherical mirror. (a) The mirror is (1) convex, (2) con-cave, (3) flat. Explain. (b) Find the radius of curvature of the mirror.
Using the spherical mirror equation and the magnification factor, show that for a convex mirror, the image of an object is always virtual, upright, and reduced.
When a man’s face is in front of a concave mirror of radius 100 cm, the lateral magnification of the image is + 1.5. What is the image distance?
A convex mirror in a department store produces an upright image 0.25 times the size of a person who is standing 200 cm from the mirror. What is the focal length of the mirror?
The image of an object located 30 cm from a mirror is formed on a screen located 20 cm from the mirror. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) What is the mirror’s radius of curvature?
The upright image of an object 18 cm in front of a mirror is half the size of the object. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) What is the focal length of the mirror?
A concave mirror has a magnification + 3.0 of for an object placed 50 cm in front of it. (a) The type of image produced is (1) virtual and upright, (2) real and upright, (3) virtual and inverted, (4) real and inverted. Explain. (b) Find the radius of curvature of the mirror.
A concave mirror is constructed so that a man at a distance of 20 cm from the mirror sees his image magnified 2.5 times. What is the radius of curvature of the mirror?
A child looks at a reflective Christmas tree ball ornament that has a diameter of 9.0 cm and sees an image of her face that is half the real size. How far is the child’s face from the ball?
An object 5.0 cm tall is placed 40 cm from a plane mirror. Find (a) The distance from the object to the image, (b) The height of the image, and (c) The image’s magnification.
A dentist uses a spherical mirror that produces an upright image of a tooth that is magnified four times. (a) The mirror is (1) converging, (2) diverging, (3) flat. Explain. (b) What is the mirror’s focal length in terms of the object distance?
A 15-cm-long pencil is placed with its eraser on the optic axis of a concave mirror and its point directed upward at a distance of 20 cm in front of the mirror. The radius of curvature of the mirror is 30 cm. Use (a) A ray diagram and (b) The mirror equation to locate the image and determine the
A spherical mirror at an amusement park has a radius of If 10 m. it forms an image that has a lateral magnification of +2.0, what are the object and image distances?
A pill bottle 3.0 cm tall is placed 12 cm in front of a mirror. A 9.0-cm-tall upright image is formed. (a) The mirror is (1) convex, (2) concave, (3) flat. Explain. (b) What is its radius of curvature?
A convex mirror is on the exterior of the passenger side of many trucks (see Conceptional Question 8a). If the focal length of such a mirror is – 40.0 cm, what will be the location and height of the image of a car that is 2.0 m high and (a) 100 m and (b) 10.0 m behind the truck mirror?
For values of do from 0 to ∞, (a) Sketch graphs of (1) di versus do and (2) Mversus do for a converging mirror, (b) Sketch similar graphs for a diverging mirror.
The front surface of a glass cube 5.00 cm on each side is placed a distance of 30.0 cm in front of a converging mirror that has a focal length of 20.0 cm. (a) Where is the image of the front and back surface of the cube located, and what are the image characteristics? (b) Is the image of the cube
A section of a sphere is mirrored on both sides. If the magnification of the image of an object is +1.8 when the section is used as a concave mirror, what is the magnification of the same object at the same object distance in front of the convex side?
A concave mirror of radius of curvature of 20 cm forms an image of an object that is twice the height of the object. (a) There could be (1) one, (2) two, (3) three object distance(s) that satisfy the image characteristics. Explain. (b) What are the object distances?
Two students in a physics laboratory each have a concave mirror with the same radius of curvature, 40 cm. Each student places an object in front of their mirror. The image in both mirrors is three times the size of the object. However, when the students compare notes, they find that the object
If you hold a 900-cm2 square plane mirror 45 cm from your eyes and can just see the full length of an 8.5-m flagpole behind you, how far are you from the pole?
When an object is moved closer to a convex mirror, its image size (1) increases, (2) remains the same, (3) decreases. Prove your answer mathematically.
An object is placed 50.0 cm in front of a converging lens of focal length 10.0 cm. What are the image distance and the lateral magnification?
An object placed 30 cm in front of a converging lens forms an image 15 cm behind the lens. What are the focal length of the lens and the lateral magnification of the image?
A converging lens with a focal length of 20 cm is used to produce an image on a screen that is 2.0 m from the lens. What are the object distance and the lateral magnification of the image?
When an object is placed at 2.0 m in front of a diverging lens, a virtual image is formed at 30 cm in front of the lens. What are the focal length of the lens and the lateral magnification of the image?
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