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Chapter 34: Q47P (page 1040)
A double-convex lens is to be made of glass with an index of refraction of .One surface is to have twice the radius of curvature of the other and the focal length is to be . What is the (a) smaller and (b) larger radius?
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The equation for spherical mirrors is an approximation that is valid if the image is formed by rays that make only small angles with the central axis. In reality, many of the angles are large, which smears the image a little. You can determine how much. Refer to Fig. 34-22 and consider a ray that leaves a point source (the object) on the central axis and that makes an angle a with that axis. First, find the point of intersection of the ray with the mirror. If the coordinates of this intersection point are x and y and the origin is placed at the center of curvature, then y=(x+p-r)tan a and x2+ y2= r2where pis the object distance and r is the mirror鈥檚 radius of curvature. Next, use tanto find the angle b at the point of intersection, and then usetofind the value of g. Finally, use the relationto find the distance iof the image. (a) Suppose r=12cmand r=12cm. For each of the following values of a, find the position of the image 鈥� that is, the position of the point where the reflected ray crosses the central axis:. Compare the results with those obtained with theequation.(b) Repeat the calculations for p=4.00cm.
You look down at a coin that lies at the bottom of a pool of liquid of depthand index of refraction(Fig. 34-57). Because you view with two eyes, which intercept different rays of light from the coin, you perceive the coin to bewhere extensions of the intercepted rays cross, at depthinstead of . Assuming that the intercepted rays in Fig. 34-57 are close to a vertical axis through the coin, show that .
You grind the lenses shown in Fig. 34-53 from flat glass disks using a machine that can grind a radius of curvature of either or . In a lens where either radius is appropriate, you select the radius. Then you hold each lens in sunshine to form an image of the Sun. What are the (a) focal length fand (b) image type (real or virtual) for (bi-convex) lens 1, (c)f and (d) image type for (plane-convex) lens 2, (e) f and (f) image type for (meniscus convex) lens 3, (g) f and (h) image type for (bi-concave) lens 4, (i) fand (j) image type for (plane-concave) lens 5, and (k) f and (l) image type for (meniscus concave) lens 6?
17 through 29 22 23, 29 More mirrors. Object stands on the central axis of a spherical or plane mirror. For this situation, each problem in Table 34-4 refers to (a) the type of mirror, (b) the focal distance , (c) the radius of curvature , (d) the object distance , (e) the image distance , and (f) the lateral magnification . (All distances are in centimeters.) It also refers to whether (g) the image is real localid="1662999140986" or virtual , (h) inverted or non-inverted from from , and (i) on the same side of the mirror as the object or the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.
58 through 67 61 59 Lenses with given radii. An object stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance , index of refraction n of the lens, radius of the nearer lens surface, and radius localid="1663061304344" of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance and (b) the lateral magnification of the object, including signs. Also, determine whether the image is (c) real or virtual ,(d) inverted from the object or non-inverted , and (e) on the same side of the lens as object or on the opposite side.
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