Physics Principles with Applications1912 solutions
95 through 100. Three-lens systems. In Fig. 34-49, stick figure O (the object) stands on the common central axis of three thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closest to O, which is at object distance p1. Lens 2 is mounted within the middle boxed region, at distance d12from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different values for distances, which are given in centimeters. The type of lens is indicated by C for converging and D for diverging; the number after C or D is the distance between a lens and either of the focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i3 \for the (final) image produced by lens 3 (the final image produced by the system) and (b) the overall lateral magnification M for the system, including signs. Also, determine whether the final image is (c) real (R)or virtual (V) , (d) inverted (I) from object O or non-inverted (Nl), and (e) on the same side of lens 3 as object O or on th
The formula 1p+1i=1f is called the Gaussian form of the thin-lens formula. Another form of this formula, the Newtonian form, is obtained by considering the distance xfrom the object to the first focal point and the distancex' from the second focal point to the image. Show thatxx'=f2 is the Newtonian form of the thin-lens formula
Figure 34-50a is an overhead view of two vertical plane mirrors with an object O placed between them. If you look into the mirrors, you see multiple images of O. You can find them by drawing the reflection in each mirror of the angular region between the mirrors, as is done in Fig. 34-50b for the left-hand mirror. Then draw the reflection of the reflection. Continue this on the left and on the right until the reflections meet or overlap at the rear of the mirrors. Then you can count the number of images of O. How many images of O would you see if θis (a) 90°, (b) 45°, and (c) 60°? If θ=120°, determine the (d) smallest and (e) largest number of images that can be seen, depending on your perspective and the location of O. (f) In each situation, draw the image locations and orientations as in Fig. 34-50b.
Two thin lenses of focal lengths f1andf2 are in contact and share the same central axis. Show that, in image formation, they are equivalent to a single thin lens for which the focal length is f=f1f2(f1+f2).
Two plane mirrors are placed parallel to each other and 40cmapart. An object is placed 10cmfrom one mirror. Determine the (a) smallest, (b) second smallest, (c) third smallest (occurs twice), and (d) fourth smallest distance between the object and image of the object.
In Fig. 34-51, a box is somewhere at the left, on the central axis of the thin converging lens. The image Imof the box produced by the plane mirror is 4.00cm “inside” the mirror. The lens–mirror separation is 10.0cm, and the focal length of the lens is 2.00cm. (a) What is the distance between the box and the lens? Light reflected by the mirror travels back through the lens, which produces a final image of the box. (b) What is the distance between the lens and that final im
In Fig. 34-52, an object is placed in front of a converging lens at a distance equal to twice the focal length f1of the lens. On the other side of the lens is a concave mirror of focal lengthf2separated from the lens by a distance 2(f1+f2). Light from the object passes rightward through the lens, reflects from the mirror, passes leftward through the lens, and forms a final image of the object. What are (a) the distance between the lens and that final image and (b) the overall lateral magnification M of the object? Is the image (c) real or virtual (if it is virtual, it requires someone looking through the lens toward the mirror), (d) to the left or right of the lens, and (e) inverted or non-inverted relative to the object?
A fruit fly of height H sits in front of lens 1 on the central axis through the lens. The lens forms an image of the fly at a distance d=20cmfrom the fly; the image has the fly’s orientation and height H1=2.0H. What are (a) the focal lengthf1 of the lens and (b) the object distance p1of the fly? The fly then leaves lens 1 and sits in front of lens 2, which also forms an image at d=20cmthat has the same orientation as the fly, but now H1=0.50H. What are (c) f2and (d) p2
You grind the lenses shown in Fig. 34-53 from flat glass disks (n=1.5)using a machine that can grind a radius of curvature of either 40cmor 60cm. In a lens where either radius is appropriate, you select the 40cmradius. 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 co
In Fig. 34-54, a fish watcher at point P watches a fish through a glass wall of a fish tank. The watcher is level with the fish; the index of refraction of the glass is 8/5, and that of the water is 4/3. The distances are d1=8.0cm,d2=3.0cm,d3=6.8cm. (a) To the fish, how far away does the watcher appear to be? (Hint: The watcher is the object. Light from that object passes through the walls outside surface, which acts as a refracting surface. Find the image produced by that surface. Then treat that image as an object whose light passes through the walls inside surface, which acts as another refracting surface.) (b) To the watcher, how far away does the fish appear
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