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Essential University Physics

Richard Wolfson

Chapter 31

Images and Optical Instruments - all with Video Answers

Educators


Chapter Questions

02:14

Problem 1

How can you see a virtual image, when it's not "really there"?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:25

Problem 2

Under what circumstances will the image in a concave mirror be the same size as the object?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:04

Problem 3

If you're handed a converging lens, what can you do to estimate its focal length quickly?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:48

Problem 4

A diverging lens always makes a reduced image. Could you use such a lens to start a fire by focusing sunlight? Explain.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:59

Problem 5

Is there any limit to the temperature you can achieve by focusing sunlight? (Hint: Think about the second law of thermodynamics.)

Mayukh Banik
Mayukh Banik
Numerade Educator
06:16

Problem 6

Can a concave mirror make a reduced real image? A reduced virtual image? An enlarged real image? An enlarged virtual image? Specify conditions for each possible image.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:03

Problem 7

If you placed a screen at the location of a virtual image, would the image appear on the screen? Why or why not?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:33

Problem 8

If you look into the bowl of a metal spoon, you see yourself upside down. Flip the spoon so you're looking at the back side, and now you're right-side up. Explain.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:13

Problem 9

Is the image on a movie screen real or virtual? How do you know?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:14

Problem 10

Does a fish in a spherical bowl appear larger or smaller than it actually is?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:42

Problem 11

A block of ice contains a hollow, air-filled space in the shape of a double-convex lens. Describe the optical behavior of this space.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:12

Problem 12

The refractive index of the human cornea is about $1.4 .$ If you can see clearly in air, why can't you see clearly underwater? Why do goggles help?

Mayukh Banik
Mayukh Banik
Numerade Educator
00:59

Problem 13

Do you want a long or short focal length for a telescope's objective lens? What about a microscope's?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:08

Problem 14

Give at least three reasons why reflecting telescopes are superior to refractors.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:50

Problem 15

A shoe store uses small floor-level mirrors to let customers view prospective purchases. At what angle should such a mirror be inclined so that a person standing $50 \mathrm{cm}$ from the mirror with eyes $140 \mathrm{cm}$ off the floor can see her feet?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:40

Problem 16

A candle is on the axis of a $15-\mathrm{cm}$ -focal-length concave mirror, $36 \mathrm{cm}$ from the mirror. (a) Where is its image? (b) How do the image and object sizes compare? (c) Is the image real or virtual?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:57

Problem 17

An object is five focal lengths from a concave mirror. (a) How do the object and image heights compare? (b) Is the image upright or inverted?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:36

Problem 18

A virtual image is located $40 \mathrm{cm}$ behind a concave mirror with focal length $18 \mathrm{cm} .$ (a) Where is the object? (b) By how much is the image magnified?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:28

Problem 19

(a) Where on the axis of a concave mirror would you place an object to get a half-size image? (b) Where will the image be located? (c) Will the image be real or virtual?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:15

Problem 20

A lightbulb is $56 \mathrm{cm}$ from a convex lens. Its image appears on a screen $31 \mathrm{cm}$ from the lens, on the other side. Find (a) the lens's focal length and (b) how much the image is enlarged or reduced.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:34

Problem 21

By what factor is the image magnified for an object 1.5 focal lengths from a converging lens? Is the image upright or inverted?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:50

Problem 22

A lens with 50 -cm focal length produces a real image the same size as the object. How far from the lens are image and object?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:37

Problem 23

By holding a magnifying glass $25 \mathrm{cm}$ from your desk lamp, you can focus an image of the lamp's bulb on a wall $1.6 \mathrm{m}$ from the lamp. What's the focal length of your magnifying glass?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:27

Problem 24

A real image is four times as far from a lens as is the object. What's the object distance, measured in focal lengths?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:04

Problem 25

A magnifying glass enlarges print by $50 \%$ when it's $9.0 \mathrm{cm}$ from a page. What's its focal length?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:59

Problem 26

You're writing specifications for a new line of magnifying glasses that have double-convex lenses with equal 32 -cm curvature radii, made from glass with $n=1.52 .$ What do you list for the focal length?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:31

Problem 27

You're standing in a wading pool and your feet appear to be $30 \mathrm{cm}$ below the surface. How deep is the pool?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:01

Problem 28

The bottom of a swimming pool looks to be $1.5 \mathrm{m}$ below the surface. Find the pool's actual depth.

Mayukh Banik
Mayukh Banik
Numerade Educator
05:45

Problem 29

A tiny insect is trapped $1.0 \mathrm{mm}$ from the center of a spherical dewdrop $4.0 \mathrm{mm}$ in diameter. As you look straight into the drop, what's the insect's apparent distance from the drop's surface?

Mayukh Banik
Mayukh Banik
Numerade Educator
05:00

Problem 30

You're underwater, looking through a spherical air bubble (Fig. 31.35 ). What's its actual diameter if it appears, along your line of sight, to be $1.5 \mathrm{cm}$ in diameter?

Mayukh Banik
Mayukh Banik
Numerade Educator
View

Problem 31

You have to hold a book $55 \mathrm{cm}$ from your eyes for the print to be in focus. What power lens would correct your farsightedness?

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
03:24

Problem 32

What focal length should you specify if you want a magnifying glass with angular magnification $3.2 ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:12

Problem 33

You're an optometrist helping a nearsighted patient who claims he can't see clearly beyond $80 \mathrm{cm} .$ Prescribe a lens that will put the images of distant objects at $80 \mathrm{cm},$ giving your patient clear vision at all distances beyond the normal near point.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:32

Problem 34

A particular eye has a focal length of $2.0 \mathrm{cm}$ instead of the $2.2 \mathrm{cm}$ that would put a sharply focused image on the retina. (a) Is this eye nearsighted or farsighted? (b) What corrective lens is needed?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:52

Problem 35

A compound microscope has objective and eyepiece focal lengths of $6.1 \mathrm{mm}$ and $1.7 \mathrm{cm},$ respectively. If the lenses are $8.3 \mathrm{cm}$ apart, what is the instrument's magnification?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:20

Problem 36

(a) Find the focal length of a concave mirror if an object placed $38.4 \mathrm{cm}$ in front of the mirror has a real image $55.7 \mathrm{cm}$ from the mirror. (b) Where and what type will the image be if the object is moved to a point $16.0 \mathrm{cm}$ from the mirror?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:00

Problem 37

A 12 -mm-high object is $10 \mathrm{cm}$ from a concave mirror with focal length $17 \mathrm{cm} .$ (a) Where is the image, (b) how high is it, and (c) what type is it?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:48

Problem 38

Repeat Problem 37 for a convex mirror, assuming all numbers stay the same.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:11

Problem 39

An object's image in a 27 -cm-focal-length concave mirror is upright and magnified by a factor of $3 .$ Where is the object?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:25

Problem 40

You're asked to design a concave mirror that will produce a virtual image, enlarged 1.8 times, of an object $22 \mathrm{cm}$ from the mirror. What do you specify for the mirror's curvature radius?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:43

Problem 41

Viewed from Earth, the Moon subtends an angle of $0.52^{\circ}$ in the sky. What will be the physical size of the Moon's image formed by either of the twin Keck telescopes, with 10 -m-diameter mirrors and 17.5 -m focal length?

Kristela Garcia
Kristela Garcia
Numerade Educator
03:53

Problem 42

At what two distances could you place an object from a $45-\mathrm{cm}-$ focal-length concave mirror to get an image 1.5 times the object's size?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:31

Problem 43

LCD projectors commonly used for computer and video projection create an image on a small LCD display (see Application on page 369 ). The display is mounted before a lens and illuminated from behind. In a projector using a $7.50-\mathrm{cm}$ -focal-length convex lens, where should the LCD display be located so the projected image is focused on a screen $6.30 \mathrm{m}$ from the lens?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:22

Problem 44

An object $15 \mathrm{cm}$ from a concave mirror has a virtual image magnified 2.5 times. What's the mirror's focal length?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:24

Problem 45

How far from a page should you hold a lens with 32 -cm focal length in order to see the print magnified 1.6 times?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:55

Problem 46

A converging lens has focal length $4.0 \mathrm{cm} .$ A 1.0 -cm-high arrow is located $7.0 \mathrm{cm}$ from the lens with its lowest point $5.0 \mathrm{mm}$ above the lens axis. Make a full-scale ray-tracing diagram to locate both ends of the image. Confirm using the lens equation.

Ajay Singhal
Ajay Singhal
Numerade Educator
04:52

Problem 47

A lens has focal length $f=35 \mathrm{cm} .$ Find the type and height of the image produced when a 2.2 -cm-high object is placed at distances (a) $f+10 \mathrm{cm}$ and (b) $f-10 \mathrm{cm} .$

Mayukh Banik
Mayukh Banik
Numerade Educator
03:09

Problem 48

How far apart are the object and image produced by a converging lens with 35 -cm focal length when the object is (a) $40 \mathrm{cm}$ and (b) $30 \mathrm{cm}$ from the lens?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:34

Problem 49

A candle and a screen are $70 \mathrm{cm}$ apart. Find two points between candle and screen where you could put a convex lens with $17-\mathrm{cm}$ focal length to give a sharp image of the candle on the screen.

Mayukh Banik
Mayukh Banik
Numerade Educator
04:15

Problem 50

The cornea of the human eye has refractive index $1.38,$ while the eye's lens has a graduated index in the range 1.38 to $1.40 ;$ use 1.39 for this problem. For the aqueous humor between cornea and lens, $n=1.34 .$ Find the angle through which light is deflected at the first surface of (a) the cornea and (b) the lens, if it's incident at $20^{\circ}$ to the normal at each surface. Your result shows that the cornea is the dominant refractive element in the eye.

Julie Farhm
Julie Farhm
Numerade Educator
02:11

Problem 51

How far from a $25-\mathrm{cm}$ -focal-length lens should you place an object to get an upright image magnified 1.8 times?

Mayukh Banik
Mayukh Banik
Numerade Educator
07:34

Problem 52

An object and its lens-produced real image are $2.4 \mathrm{m}$ apart. If the lens has $55-\mathrm{cm}$ focal length, what are the possible values for the object distance and magnification?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:15

Problem 53

An object is $68 \mathrm{cm}$ from a plano-convex lens whose curved side has curvature radius $26 \mathrm{cm} .$ The refractive index of the lens is 1.62. Where is the image, and what type is it?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:41

Problem 54

Use Equation 31.6 to show that an object at the center of a glass sphere will appear to be its actual distance-one radius-from the edge. Draw a ray diagram showing why this makes sense.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:53

Problem 55

Rework Example 31.4 for a fish $15.0 \mathrm{cm}$ from the far wall of the tank.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:08

Problem 56

Consider the inverse of Example 31.4: You're inside a $70.0-\mathrm{cm}-$ diameter hollow tube containing air, and the tip of your nose is $15.0 \mathrm{cm}$ from the tube's wall. The tube is immersed in water, and a fish looks in. To the fish, what's the apparent distance from your nose to the tube wall?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:35

Problem 57

Two specks of dirt are trapped in a crystal ball, one at the center and the other halfway to the surface. If you peer into the ball on a line joining the two specks, the outer one appears to be only one-third of the way to the other. Find the refractive index of the ball.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:11

Problem 58

A contact lens is in the shape of a convex meniscus (see Fig. 31.25 ). The inner surface is curved to fit the eye, with curvature radius $7.80 \mathrm{mm}$. The lens is made from plastic with refractive index $n=1.56 .$ If it has a $44.4-\mathrm{cm}$ focal length, what's the curvature radius of its outer surface?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:03

Problem 59

For what refractive index would the focal length of a plano-convex lens be equal to the curvature radius of its one curved surface?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:28

Problem 60

An object is $28 \mathrm{cm}$ from a double-convex lens with $n=1.5$ and curvature radii $35 \mathrm{cm}$ and $55 \mathrm{cm} .$ Where is the image, and what type is it?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:47

Problem 61

You're an optician who's been asked to design a new replacement lens for cataract patients. The lens must be $5.5 \mathrm{mm}$ in diameter, with focal length $17 \mathrm{mm},$ and it can't be thicker than $0.8 \mathrm{mm} .$ For the lens material, you have a choice of plastic with refractive index 1.49 or more expensive silicone with $n=1.58 .$ Which material do you choose, and why?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:29

Problem 62

A double-convex lens with equal 28.5 -cm curvature radii is made from glass with refractive indices $n_{\mathrm{red}}=1.512$ and $n_{\text {violet }}=1.547 .$ If a point source of white light is located on the lens axis at $75.0 \mathrm{cm}$ from the lens, over what distance will its visible image be smeared?

Mayukh Banik
Mayukh Banik
Numerade Educator
05:16

Problem 63

An object placed $17.5 \mathrm{cm}$ from a convex lens of glass with $n=1.524$ forms a virtual image twice the object's size. If the lens is replaced with an identically shaped one made of diamond, (a) what type of image will appear and (b) what will be its magnification?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:41

Problem 64

You're taking a photography class, working with a camera whose zoom lens covers the focal-length range $38 \mathrm{mm}-110 \mathrm{mm}$. Your instructor asks you to compare the sizes of the images of a distant object when photographed at the two zoom extremes. Your answer?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:57

Problem 65

A camera can normally focus as close as $60 \mathrm{cm},$ but it has provisions for mounting additional lenses just in front of the main lens to provide close-up capability. What type and power of auxiliary lens will allow the camera to focus as close as $20 \mathrm{cm} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
02:28

Problem 66

A 300 -power compound microscope has a 4.5 -mm-focal-length objective lens. If the distance from objective to eyepiece is $10 \mathrm{cm}$ what should be the focal length of the eyepiece?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:16

Problem 67

To the unaided eye, Jupiter has an angular diameter of 50 arcseconds. What will its angular size be when viewed through a 1-mm-focal-length refracting telescope with a 40-mm-focal-length eyepiece?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:29

Problem 68

A Cassegrain telescope like that shown in Fig. $31.34 b$ has $1.0-\mathrm{m}$ focal length, and the convex secondary mirror is located $0.85 \mathrm{m}$ from the primary. What should be the focal length of the secondary in order to put the final image $0.12 \mathrm{m}$ behind the front surface of the primary mirror?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:53

Problem 69

You stand with your nose $6.0 \mathrm{cm}$ from the surface of a reflecting ball, and your nose's image appears three-quarters full size. What's the ball's diameter?

Mayukh Banik
Mayukh Banik
Numerade Educator
06:04

Problem 70

A contact lens prescription calls for +2.25 -diopter lenses with inner curvature radius $8.6 \mathrm{mm}$ to fit the patient's cornea. (a) If the lenses are plastic with $n=1.56,$ what should be the outer curvature radius? (b) With these lenses, the patient comfortably reads a newspaper $30 \mathrm{cm}$ from her eyes. Where's the image as viewed through the lenses?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:15

Problem 71

Show that placing a 1 -diopter lens in front of a 2 -diopter lens gives the equivalent of a single 3 -diopter lens (i.e., the powers of closely spaced lenses add).

Mayukh Banik
Mayukh Banik
Numerade Educator
01:06

Problem 72

Derive an expression for the thickness $t$ of a plano-convex lens with diameter $d$, focal length $f$, and refractive index $n$.

Mayukh Banik
Mayukh Banik
Numerade Educator
06:26

Problem 73

Show that identical objects placed equal distances on either side of the focal point of a concave mirror or converging lens produce images of equal size. Are the images of the same type?

Julie Farhm
Julie Farhm
Numerade Educator
01:52

Problem 74

Generalize the derivation of the lensmaker's formula (Equation 31.7 ) to show that a lens of refractive index $n_{\text {lens }}$ in an external medium with index $n_{\mathrm{ext}}$ has focal length given by $$\frac{1}{f}=\left(\frac{n_{\mathrm{lens}}}{n_{\mathrm{ext}}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$$

Mayukh Banik
Mayukh Banik
Numerade Educator
06:04

Problem 75

Draw a diagram like Fig. $31.10,$ but showing a ray from the arrowhead through the center of curvature. Using the fact that this ray reflects back on itself, draw similar triangles with object and image as their vertical sides, and show that the center of curvature is twice as far from the mirror as the focal point-that is, $R=2 f,$ with $R$ the curvature radius.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:58

Problem 76

Galileo's first telescope used the arrangement shown in Fig. $31.36,$ with a double-concave eyepiece slightly before the focus of the objective lens. Use ray tracing to show that this design gives an upright image, which makes the Galilean telescope useful in terrestrial observing. (FIGURE CAN'T COPY)

Mayukh Banik
Mayukh Banik
Numerade Educator
01:05

Problem 77

The maximum magnification of a simple magnifier occurs with the image at the 25 -cm near point. Show that the angular magnification is $m=1+(25 \mathrm{cm} / \mathrm{f}),$ where $f$ is the focal length.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:45

Problem 78

Chromatic aberration results from variation of the refractive index with wavelength. Starting with the lensmaker's formula, find an expression for the fractional change $d f / f$ in the focal length of a thin lens in terms of the change $d n$ in refractive index.

Mayukh Banik
Mayukh Banik
Numerade Educator
10:50

Problem 79

For visible wavelengths, the refractive index of the polycarbonate plastic widely used in eyeglasses is given approximately by $n(\lambda)=b+c / \lambda^{2},$ where $b=1.55$ and $c=11,500 \mathrm{nm}^{2} .$ (a) Find an expression for the change in refractive index $d n$ corresponding to a small wavelength change $d \lambda$. (b) Use the results of part (a) and of Problem 78 to determine the variation $d f$ in focal length for a +2.25 -diopter polycarbonate lens, over a wavelength range of 10.0 nm centered on $589 \mathrm{nm}$.

Mayukh Banik
Mayukh Banik
Numerade Educator
03:43

Problem 80

The table below shows measurements of magnification versus object distance for a lens. Determine a quantity that, when you plot object distance against it, should give a straight line. Make your plot, establish a best-fit line, and use your line to find the focal length of the lens. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Object distance, } s(\mathrm{cm}) & 10.1 & 29.2 & 51.6 & 78.3 & 98.9 \\\hline \text { Magnification, } M & 1.31 & 4.77 & -4.38 & -1.27 & -0.724 \\\hline\end{array}$$

Jacob Shpiece
Jacob Shpiece
Numerade Educator
01:43

Problem 81

The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by $f$ -ratio, also called the $f$ -number, defined as the ratio of focal length $f$ to lens diameter $d$. Thus an $f / 2.8$ lens, for example, has diameter $d=f / 2.8 .$ The actual amount of light a lens admits depends on its area $A$, but the inverse-square law shows that the light intensity at the camera's imaging sensor is proportional to $A / f^{2} .$ Most cameras have an adjustable iris that obscures part of the lens to change the f-ratio in response to available light. Point-and-shoot cameras adjust the f-ratio automatically, but serious photographers use their camera's manual f-ratio adjustment (Fig. 31.37 ). Stopping down is the photographer's term for reducing the lens area using the adjustable iris. A 35 -mm camera lens. The numbers from 22 to 2.8 at the bottom are values for the f-ratio, $f / d .$ Turning the ring with these numbers adjusts the iris that covers the outer part of the lens, thus changing the f-ratio. (FIGURE CAN'T COPY)
Zooming your camera's lens for telephoto shots increases the focal length. With no change in the lens area, this will
a. increase the f-ratio and increase the lens speed.
b. decrease the f-ratio and decrease the lens speed.
c. increase the $\mathrm{f}$ -ratio and decrease the lens speed.
d. not change the $\mathrm{f}$ -ratio or the lens speed.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:58

Problem 82

The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by $f$ -ratio, also called the $f$ -number, defined as the ratio of focal length $f$ to lens diameter $d$. Thus an $f / 2.8$ lens, for example, has diameter $d=f / 2.8 .$ The actual amount of light a lens admits depends on its area $A$, but the inverse-square law shows that the light intensity at the camera's imaging sensor is proportional to $A / f^{2} .$ Most cameras have an adjustable iris that obscures part of the lens to change the f-ratio in response to available light. Point-and-shoot cameras adjust the f-ratio automatically, but serious photographers use their camera's manual f-ratio adjustment (Fig. 31.37 ). Stopping down is the photographer's term for reducing the lens area using the adjustable iris. A 35 -mm camera lens. The numbers from 22 to 2.8 at the bottom are values for the f-ratio, $f / d .$ Turning the ring with these numbers adjusts the iris that covers the outer part of the lens, thus changing the f-ratio. (FIGURE CAN'T COPY)
Increasing the f-ratio from 2.8 to 5.6.
a. decreases the light admitted by a factor of 2.
b. decreases the light admitted by a factor of 4.
c. increases the light admitted by a factor of 2.
d. increases the light admitted by a factor of 4.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:22

Problem 83

The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by $f$ -ratio, also called the $f$ -number, defined as the ratio of focal length $f$ to lens diameter $d$. Thus an $f / 2.8$ lens, for example, has diameter $d=f / 2.8 .$ The actual amount of light a lens admits depends on its area $A$, but the inverse-square law shows that the light intensity at the camera's imaging sensor is proportional to $A / f^{2} .$ Most cameras have an adjustable iris that obscures part of the lens to change the f-ratio in response to available light. Point-and-shoot cameras adjust the f-ratio automatically, but serious photographers use their camera's manual f-ratio adjustment (Fig. 31.37 ). Stopping down is the photographer's term for reducing the lens area using the adjustable iris. A 35 -mm camera lens. The numbers from 22 to 2.8 at the bottom are values for the f-ratio, $f / d .$ Turning the ring with these numbers adjusts the iris that covers the outer part of the lens, thus changing the f-ratio. (FIGURE CAN'T COPY)
You're given two lenses with different diameters. Knowing nothing else, you can conclude that
a. the larger lens is faster.
b. the smaller lens has the shorter focal length.
c. the smaller lens suffers less spherical aberration.
d. none of the above

Mayukh Banik
Mayukh Banik
Numerade Educator
01:03

Problem 84

The speed of a camera lens measures its ability to photograph in dim light. Speed is characterized by $f$ -ratio, also called the $f$ -number, defined as the ratio of focal length $f$ to lens diameter $d$. Thus an $f / 2.8$ lens, for example, has diameter $d=f / 2.8 .$ The actual amount of light a lens admits depends on its area $A$, but the inverse-square law shows that the light intensity at the camera's imaging sensor is proportional to $A / f^{2} .$ Most cameras have an adjustable iris that obscures part of the lens to change the f-ratio in response to available light. Point-and-shoot cameras adjust the f-ratio automatically, but serious photographers use their camera's manual f-ratio adjustment (Fig. 31.37 ). Stopping down is the photographer's term for reducing the lens area using the adjustable iris. A 35 -mm camera lens. The numbers from 22 to 2.8 at the bottom are values for the f-ratio, $f / d .$ Turning the ring with these numbers adjusts the iris that covers the outer part of the lens, thus changing the f-ratio. (FIGURE CAN'T COPY)
If a lens suffers from spherical aberration, stopping down will
a. worsen the focus.
b. improve the focus.
c. not affect the focus.

Mayukh Banik
Mayukh Banik
Numerade Educator