Principles of Physics

David Halliday , Robert Resnick , Jearl Walker

Chapter 34

Images - all with Video Answers

Educators

Chapter Questions

Problem 1

1 through 8 Spherical mirrors. Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Zachary Warner

Zachary Warner

Numerade Educator

Problem 2

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 3

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 4

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 5

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 6

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 7

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 8

Object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in Table 34-3 gives object distance $p_{s}$ (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 ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), (e) inverted (I) from object $O$ or noninverted (NI), and (f) on the same side of the mirror as $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 9

A lens is made of glass having an index of refraction of $1.5$. One side of the lens is flat, and the other is convex with a radius of curvature of $20 \mathrm{~cm}$. (a) Find the focal length of the lens. (b) If an object is placed $85 \mathrm{~cm}$ in front of the lens, where is the image?

Prabhu Ramji

Numerade Educator

Problem 10

In Fig. $34-25$, a real inverted
image $I$ of an object $O$ is formed
by a particular lens (not shown);
the object-image separation is
$d=50.0 \mathrm{~cm}$, measured along the

Averell Hause

Carnegie Mellon University

Problem 11

You produce an image of the Sun on a screen, using a thin lens whose focal length is $45.0 \mathrm{~cm}$. What is the diameter of the image?

Zachary Warner

Numerade Educator

Problem 12

An object is moved along the central axis of a spherical mirror while the lateral magnification $m$ of it is measured. Figure 34-26 gives $m$ versus object distance $p$ for the range $p_{a}=2.0 \mathrm{~cm}$ to $p_{b}=8.0 \mathrm{~cm}$. What is $m$ for $p=20.0 \mathrm{~cm}$ ?

Averell Hause

Carnegie Mellon University

Problem 13

through 25 More mirrors. $p(\mathrm{~cm})$
Object $O$ stands on the central axis
Figure 34-26 Problem 12 . 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 $f,(\mathrm{c})$ the radius of curvature $r,(\mathrm{~d})$ the object distance $p,(\mathrm{e})$ the image distance $i$, and $(\mathrm{f})$ the lateral magnification $m$. (All distances are in centimeters.) It also refers to whether $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted $(\mathrm{I})$ or

Sheh Lit Chang

University of Washington

Problem 14

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 15

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 16

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 17

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 18

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 19

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 20

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 21

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 22

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 23

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 24

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 25

Object $O$ stands on the central axis
Figure 34-26 Problem $12 .$ 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 $(\mathrm{g})$ the image is real $(\mathrm{R})$ or virtual $(\mathrm{V}),(\mathrm{h})$ inverted (I) or

Eduard Sanchez

Numerade Educator

Problem 26

An object is moved along the central axis of a thin lens while the lateral magnification $m$ is measured. Figure 34-27 gives $m$ versus object distance $p$ out to $p_{s}=16.0 \mathrm{~cm}$. What is the magnification of the object when the object is $14.0 \mathrm{~cm}$ from the lens?

Averell Hause

Carnegie Mellon University

Problem 27

Someone with a near point $P_{n}$
of $25 \mathrm{~cm}$ views a thimble through a 0

Zachary Warner

Numerade Educator

Problem 28

An object is $12.0 \mathrm{~mm}$ from the objective of a certain compound microscope. The lenses are $300 \mathrm{~mm}$ apart, and the intermediate image is $50.0 \mathrm{~mm}$ from the eyepiece. What overall magnification is produced by the instrument?

Averell Hause

Carnegie Mellon University

Problem 29

In a microscope of the type shown in Fig. 34-20, the focal length of the objective is $3.00 \mathrm{~cm}$, and that of the eyepiece is $8.00 \mathrm{~cm}$. The distance between the lenses is $25.0 \mathrm{~cm}$. (a) What is the tube length $s$ ? (b) If image $I$ in Fig. 34-20 is to be just inside focal point $F_{1}^{\prime}$, how far from the objective should the object be? What then are (c) the lateral magnification $m$ of the objective, (d) the angular magnification $m_{\theta}$ of the eyepiece, and (e) the overall magnification $M$ of the microscope?

Eduard Sanchez

Numerade Educator

Problem 30

A glass sphere has radius
$R=5.0 \mathrm{~cm}$ and index of refraction
1.6. A paperweight is constructed
by slicing through the sphere along
a plane that is $2.0 \mathrm{~cm}$ from the cen-
ter of the sphere, leaving height
$h=3.0 \mathrm{~cm}$. The paperweight is
placed on a table and viewed from

Sheh Lit Chang

University of Washington

Problem 31

A double-convex lens is to be made of glass with an index of refraction of 1.5. One surface is to have $1.5$ times the radius of curvature of the other and the focal length is to be $60 \mathrm{~mm}$. What is the (a) smaller and (b) larger radius?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

Figure 34-29 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 $p_{s}=20.0 \mathrm{~cm}$. What is the magnification of the object when the object is $38 \mathrm{~cm}$ from the lens?

Averell Hause

Carnegie Mellon University

Problem 33

33 through 43 Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral magnification $m$. (All distances are in centimeters.) It also refers to whether (f) the image is real ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), ( $\mathrm{g}$ ) inverted (I) or noninverted (NI) from $O$, and (h) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 34

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table $34-5$ refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral magnification $m$. (All distances are in centimeters.) It also refers to whether (f) the image is real ( $\mathrm{R}$ ) or virtual ( $\mathrm{V}$ ), ( $\mathrm{g}$ ) inverted (I) or noninverted (NI) from $O$, and $(\mathrm{h})$ on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 35

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 36

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 37

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 38

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 39

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 40

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 41

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 42

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 43

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-5 refers to (a) the lens type, converging (C) or diverging (D), (b) the focal distance $f$, (c) the object distance $p$, (d) the image distance $i$, and (e) the lateral 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 $O$, and ( $h$ ) on the same side of the lens as $O$ 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.

Eduard Sanchez

Numerade Educator

Problem 44

Figure $34-30$ gives the lateral magnification $m$ of an object versus the object distance $p$ from a spherical mirror as the object is moved along the mirror's central axis through a range of values for $p$. The horizontal scale is set by $p_{s}=10.0 \mathrm{~cm}$. What is the magnification of the object when the object is $24 \mathrm{~cm}$ from the mirror?

Averell Hause

Carnegie Mellon University

Problem 45

In Fig. 34-31, an isotropic point source of light $S$ is positioned at distance $d$ from a viewing screen $A$ and the light intensity $I_{P}$ at point $P$ (level with $S)$ is measured. Then a plane mirror $M$ is placed behind $S$ at distance $2 d$. By how much is $I_{P}$ multiplied by the presence of the mirror?

Zachary Warner

Numerade Educator

Problem 46

Figure $34-32 a$ shows the basic structure of an $\quad|-d \rightarrow|-d \rightarrow \mid$ old film camera. A lens can be moved forward or $\quad$ Figure 34-31 back to produce an image on film at the back of the Problem 45 . camera. For a certain camera, with the distance $i$
between the lens and the film set at $f=5.0 \mathrm{~cm}$, parallel light rays from a very distant object $O$ converge to a point image on the film, as shown. The object is now brought closer, to a distance of $p=120 \mathrm{~cm}$, and the lens-film distance is adjusted so that an inverted real image forms on the film (Fig. 34-32b). (a) What is the lens-film distance $i$ now? (b) By how much was distance $i$ changed?

Eduard Sanchez

Numerade Educator

Problem 47

In Fig. 34-33, a beam of parallel 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 refracFigure 34-33 Problem 47. tion of the sphere? (b) What index of refraction, if any, will produce a point image at the center of the sphere?

Zachary Warner

Numerade Educator

Problem 48

If the angular magnification of an astronomical telescope is 40 and the diameter of the objective is $75 \mathrm{~mm}$, 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?

Averell Hause

Carnegie Mellon University

Problem 49

A movie camera with a (single) lens of focal length $75 \mathrm{~mm}$ takes a picture of a person standing $15 \mathrm{~m}$ away. If the person is $180 \mathrm{~cm}$ tall, what is the height of the image on the film?

Zachary Warner

Numerade Educator

Problem 50

50 through 56 Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 51

Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 52

Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 53

Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 54

Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 55

Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 56

Spherical refracting surfaces. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-6 refers to the index of refraction $n_{1}$ where the object is located, (a) the index of refraction $n_{2}$ 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.

Sheh Lit Chang

University of Washington

Problem 57

Figure $34-34$ shows a small lightbulb suspended at distance $d_{1}=300 \mathrm{~cm}$ above the surface of the water in a swimming pool where the water depth is $d_{2}=200 \mathrm{~cm}$. The bottom of the pool is a large mirror. How far below the mirror surface is the image of the bulb? (Hint: Assume that the rays are close to a vertical axis through the bulb, and use the small-angle approximation in which $\sin \theta \approx \tan \theta \approx \theta$.)

Zachary Warner

Numerade Educator

Problem 58

58 through 65 Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 59

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 60

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 61

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 62

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 63

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 64

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 65

Two-lens systems. In Fig. 34-35, stick figure $O$ (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 $O$, which is at object distance $p_{1}$. Lens 2 is mounted within the farther boxed region, at distance $d$. Each problem in Table $34-7$ 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 $\mathrm{D}$ for diverging; the number after $\mathrm{C}$ or $\mathrm{D}$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Eduard Sanchez

Numerade Educator

Problem 66

An object is placed against the center of a spherical mirror and then moved $60 \mathrm{~cm}$ from it along the central axis as the image distance $i$ is measured. Figure $34-36$ gives $i$ versus object distance $p$ out to $p_{s}=40 \mathrm{~cm}$. What is $i$ for $p=60 \mathrm{~cm}$ ?

Sheh Lit Chang

University of Washington

Problem 67

Figure $34-37 a$ 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. 34-37b). A "normal" eye can focus parallel light rays from a distant object $O$ 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. $34-37 c$ ). (a) Suppose that for the parallel rays of Figs. $34-37 a$ and $b$, the focal length $f$ of the effective thin lens of the eye is $2.50 \mathrm{~cm}$. For

Eduard Sanchez

Numerade Educator

Problem 68

A moth at about eye level is $20 \mathrm{~cm}$ in front of a plane mirror; you are behind the moth, $30 \mathrm{~cm}$ from the mirror. What is the distance between your eyes and the apparent position of the moth's image in the mirror?

Averell Hause

Carnegie Mellon University

Problem 69

(a) A luminous point is moving at speed $v_{O}$ 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
$$
v_{I}=-\left(\frac{r}{2 p-r}\right)^{2} v_{O}
$$
where $p$ is the distance of the luminous point from the mirror at any given time. Now assume the mirror is concave, with $r=15 \mathrm{~cm}$, and let $v_{o}=5.0 \mathrm{~cm} / \mathrm{s}$. Find $v_{l}$ when (b) $p=40 \mathrm{~cm}$ (far outside the focal point), (c) $p=7.8 \mathrm{~cm}$ (just outside the focal point), and (d) $p=10 \mathrm{~mm}$ (very near the mirror).

Eduard Sanchez

Numerade Educator

Problem 70

70 through 79 Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 71

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 72

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 73

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 74

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 75

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 76

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 77

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 78

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 79

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in Table 34-8 gives object distance $p$, index of refraction $n$ of the lens, radius $r_{1}$ of the nearer lens surface, and radius $r_{2}$ 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 80

80 through 87 Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 81

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 82

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 83

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 84

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 85

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 86

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 87

Thin lenses. Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-9 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 $O$ or noninverted (NI), and (e) on the same side of the lens as object $O$ or on the opposite side.

Sheh Lit Chang

University of Washington

Problem 88

Figure $34-38$ shows an overhead view of a corridor with a plane mirror $M$ mounted at one end. A burglar $B$ sneaks along the corridor directly toward the center of the mirror. If $d=3.5 \mathrm{~m}$, how far from the mirror will she be when the security guard $S$ can first see her in the mirror?

Naresh Bagrecha

Naresh Bagrecha

Numerade Educator

Problem 89

An illuminated slide is held $68 \mathrm{~cm}$ from a screen. How far from the slide must a lens of focal length $11 \mathrm{~cm}$ be placed (between the slide and the screen) to form an image of the slide's picture on the screen?

Sheh Lit Chang

University of Washington

Problem 90

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 $34-39$ gives $i$ versus object distance $p$ out to $p_{s}=60 \mathrm{~cm}$. What is the image distance when $p=120 \mathrm{~cm}$ ?

Eduard Sanchez

Numerade Educator

Problem 91

You look through a camera toward an image of a hummingbird in a plane mirror. The camera is $4.30 \mathrm{~m}$ in front of the mirror. The bird is at camera level, $8.00 \mathrm{~m}$ to your right and $3.30 \mathrm{~m}$ from the mirror. What is the distance between the camera and the apparent position of the bird's image in the mirror?

Zachary Warner

Numerade Educator

Problem 92

An object is placed against the center of a thin lens and then moved $60 \mathrm{~cm}$ from it along the central axis as the image distance $i$ is measured. Figure 34-40 gives $i$ versus object distance $p$ out to $p_{s}=40 \mathrm{~cm}$. What is the image distance when $p=60 \mathrm{~cm} ?$

Eduard Sanchez

Numerade Educator

Problem 93

A concave shaving mirror has a radius of curvature of $35.0 \mathrm{~cm}$. It is positioned so that the (upright) image of a man's face is $1.70$ times the size of the face. How far is the mirror from the face?

Zachary Warner

Numerade Educator