Mastering Physics Solutions Chapter 26 Geometrical Optics
Chapter 26 Geometrical Optics Q.1CQ
Two plane mirrors meet at right angles at the origin, as indicated in Figure. Suppose an L-shaped object has the position and orientation labeled A. Draw the location and orientation of all the images of object A formed by the two mirrors.
Solution:
Chapter 26 Geometrical Optics Q.1P
Alaserbeam is reflected by a plane mirror. Itis observed that the angle between the incident and reflected beams is 28°. If the mirror is now rotated so that the angle of incidence increases by 5.0°, what is the new angle between the incident and reflected beams?
Solution:
Chapter 26 Geometrical Optics Q.2CQ
Two plane mirrors meet at right angles at the origin, as indicated in Figure. Suppose an L-shaped object has the position and orientation labeled B. Draw the location and orientation of all the images of object B formed by the two mirrors.
Solution:
Chapter 26 Geometrical Optics Q.2P
The reflecting surfaces of two mirrors form a vertex with an angle of 120°. If a ray of light strikes mirror 1 with an angle of incidence of 55°, find the angle of reflection of the ray when it leaves mirror 2.
Solution:
Chapter 26 Geometrical Optics Q.3CQ
What is the radius of curvature of a plane mirror? What is its focal length? Explain.
Solution:
Chapter 26 Geometrical Optics Q.3P
A ray of light reflects from a plane mirror with an angle of incidence of 37°. If the mirror is rotated by an angle θ, through what angle is the reflected ray rotated?
Solution:
Chapter 26 Geometrical Optics Q.4CQ
Dish receivers for satellite TV always use the concave side of the dish, never the convex side. Explain.
Solution:
Chapter 26 Geometrical Optics Q.4P
IP Asmall vertical mirror hangs on the wall, 1.40 m above the floor. Sunlight strikes the mirror, and the reflected beam forms a spot on the floor 2.S0 m from the wall. Later in the day, you notice that the spot has moved to a point 3.75 m from the wall. (a) Were your two observations made in the morning or in the afternoon? Explain. (b) What was the change in the Sun’s angle of elevation between your two observations?
Solution:
Chapter 26 Geometrical Optics Q.5CQ
Suppose you would like to start a fire by focusing sunlight onto a piece of paper. In Conceptual Checkpoint 26-2 we saw that a concave mirror would be better than a convex mirror for this purpose. At what distance from the mirror should the paper be held for best results?
Solution:
A fire can be started by focusing sunlight onto a piece of paper. For this purpose, a concave mirror is preferred over a convex mirror, because, when the light rays strike a concave mirror, it gets reflected and meets at the focal point of the mirror. Whereas, the reflected rays from a convex mirror diverge from the mirror, and appear as they come from the focal point behind the mirror.
The parallel rays from the sun are focused on a very small area of the paper. If a concave mirror is used, the light rays will be converged in front of the mirror. Whereas, when rays are focused on a convex mirror, the light rays appear to come from the focal point behind the mirror. So, a concave mirror focuses the light rays more strongly on the paper piece, when compared to a convex mirror.
For best results, the paper should be held at the focal length of the concave mirror, such that, the light rays converge on the small area of the paper and the heating would be the greatest.
Chapter 26 Geometrical Optics Q.5P
Sunlight enters a room at an angle of 32° above the horizontal and reflects from a small mirror lying flat on the floor. The reflected light forms a spot on a wall that is 2.0 m behind the mirror, as shown in Figure If you now place a pencil under the
Solution:
Chapter 26 Geometrical Optics Q.6CQ
When light propagates from one medium to another, does it always bend toward the normal? Explain.
Solution:
No, the bending of light depends upon the speed of the medium.
The light bends towards the normal when the light enters a medium in which its speed of propagation is less than it was in the first medium.
The light bends away from the normal when the light enters a medium in which its speed of propagation is greater than the first medium.
Chapter 26 Geometrical Optics Q.6P
You stand 1.50 m m front of a wall and gaze downward at a small vertical mirror mounted on it. In this mirror you can see the reflection of your shoes. If your eyes are 1.85 m above your feet, through what angle should the mirror be tilted for you to see your eyes reflected in the mirror? (The location of the mirror remains the same, only its angle to the vertical is changed.)
Solution:
Chapter 26 Geometrical Optics Q.7CQ
A swimmer at point B in Figure needs help. Two lifeguards depart simultaneously from their tower at point A, but they follow different paths. Although both lifeguards run with equal speed on the sand and swim with equal speed in the water, the lifeguard who follows the longer path, ACB, arrives at point B before the lifeguard who follows the shorter, straight-line path from A to B. Explain.
Solution:
One can run on sand with speed more than the speed with which one swim in water.
Since the lifeguard who follows the path ACB run more distance on sand compared to other, hence that lifeguard takes less time to travel more distance.
Distance travelled in water by lifeguard of path ACB is less than other, hence it takes less time to reach at same point B while speed of both lifeguards are same.
Chapter 26 Geometrical Optics Q.7P
IP Standing 2.3 m in front of a small vertical mirror, you see the reflection of your belt buckle, which is 0.72 m below your eyes. (a) What is the vertical location of the mirror relative to the level of your eyes? (b) What angle do your eyes make with the horizontal when you look at the buckle? (c) If you now move backward until you are 6.0 m from the mirror, will you still see the buckle, or will you see a point on your body that is above or below the buckle? Explain.
Solution:
Chapter 26 Geometrical Optics Q.8CQ
When you observe a mirage on a hot day, what are you actually seeing when you gaze at the “pool of water” in the distance?
Solution:
Chapter 26 Geometrical Optics Q.8P
How many times does the light beam shown in Figure reflect from (a) the top and (b) the bottom mirror?
Solution:
Chapter 26 Geometrical Optics Q.9CQ
Explain the difference between a virtual and a real image.
Solution:
The main difference between real image and virtual image is
(i) Real image:– If a divergent beam of light from a point after reflection or refraction actually converges to a second point, then the second point is called the real image of first point. The real image can be caught on a screen.
(ii) Virtual Image:– If a divergent beam of light from a point , after reflection or refraction , appears to diverge from a second point, then the second point is called the virtual image of the first point. The virtual image cannot be caught on a screen. The virtual image can be photographed.
Chapter 26 Geometrical Optics Q.9P
CE If you view a clock in a mirror, do the hands rotate clockwise or counterclockwise?
Solution:
From the figure we can say that, the hands on mirror – image clock rotate counter clock wise
Chapter 26 Geometrical Optics Q.10CQ
Sitting on a deserted beach one evening, you watch as the last bit of the Sun approaches the horizon. Just before the Sun disappears from sight, is the top of the Sim actually above or below the horizon? That is, if Earth’s atmosphere could be instantly removed just before the Sun disappeared, would the Sun still be visible, or would it be below the horizon? Explain.
Solution:
Chapter 26 Geometrical Optics Q.10P
A 12.5-foot-long, nearsighted python is stretched out perpendicular to a plane mirror, admiring its reflected image. If the greatest distance to which the snake can see cleariy is 26.0 ft, how close must its head be to the mirror for it to see a clear image of its tail?
Solution:
Chapter 26 Geometrical Optics Q.11CQ
A large, empty coffee mug sits on a table. From your vantage point the bottom of the mug is not visible. When the mug is filled with wa ter, however, you can see the bottom of the mug. Explain.
Solution:
Chapter 26 Geometrical Optics Q.11P
(a) How rapidly does the distance between you and your mirror image decrease if you walk directly toward a mirror with a speed of 2.6 m/s? (b) Repeat part (a) for the case in which you walk toward a mirror but at an angle of 38° to its normal.
Solution:
Chapter 26 Geometrical Optics Q.12CQ
The Disappearing Eyedropper The accompanying photograph shows eyedroppers partially immersed in oil (left) and water (right). Explain why the dropper is invisible in the oil.
Solution:
Chapter 26 Geometrical Optics Q.12P
You are 1.9 m tall and stand 3.2 m from a plane mirror that extends vertically upward from the floor. On the floor 1.5 m in front of the mirror is a small table, 0.80 m high. What is the minimum height the mirror must have for you to be able to see the top of the table in the mirror?
Solution:
Chapter 26 Geometrical Optics Q.13CQ
The Invisible Man In the H. G. Wells novel The Invisible Man, a person becomes invisible by altering his index of refraction to match that of air. This is the idea behind the disappearing eye-dropper in Conceptual Question. If the invisible man could actually do this, would he be able to see? Explain.
Question
12. The Disappearing Eyedropper The accompanying photograph shows eyedroppers partially immersed in oil (left) and water (right). Explain why the dropper is invisible in the oil.
Solution:
Chapter 26 Geometrical Optics Q.13P
The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rearview mirror is 0.50 m from the driver’s eyes, and 1.50 m from the rear window. What are the minimum dimensions for the rearview mirror if the driver is to be able to see the entire width and height of the rear window in the mirror without moving her head?
Solution:
Chapter 26 Geometrical Optics Q.14CQ
What’s the Secret? The top of Figure shows the words SECRET CODE written in different colors. If you place a cylindrical rod of glass or plastic just above the words, you find that SECRET appears inverted, but CODE does not Explain.
Solution:
Chapter 26 Geometrical Optics Q.14P
IP You hold a small plane mirror 0.50 m in front of your eyes, as shown in Figure (not to scale). The mirror is 0.32 cm high, and in it you see the image of a tall building behind you. (a) If the building is 95 m behind you, what vertical height of the building, H,can be seen in the mirror at any one time? (b) If you move the mirror closer to your eyes, does your answer to part (a) increase, decrease, or stay the same? Explain.
Solution:
Chapter 26 Geometrical Optics Q.15P
Two rays of light converge toward each other, as sljown in Figure forming an angle of 27°. Before they intersect, however, they are reflected from a circular plane mirror with a diameter of 11 cm. If the mirror can be moved horizontally to
Solution:
Chapter 26 Geometrical Optics Q.16P
For a corner reflector to be effective, its surfaces must be pre cisely perpendicular. Suppose the surfaces of a comer reflector left on the Moon’s surface by the Apollo astronauts formed a 90.001° angle with each other. If a laser beam is bounced back to Earth from this reflector, how far (in kilometers) from its starting point will the reflected beam strike Earth? For simplicity, assume the beam reflects h-om only two sides of the reflector, and that it strikes the first surface at precisely 45°.
Solution:
Chapter 26 Geometrical Optics Q.17P
CE Astronomers often use large mirrors in their telescopes to gather as much light as possible from faint distant objects. Should the mirror in their telescopes be concave or convex? Explain.
Solution:
The mirrors used by the Astronomers in their telescopes are always concave, because concave mirrors focus all parallel rays of light (as from the stars) to a point in front of the mirror. On the other hand convex mirror disperse parallel rays of light by sending them outward on divergent paths.
Chapter 26 Geometrical Optics Q.18P
A section of a sphere has a radius of curvature of 0.86 m. If this section is painted with a reflective coating on both sides, what is the focal length of (a) the convex side and (b) the concave side?
Solution:
Chapter 26 Geometrical Optics Q.19P
Amirrored-giass gazing globe in a garden is 31.9 cm in diameter. What is the focal length of the globe?
Solution:
Chapter 26 Geometrical Optics Q.20P
Sunlight reflects from a concave piece of broken glass, converging to a point 15 cm from the glass. What is the radius of curvature of the glass?
Solution:
Chapter 26 Geometrical Optics Q.21P
CE You hold a shiny tablespoon at arm’s length and look at the back side of the spoon. (a) Is the image you see of yourself upright or inverted? (b) Is the image enlarged or reduced? (c) Is the image real or virtual?
Solution:
Here the back of the spoon behaves like a convex mirror. Therefore from the conditions of the convex mirror we can say that the image is
a) Upright
b) The image is reduced in size.
c) Behind the spoon no light passes through it. So, the image is a virtual image.
Chapter 26 Geometrical Optics Q.22P
CE You hold a shiny tablespoon at arm’s length and look at the front side of the spoon. (a) Is the image you see of yourself upright or inverted? (b) Is the image enlarged or reduced? (c) Is the image real or virtual?
Solution:
Due to the silver coating, the spoon acts as a mirror and the front side of the spoon means we are looking at a concave mirror. In addition, holding the spoon at arms length means that we are outside the focal point of the mirror – clearly the focal length of the front side of a spoon is only a few centimeters.
If follows that our image is reduced, real and inverted.
Chapter 26 Geometrical Optics Q.23P
CE An object is placed in front of a convex mirror whose radius of curvature is R. What is the greatest distance behind the mirror that the image can be formed?
Solution:
We know that if the object is in front of the mirror then image produced by a convex mirror will be always behind the mirror. The greatest image distance occurs when the object is infinitely far from the mirror. In the case when the image is at the focal point, the greatest distance the image can be behind the mirror is \( f\quad =\cfrac { R }{ 2 } \)
Chapter 26 Geometrical Optics Q.24P
CE An object is placed to the left of a concave mirror, beyond its focal point. In which direction will the image move when the object is moved farther to the left?
Solution:
Chapter 26 Geometrical Optics Q.25P
CE An object is placed to the left of a convex mirror. In which direction will the image move when the object is moved farther to the left?
Solution:
We know that the image produced by a convex mirror is always behind mirror.
When the object is moved farther to the left, the image will move to right, i.e., towards the focal point of the lens.
Chapter 26 Geometrical Optics Q.26P
A small object is located 30.0 cm in frontofa concave mirror with a radius of curvature of 40.0 cm, Where will the image be formed?
Solution:
Chapter 26 Geometrical Optics Q.27P
Use ray diagrams to show whether the image formed by a convex mirror increases or decreases in size as an object is brought closer to the mirror’s surface.
Solution:
From the ray diagrams we can observe that there is an increase in size of the image if the object is brought closer to the mirror surface.
Chapter 26 Geometrical Optics Q.28P
An object with a height of 46 cm is placed 2.4 m in front of a concave mirror with a focal length of 0.50 m. (a) Determine the approximate location and size of the image using a ray diagram. (b) Is the image upright or inverted?
Solution:
(b) The image formed just before the concave mirror and the image is inverted.
Chapter 26 Geometrical Optics Q.29P
Find the location and magnification of the image produced by the mirror in Problem using the mirror and magnification equations.
Problem
28. An object with a height of 46 cm is placed 2.4 m in front of a concave mirror with a focal length of 0.50 m. (a) Determine the approximate location and size of the image using a ray diagram. (b) Is the image upright or inverted?
Solution:
∴ Image is formed at 0.63 m with a magnification -0.26
Chapter 26 Geometrical Optics Q.30P
An object with a height of 46 cm is placed 2.4 m in front of a convex mirror with a focal length of −0.50 m. (a) Determine the approximate location and size of the image using a ray diagram. (b) Is the image upright or inverted?
Solution:
Chapter 26 Geometrical Optics Q.31P
Find the loca ti on and magnification of Ehe image produced by the mirror in Problem using the mirror and magnification equations.
Problem
30. An object with a height of 46 cm is placed 2.4 m in front of a convex mirror with a focal length of −0.50 m. (a) Determine the approximate location and size of the image using a ray diagram. (b) Is the image upright or inverted?
Solution:
Chapter 26 Geometrical Optics Q.32P
During a daytime football game you notice that a player’s reflective helmet forms an image of the Sun 4.8 cm behind the surface of the helmet. What is the radius of curvature of the helmet, assuming it to be roughly spherical?
Solution:
Chapter 26 Geometrical Optics Q.33P
IP A magician wishes to create the illusion of a 2.74-m-tall elephant. He plans to do this by forming a virtual image of a 50.0-cm-tall model elephant with the help of a spherical mirror. (a) Should the mirror be concave or convex? (b) If the model must be placed 3.00 m from the mirror, what radius of curvature is needed? (c) How far from the mirror will the image be formed?
Solution:
Chapter 26 Geometrical Optics Q.34P
A person 1.7 m tall stands 0.66 m from a reflecting globe in a garden. (a) If the diameter of the globe is 18 cm, where is the image of the person, relative to the surface of the globe? (b) How large is the person’s image?
Solution:
Chapter 26 Geometrical Optics Q.35P
Shaving /makeup mirrors typically have one flat and one concave (magnifying) surface. You find that you can project a magnified image of a lightbulb onto the wall of your bathroom if you hold the mirror 1.8 m from the bulb and 3.5 m from the wall. (a) What is the magnification of the image? (b) Is the image erect or inverted? (c) What is the focal length of the mirror?
Solution:
Chapter 26 Geometrical Optics Q.36P
The Hale Telescope The 200-inch-diameter concave mirror of the Hale telescope on Mount Falomar has a focal length of 16.9 m. An astronomer stands 20.0 m in front of this mirror. (a) Where is her image located? is it in front of or behind the mirror? (b) Is her image real or virtual? How do you know? (c) What is the magnification of her image?
Solution:
Chapter 26 Geometrical Optics Q.37P
A concave mirror produces a virtual image that is three times as tall as the object. (a) If the object is 28 cm in front of the mirror, what is the image distance? (b) What is the focal length of this mirror?
Solution:
Chapter 26 Geometrical Optics Q.38P
A concave mirror produces a real image that is three times as large as the object. (a) If the object is 22 cm in front of the mirror, what is the image distance? (b) What is the focal length of this mirror?
Solution:
Chapter 26 Geometrical Optics Q.39P
The virtual image produced by a convex mirror is one-quarter the size of the object. (a) If the object is 36 cm in front of the mirror, what is the image distance? (b) What is the focal length of this mirror?
Solution:
Chapter 26 Geometrical Optics Q.40P
IP A 5.7-ft tallshopper in a department store is 17 ft from a convex security mirror. The shopper notices that his image in the mirror appears to be only 6.4 in. tali. (a) Ts the shopper’s image upright or inverted? Explain. (b) What is the mirror’s radius of curvature?
Solution:
Chapter 26 Geometrical Optics Q.41P
You view a nearby tree in a concave mirror. The inverted image of the tree is 3.8 cm high and is located 7.0 cm in front of the mirror. If the tree is 23 m from the mirror, what is its height?
Solution:
Chapter 26 Geometrical Optics Q.42P
A shaving/makeup mirror produces an erect image that is magnified by a factor of2.2 when your face is 25 cm from the mirror. What is the mirror’s radius of curvature?
Solution:
1403-26-42P SA Code: 6078.SRCode: 5784
Chapter 26 Geometrical Optics Q.43P
A concave mirror with a focal length of 36 cm produces an image whose distance from the mirror is one-third the object distance. Find the object and image distances.
Solution:
Chapter 26 Geometrical Optics Q.44P
CE Predict/Explain When a ray of light enters a glass lens surrounded by air, it slows down. (a) As it leaves the glass, does its speed increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Its speed increases because the ray is now propagating in a medium with a smaller index of refraction.
II. The speed decreases because the speed of light decreases whenever light moves from one medium to another.
III. The speed will stay the same because the speed of light is a universal constant.
Solution:
Chapter 26 Geometrical Optics Q.45P
CE Samurai Fishing A humorous scene in Akira Kurosawa’s classic film The Seven Samumi shows the young samurai Kikuchiyo wading into a small stream and plucking a fish from it for his dinner. (a) As Kikuchiyo looks through the water to the fish, does he sec it in the general direction of point 1or point 2 in Figure? (b) If the fish looks up at Kikuchiyo, does it see Kikuchiyo’s head in the general direction of point 3 or point 4?
Solution:
(b)
If the ray from the fish toward the head is extended without any bending, then the fish sees the head along the direction of point 4.
Therefore the right answer is point 4.
Chapter 26 Geometrical Optics Q.46P
CE When color A and color B are sent through a prism, color Ais bent more than color B. Which color travels more rapidly in the prism? Explain.
Solution:
The speed of light in a material is given by \( \frac { c }{ n } \) The color with the smaller reflective index has the greater speed, so from the given data we can say that the color B travels more rapidly because the color B has bent less than the color A.
Chapter 26 Geometrical Optics Q.47P
CE Day Versus Night (a) Imagine for a moment that the Earth has no atmosphere. Over the period of a year, is the number of daylight hours at your home greater than, less than, or equal to the number of nighttime hours? (b) Repeat part (a), only this time take into account the Earth’s atmosphere.
Solution:
a) The atmosphere acts as a spherical mirror by reflecting sunlight. If there is no atmosphere, Sunlight is trapped within the atmosphere due to the reflecting effects of gases. Therefore, day and night is depends upon whether the sun is shining on the planet or not. Since the Earth rotates about its axis with constant speed and resolves around the sun, half of the earth faces the sun at any given time. Thus there should be an equal number of day light times and night time hours.
b) If the atmosphere is present, some of the light is absorbed by the atmosphere of the earth. The light gets refracting during dawn and dusk adding to daylight hours and reducing night time hours, so daylight hours are greater than night time.
Chapter 26 Geometrical Optics Q.48P
CE Predict/Explain A kitchen has twin side-by-side sinks. One sink is filled with water, the other is empty. (a) Does the sink with water appear to be deeper, shallower, or the same depth as the empty sink? (b) Choose the best explanation from among the following:
I. The sink with water appears deeper because you have to look through the water to sec the bottom.
II. Water bends the light, making an object under the water appear to be closer to the surface. Thus the water-filled sink appears shallower.
III. The sinks are identical, and therefore have the same depth. This doesn’t change by putting water in one of them.
Solution:
Chapter 26 Geometrical Optics Q.49P
CE A light beam undergoes total internal reflection at the interface between medium A, in which it propagates, and medium B, on the other side of the interface. Which medium has the greater index of refraction? Explain.
Solution:
Total internal reflection takes place when light goes from denser medium to rarer medium. Here the light ray is going from medium A to medium B and it is undergoing total internal reflection.
Therefore the medium A is denser than medium B. so, the refractive index for the medium A is greater than medium B.
Chapter 26 Geometrical Optics Q.50P
Light travels a distance of 0.960 m in 4.00 ns in a given substance. What is the index of refraction of this substance?
Solution:
Chapter 26 Geometrical Optics Q.51P
Find the ratio of the speed of light in water to the speed of light in diamond.
Solution:
Chapter 26 Geometrical Optics Q.52P
Ptolemy’s Optics One of the many works published by the Greek astronomer Ptolemy (A.D. ca. 100–170) was Optics. In this book Ptolemy reports the results of refraction experiments he conducted by observing light passing from air into water. His results are as follows: angle of incidence = 10.0°, angle of refraction = 8.00°; angle of incidence = 20.0°, angle of refraction = 15.5°. Find the percentage error in the calculated index of refraction of water for each of Ptolemy’s measurements.
Solution:
Chapter 26 Geometrical Optics Q.53P
Light enters a container of benzene at an angle of 43° to the normal; the refracted beam makes an angle of 27° with the normal. Calculate the index of refraction of benzene.
Solution:
Chapter 26 Geometrical Optics Q.54P
The angle of refraction of a ray of light traveling into an ice cube from air is 38°. Find the angle of incidence.
Solution:
Chapter 26 Geometrical Optics Q.55P
IP (a) Referring to Problem, suppose the ice melts, but the angle of refraction remains the same. Is the corresponding angle of incidence greater than, less than, or the same as it was for ice? Explain. (b) Calculate the angle of incidence for part (a).
Problem
54. The angle of refraction of a ray of light traveling into an ice cube from air is 38°. Find the angle of incidence.
Solution:
Chapter 26 Geometrical Optics Q.56P
A submerged scuba diver looks up toward the calm surface of a freshwater lake and notes that the Sun. appears to be 35° from the vertical. The diver’s friend is standing on the shore of the lake. At what angle above the horizon does the friend see the sun?
Solution:
Chapter 26 Geometrical Optics Q.57P
A pond with a total depth (ice + water) of 3.25 m is covered by a transparent layer of ice, with a thickness of 0.38 m. Find the time required for light to travel vertically from the surface of the ice to the bottom of the pond.
Solution:
Chapter 26 Geometrical Optics Q.58P
Light is refracted as it travels from a point A in medium 1 to a point B in medium 2. If the index of refraction is 1.33 in médium 1 and 1.51 in medium 2, how long does it take light to go from A to B, assuming it travels 331 cm in medium 1 and 151 cm in medium 2?
Solution:
Chapter 26 Geometrical Optics Q.59P
You have a semicircular disk of glass with an index of refraction of n = 1.52, Find the incident angle θfor which the beam of light in Figure will hit the indicated point on the screen.
Solution:
Chapter 26 Geometrical Optics Q.60P
The observer in Figure is positioned so that the far edge of the bottom of the empty glass (not to scale) is just visible. When the glass is filled to the top with water, the center oi the bottom of the glass is just visible to the observer. Find the height, H, of the glass, given that its width is W = 6.2 cm.
Solution:
Chapter 26 Geometrical Optics Q.61P
Solution:
Chapter 26 Geometrical Optics Q.62P
A ray of light enters the long side of a 45°–90°–45° prism and undergoes two total internal reflections, as indicated in Figure. The result is a reversal in the ray’s direction of propagation. Find the minimum value of the prism’s index of refraction, n, for these internal reflections to be total.
Solution:
From the given figure if the light ray is incident normally on the hypotenuse face, it is incident on the opposite face at an angle of 45 and suffers total internal reflection. The same thing happens at the next face and the ray emerges out of the prism parallel to incident direction from the given figure.
Chapter 26 Geometrical Optics Q.63P
When the prism in Problem is immersed in a fluid with an index of refraction of 1.21, the internal reflections shown in Figure are still total. Thereflections are no longer totaj however, when the prism is immersed in a fluid with n = 1.43. Use this information to set upper and lower limits on the possi-ble values of the prism’s index of refraction.
Problem
62. A ray of light enters the long side of a 45°–90°–45° prism and undergoes two total internal reflections, as indicated in Figure. The result is a reversal in the ray’s direction of propagation. Find the minimum value of the prism’s index of refraction, n, for these internal reflections to be total.
Solution:
Chapter 26 Geometrical Optics Q.64P
IP A glass paperweight with an index of refraction n rests un a desk, as shown in Figure. An incident ray of light enters the horizontal top surface of the paperweight at an angle θ = 77° to the vertical. (a) Find the minimum value of n for which the internal reflection on the vertical surface of the paperweight is total. (b) If θ is decreased, is the minimum value of n increased or decreased? Explain.
Solution:
Chapter 26 Geometrical Optics Q.65P
IP Suppose the glass paperweight in Figure has an index of refraction n = 1.38. (a) Find the value of θ for which the reflection on the vertical surface of the paperweight exactly satisfies the condition for total internal reflection. (b) If θis increased, is the reflection at the vertical surface still total? Explain.
Solution:
Chapter 26 Geometrical Optics Q.66P
IP Consider the physical system shown in Figure and described in Problem. (a) If the index of refraction of the glass is increased, will the desired value of θ increase or decrease? Explain. (b) Find the value of θfor the case of flint glass (n = 1.66).
Problem
59. You have a semicircular disk of glass with an index of refraction of n = 1.52, Find the incident angle θfor which the beam of light in Figure will hit the indicated point on the screen.
Solution:
Chapter 26 Geometrical Optics Q.67P
While studying physics at the library late one night, you notice the image of the desk lamp reflected from the varnished tabletop. When you turn your Polaroid sunglasses sideways, the reflected image disappears. Tf this occurs when the angle between the incident and reflected rays is 110°, what is the index of refraction of the varnish?
Solution:
Chapter 26 Geometrical Optics Q.68P
A horizontal beam of light enters a 45°–90°–45° prism at the center of its long side, as shown in Figure. The emerging ray moves in a direction that is 34° below the horizontal. What is the index of refraction of this prism?
Solution:
Therefore, refractive index of the prism is.1.70
Chapter 26 Geometrical Optics Q.69P
A laser beam enters one of the sloping faces of the equilateral glass prism (n = 1.42) in Figure and refracts through the prism. Within the prism the light travels horizontally. What is the angle θ between the direction of the incident ray and the direction of the outgoing ray?
Solution:
Chapter 26 Geometrical Optics Q.70P
Solution:
Chapter 26 Geometrical Optics Q.71P
Solution:
Chapter 26 Geometrical Optics Q.72P
An object is a distance f/2 from a convex lens. (a) Use a ray diagram to find the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.
Solution:
Chapter 26 Geometrical Optics Q.73P
An object is a distance 2f from a convex lens. (a) Use a ray diagram to find the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.
Solution:
Chapter 26 Geometrical Optics Q.74P
Two lenses that are 35 cm apart are used to form an image, as shown in Figure. Lens 1 is converging and has a focal length f1 = 14 cm; lens 2 is diverging and has a focal length f2 = −7.0 cm. The object is placed 24 cm to the left of lens 1. (a) Use a ray diagram to find the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.
Solution:
The location of an image by a concave or a convex mirror can be traced with the help of a ray tracing diagram.
The properties of the three principal rays are as follows,
1. The parallel ray travels parallel to the axis and passes through the focal point of the lens if it is convex or traces back to the focal point if it is concave.
2. The focal point ray passes through the focal point of the lens if the lens is convex. For a concave lens, the focal point ray passes through the focal point on the other side of the lens by passing through the lens.
3. The midpoint ray passes through the middle of the ray.
Chapter 26 Geometrical Optics Q.75P
Two lenses that are 35 cm apart are used to form an image, as shown in Figure. Lens 1 is diverging and has a focal length f1 = −7.0 cm; lens 2 is converging and has a focal length f2 = 14cm. The object is placed 24 cm to the left of lens 1. (a) Use a ray diagram to find the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.
Solution:
Concave lens always produce upright and virtual images. Convex lens produce either upright or inverted images depending upon the position of the object, which can be either virtual or real.
Chapter 26 Geometrical Optics Q.76P
A convex lens is held over a piece of paper outdoors on a sunny day. When the paper is held 26 cm below the lens, the sunlight is focused on the paper and the paper ignites. What is the focal length of the lens?
Solution:
Chapter 26 Geometrical Optics Q.77P
A concave lens has a focal length of −32 cm. Find the image distance and magnification that result when an object is placed 29 cm in front of the lens.
Solution:
Chapter 26 Geometrical Optics Q.78P
When an object is located 46 cm to the left of a lens, the image is formed 17 cm to the right of the lens. What is the focal length of the lens?
Solution:
Chapter 26 Geometrical Optics Q.79P
Anobjectwithaheightof2.54cmisplaced36.3mmtotheleft of a lens with a focal length of 35.0 mm. (a) Where is the image located? (b) What is the height of the image?
Solution:
Chapter 26 Geometrical Optics Q.80P
A lens for a 35-mm camera has a focal length given by ƒ = 55 mm. (a) How close to the film should the lens be placed to form a sharp image of an object that is 5.0 m away? (b) What is the magnification of the image on the film?
Solution:
Chapter 26 Geometrical Optics Q.81P
IP An object is located to the left of a convex lens whose focal length is 34 cm. The magnification produced by the lens is m = 3.0. (a) To increase the magnification to 4.0, should the object be moved closer to the lens or farther away? Explain. (b) Calculate the distance through which the object should be moved.
Solution:
Chapter 26 Geometrical Optics Q.82P
IP You have two lenses at your disposal, one with a focal length f1 = +40.0 cm, the other with a focal length f2 = −40.0 cm. (a) Which of these two lenses would you use to project an image of a lightbulb onto a wall that is far away? (b) if you want to produce an image of the bulb that is enlarged by a factor of 2.00, how far from the wall should the lens be placed?
Solution:
Chapter 26 Geometrical Optics Q.83P
(a) Determine the distance from lens 1 to the final image for the system shown in Figure. (b) What is the magnification of this image?
Solution:
Chapter 26 Geometrical Optics Q.84P
(a) Determine the distance from lens 1 to the final image for the system shown in Figure. (b) What is the magnification of this image?
Solution:
Chapter 26 Geometrical Optics Q.85P
Solution:
Chapter 26 Geometrical Optics Q.86P
IP BIO Albert is nearsi ghtcd, and wi thou t his eyeglasses he can focus only on objects less than 2.2 m away. (a) Are Albert’s eyeglasses concave or convex? Explain. (b) To correct Albert’s nearsightedness, his eyeglasses must produce a virtual, upright image at a distance of 2.2 m when viewing an infinitely distant object. What is the focal length of Albert’s eyeglasses?
Solution:
Chapter 26 Geometrical Optics Q.87P
A small insect viewed through a convex lens is 1.4 cm from the lens and appears twice its actual size. What is the focal length of the lens?
Solution:
Chapter 26 Geometrical Optics Q.88P
IP A friend tells you that when he takes off his eyeglasses and holds them 23 cm above a printed page the image of the print is erect but reduced to 0:67 of its actual size. (a) Is the image real or virtual? How do you know? (b) What is the focal length of your friend’sglasses? (c) Are the lenses in the glasses concave or convex? Explain.
Solution:
Chapter 26 Geometrical Optics Q.89P
IP A friend tells you that when she takes off her eyeglasses and holds them 23 cm above a printed page the image of the print is erect but enlarged to 1.5 times its actual size. (a) Is the image real or virtual? How do you bow? (b) What is the focal length of your friend’s glasses? (c) Are the lenses in the glasses concave or convex? Explain.
Solution:
Chapter 26 Geometrical Optics Q.90P
CE Predict/Explain You take a picture of a rainbow with an infrared camera, and your friend takes a picture at the same time with visible light. (a) Is the height of the rainbow in the infrared picture greater than, less than, or the same as the height of the rainbow in the visible-light picture? (b) Choose the best explanation from among the following:
I. The height will be greater because the top of a rainbow is red, and so infrared light would be even higher.
II. The height will be less because infrared light is below the visible spectrum.
III. A rainbow is the same whether seen in visible light or infrared; therefore the height is the same.
Solution:
1403-26-90P SA Code: 6078.
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(a)
Height of the rainbow in the infrared picture is greater than the height of the rainbow in the visible-light picture. Because the top of a rainbow is red and so infrared light would be even higher and also the spectrum of infrared waves region is wider than the spectrum that contains the visible region.
(b)
Therefore the best explanation is I.
Chapter 26 Geometrical Optics Q.91P
The index of refraction for red light in a certain liquid is 1.320; the index of refraction for violet light in the same liquid is 1.332. Find the dispersion (θV − θr)for red and violet light when both arc incident on the flat surface of the liquid at an angle of 45.00° to the normal.
Solution:
Chapter 26 Geometrical Optics Q.92P
A horizontal incident beam consisting of white light passes through an equilateral prism, like the one shown in Figure. What is the dispersion (θV − θr)of the outgoing beam if the prism’s index of refraction is nv = 1.505 for violet light and nr = 1.421 for red light?
Solution:
Chapter 26 Geometrical Optics Q.93P
The focal length of a lens is inversely proportional to the quantity (n − 1), where n is the index of refraction of the lens material. The value of n, however, depends on the wavelength of the light that passes through the lens. For example, one type of flint glass has an index of refraction of nr = 1.572 for red light and nv = 1.605 in violet light. Now, suppose a white object is placed 24.00 an infront of a lens made from this type of glass. If the red light reflected from this object produces a sharp image 55.00 cm from the lens, where will the violet image be found?
Solution:
Chapter 26 Geometrical Optics Q.94GP
CE Jurassic Park A T. rex chases the heroes of Steven Spielberg’s Jurassic Park as they desperately try to escape in their Jeep. The T. rex is closing in fast, as they can see in the outside rearview mirror. Near the bottom of the mirror they also see the following helpful message: objects in the mirror are closer than they appear. Is this mirror concave or convex? Explain.
Solution:
Objects in the mirror are closer than they appear because the mirror produces an image that is reduced in size, which makes the object look as if it is farther away. In addition, we know that the rear view mirror always gives an upright image, no matter how close or far away the object. The mirror that produces upright and reduced images is the convex mirror. So the mirror is convex mirror.
Chapter 26 Geometrical Optics Q.95GP
CE The receiver for a dish antenna is placed in front of the concave surface of the dish. If the radius of curvature of the dish is R, how far in fron tof the dish should the receiver be placed? Explain.
Solution:
Chapter 26 Geometrical Optics Q.96GP
CE Predict/Explain if a lens is immersed in water, its focal length changes, as discussed in Conceptual Checkpoint 26−5. (a) if a spherical mirror is immersed in water, does its focal length increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The focal length will increase because the water will cause more bending of light.
II. Water will refract the light. This, combined with the reflection due to the mirror, will result in a decreased focal length.
III. The focal length stays the same because it depends on the fact that the angle of incidence is equal to the angle of reflection for a mirror. Thisis unaffected by the presence of the water.
Solution:
Chapter 26 Geometrical Optics Q.97GP
CE Predict/Explain A glass slab surrounded by air causes a sideways displacement in a beam of light. (a) If die slab is now placed in water, does the displacement it causes increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The displacement of the beam increases because of the in creased refraction due to the water.
II. The displacement of the beam is decreased because with water surrounding the slab there is a smaller difference m index of refraction between the slab and its surroundings
III. The displacement stays the same because it is determined only by the properties of the slab; in particular, the material it is made of and its thickness.
Solution:
(b)Therefore the best explanation is II.
Chapter 26 Geometrical Optics Q.98GP
CE Referring to Conceptual Question, suppose the same type of glass used in an eyedropper is made into a convex lens with a focal length ƒ. If this lens is immersed in the oil of the bottle on the left in the photo, will its focal length be 0, f/2, 2f, or ∞? (Hint: See Conceptual Checkpoint 26–5.)
Question
12. The Disappearing Eyedropper The accompanying photograph shows eyedroppers partially immersed in oil (left) and water (right). Explain why the dropper is invisible in the oil.
Solution:
As the index of refraction of the lens and that of the oil is same the light rays goes straight without bend. If the light rays travels straight, they will be focused at the infinity. So the focus of the lens is infinity
Chapter 26 Geometrical Optics Q.99GP
CE Two identical containers are filled with different bans-parent liquids. The container with liquid A appears to have a greater depth than the container with liquid B. Which liquid has the greater index of refraction? Explain.
Solution:
Chapter 26 Geometrical Optics Q.100GP
CE Is the image you see in a three-dimensional corner refleeter upright or inverted?
Solution:
Chapter 26 Geometrical Optics Q.101GP
CE Inverse Lenses Suppose we mold a hollow piece of plastic into the shape of a double concave lens. The “lens” is watertight, and itsinterior is filled with air. We now place this lens in water and shine a beam of light on it. (a) Does the lens converge or diverge the beam of light? Explain. (b) If our hollow lens is double convex instead, does it converge or diverge a beam of light when immersed in water? Explain.
Solution:
Normally we use a concave lens of greater refractive index. As the light is traveling from less index of refraction to high index of refraction and bends towards the normal and in case of concave it diverges.
a) But here we care using the lens with less index of refraction. So it bends towards the normal and the beam will be converged
c) Similarly, in case of convex lens, the beam will be diverged
Chapter 26 Geometrical Optics Q.102GP
IP Suppose the separation between the two mirrors in Figure is increasedby moving the top mirror upward. (a) Will this affect the number of reflections made by the beam of light? If so, how? (b) What is the total number of reflections made by the beam of light when the separation between the mirrors is 145 cm?
Figure
Solution:
Chapter 26 Geometrical Optics Q.103GP
Standing 2.0 m in front of a small vertical mirror you see the reflection of your belt buckle, which is 0.70m below your eyes. If you remain 2.0 m from the mirror but climb onto a stool, how high must the stool be to allow you to see your knees in the mirror? Assume that your knees are 1.2 m below your eyes.
Solution:
Chapter 26 Geometrical Optics Q.104GP
IP Apparent Size of Floats in a Tennoinetro Lentos
The Galileo thermometer, or Termometro Lentos (slow thermometer in Italian), consists of a vertical, cylindrical flask containing a fluid and several glass floats of different color. The floats all have the same dimensions, but they appear to differ in size depending on their location within the cylinder. (a) Does a float near the front surface of the cylinder (the surface closest to you) appear to be larger or smaller than a float near the back surface? (b) Figure shows a ray diagram for a float near the front surface of the cylinder. Draw a ray diagram for a float at the center of the cylinder, and show that the change in apparent size agrees with your answer to part (a).
Figure
Solution:
(a)
When the float is near to the front surface then the angle of incidence more then the angle of divergence is more. Then the point where the light rays are appearing to be diverging is very nearer. So the float near the front surface of the cylinder appears to be smaller than the float near the back surface.
Chapter 26 Geometrical Optics Q.105GP
(a) Find the two locations where an object can be placed in front of a concave mirror witlva radius of curvature of 39 cm such that its image is twice its size. (b) In each of these cases, state whether the image is real or virtual upright or inverted.
Solution:
Chapter 26 Geometrical Optics Q.106GP
A convex mirror with a focal length of −85 cm is used to give a truck driver a view behind the vehicle. (a) If a person who is 1.7m tall stands 2.2 m from the mirror, where is the person’s image located? (b) Is the image upright or inverted? (c) What is the size of the image?
Solution:
Chapter 26 Geometrical Optics Q.107GP
IP The three laser beams shown in Figure meet at a point at the back of a solid, transparent sphere. (a) What is the index of refraction of the sphere? (b) Ts there a finite index of refraction that will make the three beams come to a focus at the center of the sphere? If your answer is yes, give the required index of refraction; if your answer is no, explain why not.
Solution:
Chapter 26 Geometrical Optics Q.108GP
The speed of light in substance A is x times greater than the speed of light in substance B. Find the ratio nA/nB interms of x.
Solution:
Chapter 26 Geometrical Optics Q.109GP
IP A film of oil, with an index of refraction of 1.48 and a thickness of 1.50 cm, floats on a pool of water, as shown in Figure. Abeam of light is incident on the oil atan angle of 60.0° to the vertical. (a) Find the angle θ the light beam makes with the vertical as it travels through the water. (b) How does your answer to part (a) depend on the thickness of the oil film? Explain.
Solution:
b)
The answer to the part (a) does not depends upon the thick ness of the film. It depends only upon the original angle of incidence and the refractive index of water and air.
Chapter 26 Geometrical Optics Q.110GP
IP Consider the physical system shown in Figure. For this problem we assume that the angle of incidence at the air-oil interface can be varied from 0° to 90°. (a) What is the maximum possible value for 9, the angle of refraction in the water? (b) If an oil with a larger index of refraction is used, does your answer to part (a) increase or decrease? Explain.
Solution:
Chapter 26 Geometrical Optics Q.111GP
IP Consider the physical system shown in Figure, only this time let the direction of the light rays be reversed, (a) Find the angle of incidence θ at the water-oil interface such that the condition for total internal reflection at the oil-air surface is exactly satisfied. (b) If θ is decreased, is the reflection at the oil-air interface still total? Explain.
Solution:
Chapter 26 Geometrical Optics Q.112GP
Figure shows a ray of light entering one end of an optical fiber at an angle of incidence θ1 = 50.0°. The index of refraction of the fiber is 1.62. (a) Fine the angle θ the ray makes with the normal when it reaches the curved surface of the fiber. (b) Show that the internal reflection from the curved surface is total.
Solution:
Chapter 26 Geometrical Optics Q.113GP
Suppose the person’s eyes in Figure are 1.6 m above the ground and that the small plane mirror can be moved up or down. (a) Find the height of the bottom of the mirror such that the lowest point the person can see on the building is 19.6 m above the ground. (b) With the mirror held at the height found inpart (a), what is the highest point on the building the person can see?
Solution:
Chapter 26 Geometrical Optics Q.114GP
An arrow 2.00 cm long is located 75.0 cm from a lens that has a focal length ƒ = 30.0 cm. (a) If the arrow is perpendicular to the principal axis of the lens, as in Figure (a), what is its lateral magnification, defined as hi/ho? (b) Suppose, instead, that the arrow lies along the principal axis, extending from 74.0 cm to 76.0 cm from the lens, as indicated in Figure (b). What is the longitudinalmagnification of the arrow, defined as Li/Lo(Hint: Use the thin-lens equation to locate the image of each end of the arrow.)
Solution:
Chapter 26 Geometrical Optics Q.115GP
Repeat Problem, this time for a diverging lens with a focal length f = −30.0 cm.
Problem
114. An arrow 2.00 cm long is located 75.0 cm from a lens that has a focal length ƒ = 30.0 cm. (a) If the arrow is perpendicular to the principal axis of the lens, as in Figure (a), what is its lateral magnification, defined as hi/ho? (b) Suppose, instead, that the arrow lies along the principal axis, extending from 74.0 cm to 76.0 cm from the lens, as indicated in Figure (b). What is the longitudinalmagnification of the arrow, defined as Li/Lo(Hint: Use the thin-lens equation to locate the image of each end of the arrow.)
Solution:
Chapter 26 Geometrical Optics Q.116GP
Aconvex lens with f1 = 20.0cm is mounted 40.0 cm to the left of a concave lens. When an object is placed 30.0 cm to the left of the convex lens, a real image is formed 60.0 cm to the right of the concave lens. What is the focal length f2 of the concave lens?
Solution:
Chapter 26 Geometrical Optics Q.117GP
Two thin lenses, with focal lengths f1 and ƒ2, are placed in contact. What is the effective focal length of the double lens?
Solution:
Chapter 26 Geometrical Optics Q.118GP
When an object is placed a distance do in front of acurved mirror, the resulting image has a magnification m. Find an expression for the focal length of the mirror,f, interms of do and m.
Solution:
Chapter 26 Geometrical Optics Q.119GP
A Slab of Glass Give a symbolic expression for the sideways displacement d of a light ray passing through the slab of glass shown in Figure. The thickness of the glass is t, its index of refraction is n, and the angle of incidence is θ.
Solution:
Chapter 26 Geometrical Optics Q.120GP
Solution:
Chapter 26 Geometrical Optics Q.121GP
Least Time A beam of light propagates from point A in medium ’1 to point B in medium 2, as shown in Figure. The index of refraction is different in these two media; therefore, the light follows a refracted path that obeys Snell’s law. (a) Calculate the time required for light to travel from. A to B along the refracted path. (b) Compare the time found in part (a) with the time it takes for light to tra vel from A to B along a straight-line path. (Note that the time on the straight-line path is longer than the time on the refracted path. In general, the shortest time between two points in different media is along the path given by Snell’s law.)
Solution:
Chapter 26 Geometrical Optics Q.122GP
The ray of light shown in Figure passes from medium 1. to medium 2 to medium 3. The index of refraction in medium 1 is nY, in medium 2 it is n2> n1, and in medium 3 it is n3 > n2 Show that medium 2 can be ignored when calculating the angle of refraction in medium 3; that is, show that n1 sin θ1 = n3 sin 03.
Solution:
Chapter 26 Geometrical Optics Q.123GP
IP A beam of light enters the sloping side of a 45°−90°−45° glass prism with an index of refraction n = 1.66. The situation is similar to that shown in Figure, except tha t the angle of incidence of the incoming beam can be varied. (a) Find die angle of incidence for which the reflection on the vertical side of the prism exactly satisfies the condition for total internal reflection. (b) If the angle of incidence is increased, is the reflection at the vertical surface still total? Explain. (c) What Is the minimum value of n such that a horizontal beam like that in Figure undergoes total internalreflection at the vertical side of the prism?
Solution:
Chapter 26 Geometrical Optics Q.124PP
A converging lens with a focal length in air of ƒ = +5.25 cm is made from ice. What is the focal length of this lens if it is immersed in benzene? (Refer to Table.)
A. −20.7 cm
B. −18.1cm
C. −12.8 cm
D. −11.2 cm
Solution:
Chapter 26 Geometrical Optics Q.125PP
A diverging lens with ƒ = −12.5 cm is made from ice. What is the focal length of this lens if it is immersed in ethyl alcohol? (Refer to Table.)
A. 102 cm
B. 105 cm
C. 118 cm
D. 122 cm
Solution:
Chapter 26 Geometrical Optics Q.126PP
Calculate the focal length of a lens in water, given that the index of refraction of the lens is nlens = 1.52 and its focal length in air is 25.0 cm. (Refer to Table.)
A. 57.8 cm
B. 66.0 cm
C. 91.0 cm
D. 104 cm
Solution:
Chapter 26 Geometrical Optics Q.127PP
Suppose a lens is made from fused quartz (glass), and that its focal length in air is −7.75 cm. What is the focal length of this lens if it is immersed in benzene? (Refer to Table.)
A. –130 cm
B. 134 cm
C. 141 cm
D. −145 cm
Solution:
Chapter 26 Geometrical Optics Q.128IP
Referring to Example Suppose the radius of curvature of the mirror is 5.0 cm. (a) Find the object distance that gives an upright knage with a magnification of 1.5. (b) Find the object distance that gives an inverted image with a magnification of −1.5.
Solution:
Chapter 26 Geometrical Optics Q.129IP
IP Referring to Example An object is 4.5 cm in front of the mirror. (a) What radius of curvature must the mirror have if the image is to be 2.2 cm in front of the mirror? (b) What is the magnification of the image? (c) If the object is moved closer to the mirror, does the magnification of the image increase in magnitude, decrease in magnitude, or stay the same?
Solution:
Chapter 26 Geometrical Optics Q.130IP
Referring to Example (a) What object distance is required to give an image with a magnification of +2.0? Assume that the focal length of the lens is +5.0cm. (b) What is the location of the image in this case?
Solution:
Chapter 26 Geometrical Optics Q.131IP
IP Referring to Example Suppose the convex lens is replaced with a concave lens with a focal length of −5.0 cm. (a) Where must the objectbe placed to form an image with a mag-nification of 0.50? (b) What is the location of the image in this case? (c) If we now move the object closer to the lens, does the magnification of the image increase, decrease, or stay the same?
Solution:
