Answer: You produce an image of the Sun on a screen, using

Figure 34-25 shows a fish and a fish stalker in water. (a) Does the stalker see the fish in the general region of point a or point b? (b) Does the fish see the (wild) eyes of the stalker in the general region of point c or point d?

In Fig. 34-26, stick figure 0 stands in front of a spherical mirror that is mounted within the boxed region; the central axis through the mirror is shown. The four stick figures 11 to 14 suggest general locations and orientations for the images that might be produced by the mirror. (The figures are only sketched in; neither their heights nor their distances from the mirror are drawn to a b (34-6) (34-5) .c Fig. 34-25 Question 1. I I I 1.-- Fig. 34-26 Questions 2 and 10. scale.) (a) Which of the stick figures could not possibly represent images? Of the possible images, (b) which would be due to a concave mirror, (c) which would be due to a convex mirror, (d) which would be virtual, and (e) which would involve negative magnification?

Figure 34-27 is an overhead view of a mirror maze based on floor sections that are equilateral triangles. Every wall within the maze is mirrored. If you stand at entrance x, (a) which of the maze monsters a, b, and c hiding in the maze can you see along QUESTIONS 949 where h and hi are the heights (measured perpendicular to the central axis) of the object and image, respectively. Optical Instruments Three optical instruments that extend human vision are: 1. The simple magnifying lens, which produces an angular magnification me given by 25cm me=--f-' (34-12) where f is the focal length of the magnifying lens. The distance of 25 cm is a traditionally chosen value that is a bit more than the typical near point for someone 20 years old. 2. The compound microscope, which produces an overall magnification M given by s 25 cm M=mme=---;:---I'-' (34-14) Job Jey where m is the lateral magnification produced by the objective, me is the angular magnification produced by the eyepiece, s is the tube length, and fob and fey are the focal lengths of the objective and eyepiece, respectively. 3. The refracting telescope, which produces an angular magnification me given by the virtual hallways extending from entrance x; (b) how many times does each visible monster appear in a hallway; and (c) what is at the far end of a hallway?

A penguin waddles along the central axis of a concave mirror, from the focal point to an effectively infinite distance. (34-15) III (a) How does its image move? Fig.34-27 Question 3. (b) Does the height of its image increase continuously, decrease continuously, or change in some more complicated manner?

When a T. rex pursues a jeep in the movie Jurassic Park, we see a reflected image of the T. rex via a side-view mirror, on which is printed the (then darkly humorous) warning: "Objects in mirror are closer than they appear." Is the mirror flat, convex, or concave?

An object is placed against the center of a concave mirror and then moved along the central axis until it is 5.0 m from the mirror. During the motion, the distance Iii between the mirror and the image it produces is measured. The procedure is then repeated with a convex mirror and a plane mirror. Figure 34-28 gives the results versus object distance p. Which curve corresponds to which mirror? (Curve 1 has two segments.)

The table details six variations of the basic arrangement of two thin lenses represented in Fig. 34-29. (The points labeled F! and F2 are F! the focal points of lenses 1 and 2.) Lens 1 Lens 2 i j An object is distance p! to the left of Fig. 34-29 Question 7. lens 1, as in Fig. 34-18. (a) For which variations can we tell, without calculation, whether the final image (that due to lens 2) is to the left or right of lens 2 and whether it has the same orientation as the object? (b) For those "easy" variations, give the image location as "left" or "right" and the orientation as "same" or "inverted."

An object is placed against the center of a converging lens and then moved along the central axis until it is 5.0 m from the lens. During the motion, the distance Iii between the lens and the image it produces is measured. The procedure is then repeated with a diverging lens. Which of the curves in Fig. 34-28 best gives Iii versus the object distance p for these lenses? (Curve 1 consists of two segments. Curve 3 is straight.)

Figure 34-30 shows four thin lenses, all of the same material, with sides that either are fiat or have a radius of curvature of magnitude 10 cm. Without written calculation, rank the lenses according to the magnitude of the focal length, greatest first.

In Fig. 34-26, stick figure 0 stands in front of a thin, symmetric lens that is mounted within the boxed region; the central axis through the lens is shown. The four stick figures I! to 14 suggest general locations and orientations for the images that might be produced by the lens. (The figures are only sketched in; neither their height nor their distance from the lens is drawn to scale.) (a) Which of the stick figures could not possibly represent images? Of the possible images, (b) which would be due to a converging lens, (c) which would be due to a diverging lens, (d) which would be virtual, and (e) which would involve negative magnification?

Spherical mirrors. Object 0 stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance Ps (centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object 0 or noninverted (NI), and (f) on the same side of the mirror as 0 or on the opposite side

Spherical mirrors. Object 0 stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance Ps (centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object 0 or noninverted (NI), and (f) on the same side of the mirror as 0 or on the opposite side

Spherical mirrors. Object 0 stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance Ps (centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object 0 or noninverted (NI), and (f) on the same side of the mirror as 0 or on the opposite side

Spherical mirrors. Object 0 stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance Ps (centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object 0 or noninverted (NI), and (f) on the same side of the mirror as 0 or on the opposite side

Spherical mirrors. Object 0 stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance Ps (centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object 0 or noninverted (NI), and (f) on the same side of the mirror as 0 or on the opposite side

Spherical mirrors. Object 0 stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance Ps (centimeters), the type of mirror, and then the distance (centimeters, without proper sign) between the focal point and the mirror. Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real (R) or virtual (V), (e) inverted (I) from object 0 or noninverted (NI), and (f) on the same side of the mirror as 0 or on the opposite side

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

More mirrors. Object 0 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 f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real (R) or virtual (V), (h) inverted (I) or noninverted (NI) from 0, and (i) on the same side of the mirror as object 0 or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

Figure 34-36 gives the lateral magnification m of an object versus the object distance p from a spherical mirror as the object is moved ~ 0.5 along the mirror's central axis through a range of values for p. The horizontal scale is set by Ps = 10.0 o cm. What is the magnification of Ps p(cm) the object when the object is 21 cm from the mirror?

(a) A luminous point is moving at speed va toward a spherical mirror with radius of curvature r, along the central axis of the mirror. Show that the image of this point is moving at speed VI = ( 2p '- r Y Va, where p is the distance of the luminous point from the mirror at any given time. Now assume the mirror is concave, with r = 15 cm, and let va = 5.0 cm/s. Find VI when (b) p = 30 cm (far outside the focal point), (c) p = 8.0 cm (just outside the focal point), and (d) p = 10 mm (very near the mirror).

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

Spherical refracting surfaces. An object 0 stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction nl where the object is located, (a) the index of refraction n2 on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature r of the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R) or virtual (V) and (f) on the same side of the surface as object o or on the opposite side.

In Fig. 34-37, a beam of paralleI light rays from a laser is incident on a solid transparent sphere of index of refraction n. (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b) What index of refraction, if any, will produce a point image at the center of the sphere?

A glass sphere has radius R = 5.0 cm and index of refraction 1.6. A paperweight is constructed by slicing through the sphere along a plane that is 2.0 cm from the center of the sphere, leaving height h = 3.0 cm. The paperweight is placed on a table and viewed from directly above by an observer who is distance d = 8.0 cm from the tabletop Fig. 34-38 Problem 40. (Fig. 34-38). When viewed through the paperweight, how far away does the tabletop appear to be to the observer?

A lens is made of glass having an index of refraction of 1.5. One side of the lens is fiat, and the other is convex with a radius of curvature of 20 cm. (a) Find the focal length of the lens. (b) If an object is placed 40 cm in front of the lens, where is the image?

Figure 34-39 gives the lateral magnification m of an object versus the object distance p from a lens as the object is moved along the central axis of the lens through a range of values for p out to Ps = 20.0 cm. What is the magnification of the object when the object is 35 cm from the lens?

A movie camera with a (single) lens offocallength 75 mm takes a picture of a person standing 27 m away. If the person is 180 cm tall, what is the height of the image on the film?

An object is placed against the center of a thin lens and then moved away from it along the central axis as the image distance i is measured. Figure 34-40 gives i versus object distance p out to Ps = 60 cm. What is the image distance when p = 100 cm?

You produce an image of the Sun on a screen, using a thin lens whose focal length is 20.0 cm. What is the diameter of the image? (See Appendix C for needed data on the Sun.)

An object is placed against the center of a thin lens and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-41 gives i versus 0 p (em) object distance p out to Ps = 40 cm. What is the image distance when p = 70cm?

A double-convex lens is to be made of glass with an index of refraction of 1.5. One surface -20 is to have twice the radius of curva- Fig. 34-41 Problem 46. ture of the other and the focal length is to be 60 mm. What is the (a) smaller 6 and (b) larger radius?

An object is moved along the 4 central axis of a thin lens while the ~ 2~-f--I--f--f~~-I-+-i o Ps p(em) lateral magnification m is measured. Figure 34-42 gives m versus object distance p out to Ps = 8.0 cm. What is the magnification of the object when the object is 14.0 cm from the lens?

An illuminated slide is held 44 cm from a screen. How far from the slide must a lens of focal length 11 cm be placed (between the slide and the screen) to form an image of the slide's picture on the screen?

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Thin lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

Lenses with given radii. Object o stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-7 gives object distance p, index of refraction n of the lens, radius 1'1 of the nearer lens surface, and radius 1'2 of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real (R) or virtual (V), (d) inverted (I) from object 0 or noninverted (NI), and (e) on the same side of the lens as object 0 or on the opposite side.

In Fig. 34-43, a real inverted image I of an object 0 is formed by a certain lens (not shown); the object-image separation is d = 40.0 cm, measured along the central axis of the lens. The image is just half the size of the object. (a) What kind of lens must be used to produce this image? (b) How far from the object must the lens be placed? (c) What is the focal length of the lens?

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

More lenses. Object 0 stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-8 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance t, (c) the object distance P, (d) the image distance i, and (e) the lateral (d) (e) (f) (g) (h) m RIV IINI Side <1.0 NI +0.25 -0.25 -0.50 <1.0 Same >1.0 +1.25 0.50 NI >1.0 magnification m. (All distances are in centimeters.) It also refers to whether (f) the image is real (R) or virtual (V), (g) inverted (I) or noninverted (NI) from 0, and (h) on the same side of the lens as 0 or on the opposite side. Fill in the missing information, including the value of m when only an inequality is given. Where only a sign is missing, answer with the sign.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

Two-lens systems. In Fig. 34-44, stick figure 0 (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to 0, which is at object distance Pl' Lens 2 is mounted within the farther boxed region, at distance d. Each problem in Table 34-9 refers to a different combination of lensesf ,~O_----,--: -_i-t-: ___ +-i_2-,-:rand different values for distances, - :: :: which are given in centimeters. ~ _J ~ ____ J The type of lens is indicated by C r-- d ----1 for converging and D for diverging; the number after CorD is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overallia teral 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 0 or noninverted (NI), and (e) on the same side of lens 2 as object 0 or on the opposite side.

If the angular magnification of an astronomical telescope is 36 and the diameter of the objective is 75 mm, what is the minimum diameter of the eyepiece required to collect all the light entering the objective from a distant point source on the telescope axis?

In a microscope of the type shown in Fig. 34-20, the focal length of the objective is 4.00 cm, and that of the eyepiece is 8.00 cm. The distance between the lenses is 25.0 cm. (a) What is the tube length s? (b) If image I in Fig. 34-20 is to be just inside focal point Fl, how far from the objective should the object be? What then are (c) the lateral magnification m of the objective, (d) the angular magnification me of the eyepiece, and (e) the overall magnification M of the microscope?

Figure 34-45a shows the basic structure of a camera. A lens can be moved forward or back to produce an image on film at the back of the camera. For a certain camera, with the distance i between the lens and the film set at f = 5.0 cm, parallel light rays from a very distant object 0 converge to a point image on the film, as shown. The object is now brought closer, to a distance of p = 100 cm, and the lens-film distance is adjusted so that an inverted real image forms on the film (Fig. 34-45b). (a) What is the lens-film distance i now? (b) By how much was distance i changed?

Figure 34-46a shows the basic structure of a human eye. Light refracts into the eye through the cornea and is then further redirected by a lens whose shape (and thus ability to focus the light) is controlled by muscles. We can treat the cornea and eye lens as a single effective thin lens (Fig. 34-46b). A "normal" eye can focus parallel light rays from a distant object 0 to a point on the retina at the back of the eye, where processing of the visual information begins. As an object is brought close to the eye, however, the muscles must change the shape of the lens so that rays form an inverted real image on the retina (Fig. 34-46c). (a) Suppose that for the parallel rays of Figs. 34-46a and b, the focal length f of the effective thin lens of the eye is 2.50 cm. For an object at distance p = 40.0 cm, what focal length f' of the effective lens is required for the object to be seen clearly? (b) PROBLEMS 955 Must the eye muscles increase or decrease the radii of curvature of the eye lens to give focallengthf'?

An object is 10.0 mm from the objective of a certain compound microscope. The lenses are 300 mm apart, and the intermediate image is 50.0 mm from the eyepiece. What overall magnification is produced by the instrument?

Someone with a near point PI! of 25 cm views a thimble through a simple magnifying lens of focal length 10 cm by placing the lens near his eye. What is the angular magnification of the thimble if it is positioned so that its image appears at (a) Pn and (b) infinity?

An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-47 gives i versus object distance p out to Ps = 40 cm. What is the image distance when the object is 70 cm from the mirror?

Three-lens systems. In Fig. 34-48, stick figure 0 (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 0, which is at object distance Pl' Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23 from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different :a.lue~ for distances, which are given in centimeters. The type of lens IS mdIcated 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 0 or noninverted (NI), and (e) on the same side of lens 3 as object 0 or on the opposite side.

Three-lens systems. In Fig. 34-48, stick figure 0 (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 0, which is at object distance Pl' Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23 from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different :a.lue~ for distances, which are given in centimeters. The type of lens IS mdIcated 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 0 or noninverted (NI), and (e) on the same side of lens 3 as object 0 or on the opposite side.

Three-lens systems. In Fig. 34-48, stick figure 0 (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 0, which is at object distance Pl' Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23 from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different :a.lue~ for distances, which are given in centimeters. The type of lens IS mdIcated 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 0 or noninverted (NI), and (e) on the same side of lens 3 as object 0 or on the opposite side.

Three-lens systems. In Fig. 34-48, stick figure 0 (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 0, which is at object distance Pl' Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23 from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different :a.lue~ for distances, which are given in centimeters. The type of lens IS mdIcated 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 0 or noninverted (NI), and (e) on the same side of lens 3 as object 0 or on the opposite side.

Three-lens systems. In Fig. 34-48, stick figure 0 (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 0, which is at object distance Pl' Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23 from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different :a.lue~ for distances, which are given in centimeters. The type of lens IS mdIcated 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 0 or noninverted (NI), and (e) on the same side of lens 3 as object 0 or on the opposite side.

Three-lens systems. In Fig. 34-48, stick figure 0 (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 0, which is at object distance Pl' Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted in the farthest boxed region, at distance d23 from lens 2. Each problem in Table 34-10 refers to a different combination of lenses and different :a.lue~ for distances, which are given in centimeters. The type of lens IS mdIcated 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 0 or noninverted (NI), and (e) on the same side of lens 3 as object 0 or on the opposite side.

The formula 1/p + 1Ii = 1/[ is called the Gaussian form of the thin-lens formula. Another form of this formula, the Newtonian form, is obtained by considering the distance x from the object to the first focal point and the distance x' from the second focal point to the image. Show that xx' = j2 is the Newtonian form of the thin-lens formula.

Figure 34-49a is an overhead view of two vertical plane mirrors with an object 0 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. 34-49b 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 0 would you see if () is (a) 90, (b) 45, and (c) 60? If () = 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. 34-49b.

Tho thin lenses of focal lengths 11 and 12 are in contact. Show that they are equivalent to a single thin lens for which the focal length is I = Id2 / UI + [2)'

Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm from 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. 34-50, a box is somewhere at the left, on the central axis of the thin converging lens. The image 1,11 of the box produced by the plane mirror is 4.00 cm "inside" the mirror. The lens-mirror separation is 10.0 cm, and the focal length of the lens is 2.00 cm. Fig. 34-50 Problem 105. (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 image?

In Fig. 34-51, an object is placed in front of a converging lens at a distance equal to twice the focal length 11 of the lens. On the other side of the lens is a concave mirror of focal length 12 separated from the lens by a distance 2UI + 12)' 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 noninverted relative to the object?

A fruit fly of height H sits in front of lens 1 on the centt:al axis through the lens. The lens forms an image of the fly at a dIstance d = 20 cm from the fly; the image has the fly's orientation and height HI = 2.0H. What are (a) the focal length 11 of the lens and (b) the object distance PI of the fly? The fly then leaves lens 1 and sits in front of lens 2, which also forms an image at d = 20 cm that has the same orientation as the fly, but now HJ = 0.50H. What are (c) f2 and (d) P2?

You grind the lenses shown in Fig. 34-52 from flat glass disks (n = 1.5) using a machine that can grind a radius of curvature of either 40 cm or 60 cm. In a lens where either radius is (l) appropriate, you select the 40 cm radius. Then you hold each lens in sunshine to form an image of the Sun: What are the (a) focal length f and (b) image type (real or virtual) for (bi-convex) lens 1, (c)fand (d) image (4) type for (plane-convex) lens 2, (e) f and (f) image type for (meniscus convex) lens 3, (g) f and (h) image type (2) (5) Fig. 34-52 Problem 108. (3) (6) for (bi-concave) lens 4, (i) f and (j) image type for (plane-concave) lens 5, and (k) f and (1) image type for (meniscus concave) lens 6?

In Fig. 34-53, 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 dl = 8.0 cm, d2 = 3.0 cm, and d3 = 6.8 cm. (a) To the fish, how far away does the watcher appear to be? (Hint: The watcher is the object. Light from that object passes I d2 ' f+----- dl - -+- d3--..J I I I I I I .r------ - ----~ Watcher Wall Fig. 34-53 Problem 109. through the wall's 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 wall's inside surface, which acts as another refracting surface. Find the image produced by that surface, and there is the answer.) (b) To the watcher, how far away does the fish appear to be?

A goldfish in a spherical fish bowl of radius R is at the level of the center C of the bowl and at distance RI2 from the glass (Fig. 34-54). What magnification of the fish is produced by the water in Fig. 34-54 Problem 110. PROBLEMS 957 the bowl for a viewer looking along a line that includes the fish and the center, with the fish on the near side of the center? The index of refraction of the water is 1.33. Neglect the glass wall of the bowl. Assume the viewer looks with one eye. (Hint: Equation 34-5 holds, but Eq. 34-6 does not. You need to work with a ray diagram of the situation and assume that the rays are close to the observer's line of sight-that is, they deviate from that line by only small angles.)

Figure 34-55 shows a beam expander made with two coaxial converging lenses of focal lengths fl and f2 and separation d = fl + f2' The device can expand a laser beam while keeping the light rays in the beam parallel to the central axis through the lenses. Suppose a uniform laser beam of width Wi = 2.5 mm and intensity Ii = 9.0 kW/m2 enters a beam expander for which fl = 12.5 cm and f2 = 30.0 cm. What are (a) Wf and (b) If of the beam leaving the expander? (c) What value of d is needed for the beam expander if lens 1 is replaced with a diverging lens of focal length fl = -26.0 cm?

You look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refraction n (Fig. 34-56). Because you view with two eyes, which intercept different rays of light from the coin, you perceive the coin to be where extensions of the intercepted rays cross, at depth da instead of d. Assuming that the intercepted rays in Fig. 34-56 are close to a vertical axis through the coin, show that da = din. (Hint: Use the small-angle approximation sin e = tan e = e.)