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Understanding Physics

Karen Cummings, Priscilla W. Laws, Edward F. Redish

Chapter 35

Images - all with Video Answers

Educators

Chapter Questions

01:25

Problem 1

Light in vacuum is incident on the surface of a glass slab. In the vacuum the beam makes an angle of $32.0^{\circ}$ with the normal to the surface, while in the glass it makes an angle of $21.0^{\circ}$ with the normal. What is the index of refraction of the glass?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:29

Problem 2

Two Perpendicular Surfaces Figure $35-33$ shows light reflecting from two perpendicular reflecting surfaces $A$ and $B .$ Find the angle between the incoming ray $i$ and the outgoing ray $r^{\prime}$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:33

Problem 3

When the rectangular metal tank in Fig. $35-34$ is filled to the top with an unknown liquid, an observer with eyes level with the top of the tank can just see the corner $E ;$ a ray that refracts toward the observer at the top surface of the liquid is shown. Find the index of refraction of the liquid.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:35

Problem 4

In about A.D. 150 , Claudius Ptolemy gave the following measured values for the angle of incidence $\theta_{1}$ and the angle of refraction $\theta_{2}$ for a light beam passing from air to water:
$$\begin{array}{cc|cc}
\hline \boldsymbol{\theta}_{\mathbf{1}} & \boldsymbol{\theta}_{\mathbf{2}} & \boldsymbol{\theta}_{\mathbf{1}} & \boldsymbol{\theta}_{\mathbf{2}} \\
\hline 10^{\circ} & 8^{\circ} 00^{\prime} & 50^{\circ} & 35^{\circ} 00^{\prime} \\
20^{\circ} & 15^{\circ} 30^{\prime} & 60^{\circ} & 45^{\circ} 30^{\prime} \\
30^{\circ} & 22^{\circ} 30^{\prime} & 70^{\circ} & 45^{\circ} 30^{\prime} \\
40^{\circ} & 29^{\circ} 00^{\prime} & 80^{\circ} & 50^{\circ} 00^{\prime} \\
\hline
\end{array}$$
(a) Are these data consistent with the law of refraction? (b) If so, what index of refraction results? These data are interesting as perhaps the oldest recorded physical measurements.

Keshav Singh
Keshav Singh
Numerade Educator
03:04

Problem 5

In Fig. $35-35$, a 2.00-m-long vertical pole extends from the bottom of a swimming pool to a point $50.0 \mathrm{~cm}$ above the water. Sunlight is incident at $55.0^{\circ}$ above the horizon. What is the length of the shadow of the pole on the level bottom of the pool?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:13

Problem 6

In Fig. 35-36, light is incident at angle $\theta_{1}=40.1^{\circ}$ on a boundary between two transparent materials. Some of the light then travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. What are the values of (a) $\theta_{5}$ and (b) $\theta_{4}$ ?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:36

Problem 7

Prove that a ray of light incident on the surface of a sheet of plate glass of thickness $t$ emerges from the opposite face parallel to its initial direction but displaced sideways, as in Fig. 35-37. Show that, for small angles of incidence $\theta$, this displacement is given by
$$x=t \theta \frac{n-1}{n}$$
where $n$ is the index of refraction of the glass and $\theta$ is measured in radians.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:28

Problem 8

A ray of white light makes an angle of incidence of $35^{\circ}$ on one face of a prism of fused quartz; the prism's cross section is an equilateral triangle. Sketch the light as it passes through the prism, showing the paths traveled by rays representing (a) blue light, (b) yellow-green light, and (c) red light.

Narayan Hari
Narayan Hari
Numerade Educator
05:23

Problem 9

In Fig. $35-38$, a ray is incident on one face of a triangular glass prism in air. The angle of incidence $\theta$ is chosen so that the emerging ray also makes the same angle $\theta$ with the normal to the other face. Show that the index of refraction $n$ of the glass prism is given by
$$n=\frac{\sin \frac{1}{2}(\psi+\phi)}{\sin \frac{1}{2} \phi}$$
where $\phi$ is the vertex angle of the prism and $\psi$ is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle $\psi$ has the smallest possible value, which is called the angle of minimum deviation.)

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:11

Problem 10

In Fig. $35-39$ two perpendicular mirrors form the sides of a vessel filled with water. (a) A light ray is incident from above, normal to the water surface. Show that the emerging ray is parallel to the incident ray. Assume that there are reflections at both mirror surfaces. (b) Repeat the analysis for the case of oblique incidence with the incident ray in the plane of the figure.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:48

Problem 11

In Fig. 35-40 a light ray enters a glass slab at point $A$ and then undergoes total internal reflection at point $B$. What minimum value for the index of refraction of the glass can be inferred from this information?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:12

Problem 12

The index of refraction of benzene is $1.8$. What is the critical angle for a light ray traveling in benzene toward a plane layer of air above the benzene?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:46

Problem 13

In Fig. $35-41$, a ray of light is perpendicular to the face $a b$ of a glass prism $(n=$ 1.52). Find the largest value of the angle $\phi$ so that the ray is totally reflected at face $a c$ if the prism is immersed (a) in air and (b) in water.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
03:54

Problem 14

A point source of light is $80.0 \mathrm{~cm}$ below the surface of a body of water. Find the diameter of the circle at the surface through which light emerges from the water.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:06

Problem 15

A solid glass cube, of edge length $10 \mathrm{~mm}$ and index of refraction $1.5$, has a small spot at its center. (a) What parts of each cube face must be covered to prevent the spot from being seen, no matter what the direction of viewing? (Neglect light that reflects inside the cube and then refracts out into the air.) (b) What fraction of the cube surface must be so covered?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
05:01

Problem 16

A ray of white light travels through fused quartz that is surrounded by air. If all the color components of the light undergo total internal reflection at the surface, then the reflected light forms a reflected ray of white light. However, if the color component at one end of the visible range (either blue or red) partially refracts through the surface into the air, there is less of that component in the reflected light. Then the reflected light is not white but has the tint of the opposite end of the visible range. (If blue were partially lost to refraction, then the reflected beam would be reddish, and vice versa.) Is it possible for the reflected light to be (a) bluish of (b) reddish? (c) If so, what must be the angle of incidence of the original white light on the quartz surface?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
03:54

Problem 17

In Fig. $35-42$, light enters a $90^{\circ}$ trianglular prism at point $P$ with incident angle $\theta$ and then some of it refracts at point $Q$ with an angle of refraction of $90^{\circ}$. (a) What is the index of refraction of the prism in terms of $\theta ?$ (b) What, numerically, is the maximum value that the index of refraction can have? Explain what happens to the light at $Q$ if the incident angle at $Q$ is (c) increased slightly and (d) decreased slightly.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
07:22

Problem 18

Suppose the prism of Fig. $35-38$ has apex angle $\phi=60.0^{\circ}$ and index of refraction $n=1.60 .$ (a) What is smallest angle of incidence $\theta$ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of incidence $\theta$ is required for the ray to exit the prism with an identical angle $\theta$ for its refraction, as it does in Fig. $35-38 ?$ (See Problem 9.)

Keshav Singh
Keshav Singh
Numerade Educator
01:06

Problem 19

Light traveling in water of refractive index $1.33$ is incident on a plate of glass with index of refraction 1.53. At what angle of incidence is the reflected light fully polarized?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:47

Problem 20

(a) At what angle of incidence will the light reflected from water be completely polarized? (b) Does this angle depend on the wavelength of the light?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
00:41

Problem 21

A moth at about eye level is $10 \mathrm{~cm}$ 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
Averell Hause
Carnegie Mellon University
02:24

Problem 22

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, $5.00 \mathrm{~m}$ 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
Zachary Warner
Numerade Educator
View

Problem 23

Figure $35-43 a$ is an overhead view of two vertical plane mirrors with an object $O$ placed between them. If you look into the mirrors, you see multiple images of $O$. You can find them by drawing the reflection in each mirror of the angular region between the mirrors, as is done for the left-hand mirror in Fig. $35-43 b$. 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 $O$. (a) If $\theta=90^{\circ}$, how many images of $O$ would you see? (b) Draw their locations and orientations (as in Fig. $35-43 b)$

Averell Hause
Averell Hause
Carnegie Mellon University
02:25

Problem 24

Repeat Problem 23 for the mirror angle $\theta$ equal to (a) $45^{\circ}$, (b) $60^{\circ}$, and (c) $120^{\circ}$. (d) Explain why there are several possible answers for (c).

Mahendra Kumar
Mahendra Kumar
Numerade Educator
05:29

Problem 25

Prove That Prove that if a plane mirror is rotated through an angle $\alpha$, the reflected beam is rotated through an angle $2 \alpha .$ Show that this result is reasonable for $\alpha=45^{\circ}$.

Zachary Warner
Zachary Warner
Numerade Educator
01:07

Problem 26

Figure $35-44$ 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 $d=3.0$ $\mathrm{m}$, how far from the mirror will she be when the security guard $S$ can first see her in the mirror?

Averell Hause
Averell Hause
Carnegie Mellon University
02:20

Problem 27

You put a point source of light $S$ a distance $d$ in front of a screen $A$. How is the light intensity at the center of the screen changed if you put a completely reflecting mirror $M$ a distance $d$ behind the source, as in Fig. $35-45 ?$ (Hint: Use Eq. $34-25 .$ )

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:45

Problem 28

Figure $35-46$ shows a small lightbulb suspended above the surface of the water in a swimming pool. The bottom of the pool is a large mirror. How far below the mirror's surface is the image of the bulb? (Hint: Construct a diagram of two rays like that of Fig. $35-14$, but take into account the bending of light rays by refraction. Assume that the rays are close to a vertical axis through the bulb, and use the small-angle approximation that $\sin \theta \approx \tan \theta .)$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:22

Problem 29

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 $2.50$ times the size of the face. How far is the mirror from the face?

Zachary Warner
Zachary Warner
Numerade Educator
03:41

Problem 30

Fill in Table $35-4$, each row of which refers to a different combination of an object and either a plane mirror, a spherical convex mirror, or a spherical concave mirror. Distances are in centimeters. If a number lacks a sign, find the sign. Sketch each combination and draw in enough rays to locate the object and its image.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
03:58

Problem 31

A short straight object of length $L$ lies along the central axis of a spherical mirror of focal length $f$, a distance $o$ from the mirror. (a) Show that its image in the mirror has a length $L^{\prime}$ where
$$L^{\prime}=L\left(\frac{f}{o-f}\right)^{2}$$
(Hint: Locate the two ends of the object.) (b) Show that the longitudinal magnification $m^{\prime}\left(=L^{\prime} / L\right)$ is equal to $m^{2}$, where $m$ is the lateral magnification.

Averell Hause
Averell Hause
Carnegie Mellon University
07:34

Problem 32

(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
$$v_{I}=-\left(\frac{r}{2 o-r}\right)^{2} v_{O}$$
where $o$ is the distance of the luminous point from the mirror at any given time. (Hint: Start with Eq. 35-13.) Now assume that the mirror is concave, with $r=15 \mathrm{~cm}$, and let $v_{O}=5.0 \mathrm{~cm} / \mathrm{s}$. Find the speed of the image when (b) $o=30 \mathrm{~cm}$ (far outside the focal point), (c) $o=8.0 \mathrm{~cm}$ (just outside the focal point), and (d) $o=$ $10 \mathrm{~mm}$ (very near the mirror).

Eduard Sanchez
Eduard Sanchez
Numerade Educator
02:27

Problem 33

A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction $n$ (Fig. $35-47$ ). (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?

Zachary Warner
Zachary Warner
Numerade Educator
02:39

Problem 34

Fill in Table $35-5$, each row of which refers to a different combination of a point object and a spherical refracting surface separating two media with different indexes of refraction. Distances are in centimeters. If a number lacks a sign, find the sign. Sketch each combination and draw in enough rays to locate the object and image.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:54

Problem 35

You look downward at a coin that lies at the bottom of a pool of liquid with depth $d$ and index of refraction $n$ (Fig. $35-48$ ). 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 $d_{\mathrm{a}}$ instead of $d$. Assuming that the intercepted rays in Fig. $35-48$ are close to a vertical axis through the coin, show that $d_{\mathrm{a}}=d / n .$ (Hint: Use the smallangle approximation that $\sin \theta \approx \tan$ $\theta \approx \theta .)$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:28

Problem 36

A 20-mm-thick layer of water $(n=1.33)$ floats on a 40 -mm-thick layer of carbon tetrachloride $(n=1.46)$ in a tank. A coin lies at the bottom of the tank. At what depth below the top water surface do you perceive the coin? (Hint: Use the result and assumptions of Problem 35 and work with a ray diagram of the situation.)

Zachary Warner
Zachary Warner
Numerade Educator
01:51

Problem 37

An object is $20 \mathrm{~cm}$ to the left of a thin diverging lens having a $30 \mathrm{~cm}$ focal length. What is the image distance $i$ ? Find the image position with a ray diagram.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:54

Problem 38

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

Zachary Warner
Zachary Warner
Numerade Educator
01:38

Problem 39

A double-convex lens is to be made of glass with an index of refraction of $1.5 .$ One surface is to have twice the radius of curvature of the other and the focal length is to be $60 \mathrm{~mm}$. What are the radii?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:48

Problem 40

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 $40 \mathrm{~cm}$ in front of the lens, where will the image be located?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:00

Problem 41

The formula
$$\frac{1}{o}+\frac{1}{i}=\frac{1}{f}$$
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 $x^{\prime}$ from the second focal point to the image. Show that
$$x x^{\prime}=f^{2}$$
is the Newtonian form of the thin-lens formula.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:53

Problem 42

A movie camera with a (single) lens of focal length $75 \mathrm{~mm}$ takes a picture of a $180-\mathrm{cm}$ -high person standing $27 \mathrm{~m}$ away. What is the height of the image of the person on the film?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:51

Problem 43

An illuminated slide is held $44 \mathrm{~cm}$ from a screen. How far from the slide must a lens of focal length $11 \mathrm{~cm}$ be placed to form an image of the slide's picture on the screen?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:04

Problem 44

To the extent possible, fill in Table $35-6$, each row of which refers to a different combination of an object and a thin lens. Distances are in centimeters. For the type of lens, use $\mathrm{C}$ for converging and $\mathrm{D}$ for diverging. If a number (except for the index of refraction) lacks a sign, find the sign. Sketch each combination and draw in enough rays to locate the object and image.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:35

Problem 45

Show that the distance between an object and its real image formed by a thin converging lens is always greater than or equal to four times the focal length of the lens.

Averell Hause
Averell Hause
Carnegie Mellon University
03:35

Problem 46

A diverging lens with a focal length of $-15 \mathrm{~cm}$ and a converging lens with a focal length of $12 \mathrm{~cm}$ have a common central axis. Their separation is $12 \mathrm{~cm}$. An object of height $1.0 \mathrm{~cm}$ is $10 \mathrm{~cm}$ in front of the diverging lens, on the common central axis. (a) Where does the lens combination produce the final image of the object (the one produced by the second, converging lens)? (b) What is the height of that image? (c) Is the image real or virtual? (d) Does the image have the same orientation as the object or is it inverted?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:51

Problem 47

A converging lens with a focal length of $+20 \mathrm{~cm}$ is located $10 \mathrm{~cm}$ to the left of a diverging lens having a focal length of $-15 \mathrm{~cm}$. If an object is located $40 \mathrm{~cm}$ to the left of the converging lens, locate and describe completely the final image formed by the diverging lens.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:46

Problem 48

An object is $20 \mathrm{~cm}$ to the left of a lens with a focal length of $+10 \mathrm{~cm}$. A second lens of focal length $+12.5 \mathrm{~cm}$ is $30 \mathrm{~cm}$ to the right of the first lens. (a) Find the location and relative size of the final image. (b) Verify your conclusions by drawing the lens system to scale and constructing a ray diagram. (c) Is the final image real of virtual? (d) Is it inverted?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:06

Problem 49

Two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are in contact. Show that they are equivalent to a single thin lens with
$$f=\frac{f_{1} f_{2}}{f_{1}+f_{2}}$$
as its focal length.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:16

Problem 50

50. Real Inverted In Fig 35-49, a real inverted image $I$ of an object $O$ is formed by a certain lens (not shown); the object-image separation is $d=40.0 \mathrm{~cm}$, 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?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
08:16

Problem 51

A luminous object and a screen are a fixed distance $D$ apart. (a) Show that a converging lens of focal length $f$, placed between object and screen, will form a real image on the screen for two lens positions that are separated by a distance
$$d=\sqrt{D(D-4 f)}$$
(b) Show that
$$\left(\frac{D-d}{D+d}\right)^{2}$$
gives the ratio of the two image sizes for these two positions of the lens.

Zachary Warner
Zachary Warner
Numerade Educator
00:30

Problem 52

If an angular magnification of an astronomical telescope is 36 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
Averell Hause
Carnegie Mellon University
07:01

Problem 53

In a microscope of the type shown in Fig. $35-28$, the focal length of the objective is $4.00 \mathrm{~cm}$, 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. $35-28$ 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
Eduard Sanchez
Numerade Educator
07:57

Problem 54

A simple magnifying lens of focal length $\bar{f}$ is placed near the eye of someone whose near point $P_{n}$ is $25 \mathrm{~cm}$ from the eye. An object is positioned so that its image in the magnifying lens appears at $P_{n} .$ (a) What is the lens's angular magnification? (b) What is the angular magnification if the object is moved so that its image appears at infinity? (c) Evaluate the angular magnifications of (a) and (b) for $f=10 \mathrm{~cm}$. (Viewing an image at $P_{n}$ requires effort by muscles in the eye, whereas for many people viewing an image at infinity requires no effort.)

Eduard Sanchez
Eduard Sanchez
Numerade Educator
05:34

Problem 55

Figure $\quad 35-50 a$ 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. 35$50 b$ ). A "normal" eye can focus parallel light rays from a distance 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. $35-50 c$ ). (a) Suppose that for the parallel rays of Figs. $35-50 a$ and $b$, the focal length $f$ of the effective thin lens of the eye is $2.50 \mathrm{~cm}$. For an object at distance $o=40.0 \mathrm{~cm}$, what focal length $f^{\prime}$ of the effective lens is required for it to be seen clearly? (b) Must the eye muscles increase or decrease the radii of curvature of the eye lens to give focal length $f^{\prime}$ ?

Eduard Sanchez
Eduard Sanchez
Numerade Educator
03:16

Problem 56

An object is $10.0 \mathrm{~mm}$ 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
Averell Hause
Carnegie Mellon University
02:49

Problem 57

Figure $35-51 a$ shows the basic structure of a camera. $\mathrm{A}$ 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 $f=5.0$ $\mathrm{cm}$, 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 $o=100 \mathrm{~cm}$, and the lens-film distance is adjusted so that an inverted real image forms on the film (Fig. $35-51 b$ ). (a) What is the lens-film distance $i$ now? (b) By how much was $i$ changed?

Eduard Sanchez
Eduard Sanchez
Numerade Educator
03:15

Problem 58

You may have observed people with cameras behaving strangely:
(a) At a conference in North Carolina, one of the physics graduate students (who should have known better!) tried to take a picture of the overheads projected on a white screen. Since the room was darkened, he used a flash. Explain why this is a bad idea and what his pictures are likely to show.
(b) Someone mentioned to the student that he probably should not be using his flash, so he turned it off. He then proceeded to try and take pictures of the participants in the darkened room! Explain why this is a bad idea and what his pictures are likely to show.
(c) A woman on an airplane at night with a camera was impressed with the view of the city lights in the dark as the plane flew over Washington, D.C. She stood back in the aisle with her camera and tried to take a picture through the window using her flash. Explain why this is a bad idea and what her pictures are likely to show.

Linda Winkler
Linda Winkler
Numerade Educator
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Problem 59

When a T. rex pursues a jeep in the movie Jurassic Park, we see a reflected image of the (very large) 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? Why do you think so?

Hubert Agamasu
Hubert Agamasu
Numerade Educator
03:46

Problem 60

In Fig. 35 $52, M$ is a plane mirror; $B$ is a very small bright lightbulb that can be treated as a point source of light; and $H$ is an opaque housing that does not transmit light. An observer can stand anywhere along a line $O$ to try to see the image of the lightbulb in the mirror. By using relevant rays of light, determine those locations along the line $O$ from which the image of $B$ is visible and those locations from which it is not visible. Mark the regions along line $O$ accordingly, and explain the reasoning you used in drawing the rays.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
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Problem 61

Figure $35-53$ shows a small object (represented by an arrow) in front of a curved mirror. At the tip of the arrow is a black dot. The mirror is a piece of a sphere. The center of the sphere is marked in the picture with an $x .$ Eyes corresponding to three different observers are shown. For each question, explain how you got your result. Be sure to include a ray diagram as part of your explanation.
(a) How many black dots will the observer at position $A$ see? Where will the dots appear to be? Specify quantitatively how far from the mirror the dots will appear to be and how far off the axis they will be.
(b) How many black dots will the observer at position $B$ see? Explain how you know.
(c) How many black dots will the observer at position $C$ see? Explain how you know.

Averell Hause
Averell Hause
Carnegie Mellon University
06:25

Problem 62

Address each part of this question in two ways: (1) by drawing and interpreting appropriate geometrical diagrams and (2) by appealing to the lens equation and the expression for lateral magnification and demonstrating your result mathematically. If your two approaches do not agree, explain which one is correct and why the other is wrong.
(a) Suppose you are using a camera and wish to have a larger image of a distant object than you are obtaining with the lens currently in use. Would you change to a lens with a longer or a shorter focal length? Explain your reasoning. (Hint: Note that the object distance is essentially fixed.)
(b) Suppose you are using a slide projector and wish to obtain a larger image on the screen. You cannot achieve this by moving the screen farther from the projector because you are already using the entire length of the room. Would you change to a lens with a longer or a shorter focal length than the one you are using? Explain your reasoning. (Hint: Note that the image distance is essentially fixed.)

Carlos Henrique De Lima
Carlos Henrique De Lima
Numerade Educator
07:22

Problem 63

Each of the parts of this problem has a description of an object and an optical device (lens or mirror). A sketch is shown in Fig. $35-54$. For each case, specify whether
- The image is real (R), virtual (V), or no image is formed (N).
- The image is on the same side of the device as the object (S) on the opposite side (O). If there is no image put a null mark $(\varnothing)$.
- If an image is formed, on which side of the system must the observer be in order to see it, left $(-)$ or right $(+) ?$ For each problem you should therefore give three answers (for example, $\mathrm{VO}+$ ). For the mirrors, the center is shown. For the lenses, the focal points are shown. The radius of curvature of the mirrors is $R$, and the focal length of the lenses is $f$.
(a) An object on the right side of a spherical mirror, a distance $s>R$ from the mirror. The mirror is concave toward the object.
(b) An object on the right side of a spherical mirror, a distance $s<R / 2$ from the mirror. The mirror is convex toward the object.
(c) An object on the left side of a spherical mirror, a distance $R>s$ $>R / 2$ from the mirror. The mirror is concave toward the object.
(d) An object on the right side of a convex lens, a distance $s>f$ from the lens.
(e) An object on the left side of a convex lens, a distance $s<f$ from the lens.

Vishal Gupta
Vishal Gupta
Numerade Educator
05:13

Problem 64

In Fig. $35-55$, point $A$ (marked by a circle) is the top of a small object (indicated as an arrow). Near it is a concave lens, as shown. The focal points of the lens are marked with black dots.
(a) Using a ray diagram, show where an image of point $A$ would be formed.
(b) If the focal length of the lens is $8 \mathrm{~cm}$ and the object is $6 \mathrm{~cm}$ from the lens, where will the image be?
(c) If the object is $1 \mathrm{~cm}$ tall, how tall will the image be?
(d) Will the image created by the lens be real or virtual?
(e) Where will you have to be to see the image?

Vishal Gupta
Vishal Gupta
Numerade Educator
00:54

Problem 65

A projector has an arrangement of lenses as shown in Fig. 35-56. A bulb illuminates an object (a slide) and the light then passes through a lens that creates an image on a distant screen as shown.When a sheet of a cardboard is brought up to cover the lower half of the lens, what happens to the image on the screen?
(a) The top half of the image disappears.
(b) The bottom half of the image disappears.
(c) The image remains but is weaker (not as bright).
(d) The image remains unchanged.
(e) The bottom half of the image becomes weaker, the top is unchanged.
(f) The top half of the image becomes weaker, the bottom is unchanged.
(g) Something else happens. (Tell what it is.) Explain your reasoning, drawing whatever rays are needed to make your point clear.

Prem Bijarniya
Prem Bijarniya
Numerade Educator
View

Problem 66

Alice faces a looking glass (mirror) and is standing at a level so that her eyes appear to her to be right at the top of the mirror as shown in Fig. $35-57$. At the position she is standing, she can just see her hands at the bottom of the mirror. If she steps back far enough,
(a) She will eventually be able to see all of herself in the mirror at the same time.
(b) There will be no change in how much of herself she can see.
(c) She will see less of herself as she steps back.
(d) Some other result (explain). Choose the letter of the choice that completes the sentence correctly and explain why you think so with a few sentences and some rays on the diagram.

Victor Salazar
Victor Salazar
Numerade Educator
04:12

Problem 67

Point $O$ in Fig. $35-58$ is a source of light. Two rays from $O$ are shown passing through a thin converging lens and crossing each other at the point marked $C$.
(a) On a copy of the figure on your answer sheet, find the two principal foci of the lens by drawing appropriate rays. Label the foci $\mathrm{F} 1$ and F2. Explain your reasoning.
(b) Suppose the lens is replaced by another lens having the same focal length but a larger diameter. Indicate whether each of the following partial sentences is correctly completed by the phrase greater than $(>)$, less than $(<)$, or the same as $(=)$.
- The distance of the image from the principal axis is _____ it was with the smaller lens.
- The brightness of the image with the large lens is _____ it was with the smaller lens.

Katie Mcalpine
Katie Mcalpine
Numerade Educator
05:48

Problem 68

Figure $35-59$ shows a thin lens (indicated by a gray rectangle) and a coordinate system. The $x$ axis passes through the center of the lens and runs along its axis of symmetry, with the positive $x$ direction indicated by the arrowhead. The lens may be treated as being of negligible thickness and has a focal length $f$. The points $(x, y)=(f, 0)$ and $(-f, 0)$ are marked by black dots.
A small object is placed at the position $(x, 0)$. For each of the four cases (i)-(iv) below, indicate whether the location of the image formed $\left(=x^{\prime}\right)$ is on the positive or negative side of the axis, and closer to the lens than the focal point or farther away.
i. $-f<x<0$
iii. $x<f<0$
ii. $f<0<x$
iv. $0<f<x$
Hint: Your answer should take a form such as $\left(x^{\prime}>f>0\right)$ to indicate that the image is on the positive side of the axis and farther away than the focal point or $\left(0>x^{\prime}>f\right)$ to indicate that the image is on the negative side of the axis between the lens and the focal point. Note that in some cases the focal length specified is negative and in some cases it is positive.

Saikat Chatterjee
Saikat Chatterjee
Numerade Educator