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College Physics With an Integrated Approach to Forces and Kinematics

Alan Giambattista, Betty McCarthy Richardson , Robert C. Richardson

Chapter 24

Optical Instruments - all with Video Answers

Educators

Chapter Questions

02:32

Problem 1

An object is placed $12.0 \mathrm{~cm}$ in front of a lens of focal length $5.0 \mathrm{~cm}$. Another lens of focal length $4.0 \mathrm{~cm}$ is placed $2.0 \mathrm{~cm}$ past the first lens. (a) Where is the final image? Is it real or virtual? (b) What is the overall magnification?

Narayan Hari
Narayan Hari
Numerade Educator
05:23

Problem 2

A converging lens and a diverging lens, separated by a distance of $30.0 \mathrm{~cm}$, are used in combination. The converging lens has a focal length of $15.0 \mathrm{~cm}$. The diverging lens is of unknown focal length. An object is placed $20.0 \mathrm{~cm}$ in front of the converging lens; the final image is virtual and is formed $12.0 \mathrm{~cm}$ before the diverging lens. What is the focal length of the diverging lens?

Elizabeth Clark
Elizabeth Clark
Numerade Educator
04:48

Problem 3

Two converging lenses are placed $88.0 \mathrm{~cm}$ apart. An object is placed $1.100 \mathrm{~m}$ to the left of the first lens, which has a focal length of $25.0 \mathrm{~cm}$. The final image is located $15.0 \mathrm{~cm}$ to the right of the second lens. (a) What is the focal length of the second lens? (b) What is the total magnification?

Daniel Alva
Daniel Alva
Numerade Educator
03:05

Problem 4

A converging lens with a focal length of $15.0 \mathrm{~cm}$ and a diverging lens are placed $25.0 \mathrm{~cm}$ apart, with the converging lens on the left. A $2.00-\mathrm{cm}$ -high object is placed $22.0 \mathrm{~cm}$ to the left of the converging lens. The final image is $34.0 \mathrm{~cm}$ to the left of the converging lens.
(a) What is the focal length of the diverging lens?
(b) What is the height of the final image? (c) Is the final image upright or inverted?

Mayukh Banik
Mayukh Banik
Numerade Educator
08:43

Problem 5

An object is located $16.0 \mathrm{~cm}$ in front of a converging lens with focal length $12.0 \mathrm{~cm}$. To the right of the converging lens, separated by a distance of $20.0 \mathrm{~cm}$, is a diverging lens of focal length $-10.0 \mathrm{~cm} .$ Find the location of the final image by ray tracing and verify using the lens equations.

Daniel Alva
Daniel Alva
Numerade Educator
09:49

Problem 6

An object is located $10.0 \mathrm{~cm}$ in front of a converging lens with focal length $12.0 \mathrm{~cm}$. To the right of the converging lens is a second converging lens, $30.0 \mathrm{~cm}$ from the first lens, of focal length $10.0 \mathrm{~cm}$. Find the location of the final image by ray tracing and verify by using the lens equations.

Elizabeth Clark
Elizabeth Clark
Numerade Educator
04:19

Problem 7

Verify the locations and sizes of the images formed by the two lenses in Fig. 24.1b using the lens equation and the following data: $f_{1}=+4.00 \mathrm{~cm}, f_{2}=-2.00 \mathrm{~cm}, s=$
$8.00 \mathrm{~cm}$ (where $s$ is the distance between the lenses), $p_{1}=+6.00 \mathrm{~cm}$, and $h=2.00 \mathrm{~mm} .$ (Note that the vertical scale is different from the horizontal scale.)

Manish Jain
Manish Jain
Numerade Educator
00:24

Problem 8

Show that if two thin lenses are close together $(s$, the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length $f_{\mathrm{eq}} .$ Find the value of $f_{\mathrm{eq}}$ in terms of $f_{1}$ and $f_{2}$.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:10

Problem 9

You would like to project an upright image at a position $32.0 \mathrm{~cm}$ to the right of an object. You have a converging lens with focal length $3.70 \mathrm{~cm}$ located $6.00 \mathrm{~cm}$ to the right of the object. By placing a second lens at $24.65 \mathrm{~cm}$ to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is $12.0 \mathrm{~cm}$ high, what is the image height?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:50

Problem 10

You plan to project an inverted image $30.0 \mathrm{~cm}$ to the right of an object. You have a diverging lens with focal length $-4.00 \mathrm{~cm}$ located $6.00 \mathrm{~cm}$ to the right of the object. Once you put a second lens at $18.0 \mathrm{~cm}$ to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is $12.0 \mathrm{~cm}$ high, what is the image height?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:02

Problem 11

A camera uses a $200.0$ -mm focal length telephoto lens to take pictures from a distance of infinity to as close as $2.0 \mathrm{~m}$. What are the minimum and maximum distances from the lens to the film?

Daniel Alva
Daniel Alva
Numerade Educator
05:45

Problem 12

Kim says that she was less than $10 \mathrm{ft}$ away from the president when she took a picture of him with her 50-mm focal length camera lens. The picture shows the upper half of the president's body (or $3.0 \mathrm{ft}$ of his total height). On the negative of the film, this part of his body is $18 \mathrm{~mm}$ high. How close was Kim to the president when she took the picture?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
05:29

Problem 13

A statue is $6.6 \mathrm{~m}$ from the opening of a pinhole camera, and the screen is $2.8 \mathrm{~m}$ from the pinhole. (a) Is the image erect or inverted? (b) What is the magnification of the image? (c) To get a brighter image, we enlarge the pinhole to let more light through, but then the image looks blurry. Why? (d) To admit more light and still have a sharp image, we replace the pinhole with a lens. Should it be a converging or diverging lens? Why? (e) What should the focal length of the lens be?

Daniel Alva
Daniel Alva
Numerade Educator
04:30

Problem 14

Esperanza uses a 35-mm camera with a standard lens of focal length $50.0 \mathrm{~mm}$ to take a photo of her son Carlos, who is $1.2 \mathrm{~m}$ tall and standing $3.0 \mathrm{~m}$ away. (a) What must be the distance between the lens and the film to get a properly focused picture? (b) What is the magnification of the image? (c) What is the height of the image of Carlos on the film?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
07:12

Problem 15

A person on a safari wants to take a photograph of a hippopotamus from a distance of $75.0 \mathrm{~m}$. The animal is $4.00 \mathrm{~m}$ long and its image is to be $1.20 \mathrm{~cm}$ long on the film. (a) What focal length lens should be used?
(b) What would be the size of the image if a lens of 50.0-mm focal length were used? (c) How close to the hippo would the person have to be to capture a $1.20-\mathrm{cm}-$ long image using a 50.0-mm lens?

Daniel Alva
Daniel Alva
Numerade Educator
05:03

Problem 16

Jim plans to take a picture of McGraw Tower with a 35$\mathrm{mm}$ camera that has a $50.0$ -mm focal length lens. A roll of $35-\mathrm{mm}$ film is $35 \mathrm{~mm}$ wide; each frame is $24 \mathrm{~mm}$ by $36 \mathrm{~mm}$. The tower has a height of $52 \mathrm{~m}$ and Jim wants a detailed close-up picture. How close to the tower should Jim be to capture the largest possible image of the entire tower on his film?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
03:54

Problem 17

A photographer wishes to take a photograph of the Eiffel Tower $(300 \mathrm{~m}$ tall $)$ from across the Seine River, a distance of $300 \mathrm{~m}$ from the tower. What focal length lens should she use to get an image that is $20 \mathrm{~mm}$ high on the film?

Daniel Alva
Daniel Alva
Numerade Educator
03:13

Problem 18

If a slide of width $36 \mathrm{~mm}$ (see the figure with Problem 16) is to be projected onto a screen of $1.50 \mathrm{~m}$ width located $12.0 \mathrm{~m}$ from the projector, what focal length lens is required to fill the width of the screen?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
04:08

Problem 19

A slide projector has a lens of focal length $12 \mathrm{~cm}$. Each slide is $24 \mathrm{~mm}$ by $36 \mathrm{~mm}$ (see the figure with Problem 16). The projector is used in a room where the screen is $5.0 \mathrm{~m}$ from the projector. How large must the screen be?

Daniel Alva
Daniel Alva
Numerade Educator
05:24

Problem 20

A converging lens with focal length $3.00 \mathrm{~cm}$ is placed $4.00 \mathrm{~cm}$ to the right of an object. A diverging lens with focal length $-5.00 \mathrm{~cm}$ is placed $17.0 \mathrm{~cm}$ to the right of the converging lens. (a) At what location(s), if any, can you place a screen in order to display an image? (b) Repeat part (a) for the case where the lenses are separated by $10.0 \mathrm{~cm}$.

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
08:55

Problem 21

A converging lens with a focal length of $3.00 \mathrm{~cm}$ is placed $24.00 \mathrm{~cm}$ to the right of a concave mirror with a focal length of $4.00 \mathrm{~cm}$. An object is placed between the mirror and the lens, $6.00 \mathrm{~cm}$ to the right of the mirror and $18.00 \mathrm{~cm}$ to the left of the lens. Name threeplaces where you could find an image of this object. For each image tell whether it is inverted or upright and give the total magnification.

Daniel Alva
Daniel Alva
Numerade Educator
01:59

Problem 22

Assume that the distance from the cornea-lens system to the retina is $2.0 \mathrm{~cm}$ and the normal near point is $25 \mathrm{~cm}$.
If the distance from the lens system (cornea + lens) to the retina is $2.00 \mathrm{~cm}$, show that the focal length of the lens system must vary between $1.85 \mathrm{~cm}$ and $2.00 \mathrm{~cm}$ to see objects from $25.0 \mathrm{~cm}$ to infinity.

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
04:57

Problem 23

Suppose that the lens system (cornea + lens) in a particular eye has a focal length that can vary between $1.85 \mathrm{~cm}$ and $2.00 \mathrm{~cm}$, but the distance from the lens system to the retina is only $1.90 \mathrm{~cm}$. (a) Is this eye nearsighted or farsighted? Explain. (b) What range of distances can the eye see clearly without corrective lenses?

Daniel Alva
Daniel Alva
Numerade Educator
01:43

Problem 24

Assume that the distance from the cornea-lens system to the retina is $2.0 \mathrm{~cm}$ and the normal near point is $25 \mathrm{~cm}$.
If Michaela needs to wear reading glasses with refractive power of $+3.0 \mathrm{D}$, what is her uncorrected near point? Neglect the distance between the glasses and the eye.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
02:06

Problem 25

Assume that the distance from the cornea-lens system to the retina is $2.0 \mathrm{~cm}$ and the normal near point is $25 \mathrm{~cm}$.
The uncorrected far point of Colin's eye is $2.0 \mathrm{~m}$. What refractive power contact lens enables him to clearly distinguish objects at large distances?

Daniel Alva
Daniel Alva
Numerade Educator
00:53

Problem 26

Assume that the distance from the cornea-lens system to the retina is $2.0 \mathrm{~cm}$ and the normal near point is $25 \mathrm{~cm}$.
The distance from the lens system (cornea + lens) of a particular eye to the retina is $1.75 \mathrm{~cm}$. What is the focal length of the lens system when the eye produces a clear image of an object $25.0 \mathrm{~cm}$ away?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
12:58

Problem 27

Assume that the distance from the cornea-lens system to the retina is $2.0 \mathrm{~cm}$ and the normal near point is $25 \mathrm{~cm}$.
A nearsighted man cannot clearly see objects more than $2.0 \mathrm{~m}$ away. The distance from the lens of the eye to the retina is $2.0 \mathrm{~cm}$, and the eye's power of accommodation is $4.0 \mathrm{D}$ (the focal length of the cornea-lens system increases by a maximum of $4.0 \mathrm{D}$ over its relaxed focal length when accommodating for nearby objects). (a) As an amateur optometrist, what corrective eyeglass lenses would you prescribe to enable him to clearly see distant objects? Assume the corrective lenses are $2.0 \mathrm{~cm}$ from the eyes. (b) Find the nearest object he can see clearly with and without his glasses.

Daniel Alva
Daniel Alva
Numerade Educator
02:33

Problem 28

Assume that the distance from the cornea-lens system to the retina is $2.0 \mathrm{~cm}$ and the normal near point is $25 \mathrm{~cm}$.
Anne is farsighted; the nearest object she can see clearly without corrective lenses is $2.0 \mathrm{~m}$ away. It is $1.8 \mathrm{~cm}$ from the lens of her eye to the retina. (a) Sketch a ray diagram to show (qualitatively) what happens when she tries to look at something closer than $2.0 \mathrm{~m}$ without corrective lenses. (b) What should the focal length of her contact lenses be so that she can see clearly objects as close as $20.0 \mathrm{~cm}$ from her eye?

DM
Debra Mangion
Numerade Educator
02:47

Problem 29

Thomas wants to use his $5.5$ -D reading glasses as a simple magnifier. What is the angular magnification of this lens when Thomas's eye is relaxed?

Daniel Alva
Daniel Alva
Numerade Educator
01:45

Problem 30

(a) What is the focal length of a magnifying glass that gives an angular magnification of $8.0$ when the image is at infinity? (b) How far must the object be from the lens? Assume the lens is held close to the eye.

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
02:19

Problem 31

Keesha is looking at a beetle with a magnifying glass. She wants to see an upright, enlarged image at a distance of $25 \mathrm{~cm}$. The focal length of the magnifying glass is $+5.0 \mathrm{~cm}$. Assume that Keesha's eye is close to the magnifying glass. (a) What should be the distance between the magnifying glass and the beetle? (b) What is the angular magnification?

DM
Debra Mangion
Numerade Educator
04:27

Problem 32

Callum is examining a square stamp of side $3.00 \mathrm{~cm}$ with a magnifying glass of refractive power $+40.0 \mathrm{D}$. The magnifier forms an image of the stamp at a distance of $25.0 \mathrm{~cm}$. Assume that Callum's eye is close to the magnifying glass. (a) What is the distance between the stamp and the magnifier? (b) What is the angular magnification?
(c) How large is the image formed by the magnifier?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
06:17

Problem 33

A simple magnifying glass can focus sunlight enough to heat up paper or dry grass and start a fire. A magnifying glass with a diameter of $4.0 \mathrm{~cm}$ has a focal length of $6.0 \mathrm{~cm}$. (a) Using the information found on the inside back cover of the book, estimate the size of the image of the Sun when the magnifying glass focuses the image to its smallest size. (b) If the intensity of the Sun falling on the magnifying glass is $0.85 \mathrm{~kW} / \mathrm{m}^{2}$, what is the intensity of the image of the Sun?

Daniel Alva
Daniel Alva
Numerade Educator
04:25

Problem 34

An insect that is $5.00 \mathrm{~mm}$ long is placed $10.0 \mathrm{~cm}$ from a converging lens with a focal length of $12.0 \mathrm{~cm}$. (a) What is the position of the image? (b) What is the size of the image? (c) Is the image upright or inverted? (d) Is the image real or virtual? (e) What is the angular magnification if the lens is close to the eye?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
03:07

Problem 35

A simple magnifier gives the maximum angular magnification when it forms a virtual image at the near point of the eye instead of at infinity. For simplicity, assume that the magnifier is right up against the eye, so that distances from the magnifier are approximately the same as distances from the eye. (a) For a magnifier with focal length $f$, find the object distance $p$ such that the image is formed at the near point, a distance $N$ from the lens. (b) Show that the angular size of this image as seen by the eye is
$$
\theta=\frac{h(N+f)}{N f}
$$
where $h$ is the height of the object. [Hint: Refer to Fig. 24.15.] (c) Now find the angular magnification and compare it to the angular magnification when the virtual image is at infinity.

Narayan Hari
Narayan Hari
Numerade Educator
04:12

Problem 36

The figure shows a schematic diagram of a microscope. For the object and image locations shown, which of the points $(A, B, C$, or $D)$ represents a focal point of the eyepiece? Draw a ray diagram.

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
04:12

Problem 37

The eyepiece of a microscope has a focal length of $1.25 \mathrm{~cm}$ and the objective lens focal length is $1.44 \mathrm{~cm}$.
(a) If the tube length is $18.0 \mathrm{~cm}$, what is the angular magnification of the microscope? (b) What objective focal length would be required to double this magnification?

Daniel Alva
Daniel Alva
Numerade Educator
04:06

Problem 38

Jordan is building a compound microscope using an eyepiece with a focal length of $7.50 \mathrm{~cm}$ and an objective with a focal length of $1.500 \mathrm{~cm}$. He will place the specimen a distance of $1.600 \mathrm{~cm}$ from the objective. (a) How far apart should Jordan place the lenses? (b) What will be the angular magnification of this microscope?

Alexandra Nastasa
Alexandra Nastasa
Numerade Educator
02:42

Problem 39

The wing of an insect is $1.0 \mathrm{~mm}$ long. When viewed through a microscope, the image is $1.0 \mathrm{~m}$ long and is located $5.0 \mathrm{~m}$ away. Determine the angular magnification.

Daniel Alva
Daniel Alva
Numerade Educator
01:27

Problem 40

A microscope has an eyepiece that gives an angular magnification of $5.00$ for a final image at infinity and an objective lens of focal length $15.0 \mathrm{~mm}$. The tube length of the microscope is $16.0 \mathrm{~cm}$. (a) What is the transverse magnification due to the objective lens alone? (b) What is the angular magnification due to the microscope? (c) How far from the objective should the object be placed?

Narayan Hari
Narayan Hari
Numerade Educator
09:15

Problem 41

Repeat Problem $40(\mathrm{c})$ using a different eyepiece that gives an angular magnification of $5.00$ for a final image at the viewer's near point $(25.0 \mathrm{~cm})$ instead of at infinity.

Daniel Alva
Daniel Alva
Numerade Educator
01:47

Problem 42

A microscope has an objective lens of focal length $5.00 \mathrm{~mm} .$ The objective forms an image $16.5 \mathrm{~cm}$ from the lens. The focal length of the eyepiece is $2.80 \mathrm{~cm}$.
(a) What is the distance between the lenses?
(b) What is the angular magnification? The near point is $25.0 \mathrm{~cm}$.
(c) How far from the objective should the object be placed?

Mayukh Banik
Mayukh Banik
Numerade Educator
07:31

Problem 43

Repeat Problem 42 if the eyepiece location is adjusted slightly so that the final image is at the viewer's near point $(25.0 \mathrm{~cm})$ instead of at infinity.

Daniel Alva
Daniel Alva
Numerade Educator
01:46

Problem 44

Use the thin-lens equation to show that the transverse magnification due to the objective of a microscope is $m_{\mathrm{o}}=-L / f_{\mathrm{o}}$. [Hints: The object is near the focal point of the objective; do not assume it is at the focal point. Eliminate $p_{\mathrm{o}}$ to find the magnification in terms of $q_{\mathrm{o}}$ and $f_{\mathrm{o}}$. How is $L$ related to $q_{\mathrm{o}}$ and $f_{\mathrm{o}}$ ?]

Narayan Hari
Narayan Hari
Numerade Educator
03:10

Problem 45

(a) If you were stranded on an island with only a pair of 3.5-D reading glasses, could you make a telescope? If so, what would be the length of the telescope and what would be the best possible angular magnification?
(b) Answer the same questions if you also had a pair of 1.3-D reading glasses.

DM
Debra Mangion
Numerade Educator
02:06

Problem 46

A telescope mirror has a radius of curvature of $10.0 \mathrm{~m}$. It is used to take a picture of the Moon. What is the diameter of the image of the Moon produced by this mirror? (See the inside back cover for necessary information.)

Mayukh Banik
Mayukh Banik
Numerade Educator
04:03

Problem 47

(a) What is the angular size of the Moon as viewed from Earth's surface? See the inside back cover for necessary information. (b) The objective and eyepiece of a refracting telescope have focal lengths $80 \mathrm{~cm}$ and $2.0 \mathrm{~cm}$, respectively. What is the angular size of the Moon as viewed through this telescope?

Daniel Alva
Daniel Alva
Numerade Educator
00:38

Problem 48

What is the distance between the objective and eyepiece in the Yerkes telescope? (See Example 24.8.)

Mayukh Banik
Mayukh Banik
Numerade Educator
03:36

Problem 49

You have a set of converging lenses with focal lengths $1.00 \mathrm{~cm}, 10.0 \mathrm{~cm}, 50.0 \mathrm{~cm}$, and $80.0 \mathrm{~cm} .$ (a) Which two lenses would you select to make a telescope with the largest magnifying power? What is the angular magnification of the telescope when viewing a distant object? (b) Which lens is used as objective and which as eyepiece? (c) What should be the distance between the objective and eyepiece?

Daniel Alva
Daniel Alva
Numerade Educator
00:50

Problem 50

A refracting telescope is $45.0 \mathrm{~cm}$ long and the caption states that the telescope magnifies images by a factor of 30.0. Assuming these numbers are for viewing an object an infinite distance away with minimum eyestrain, what is the focal length of each of the two lenses?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:24

Problem 51

The objective lens of an astronomical telescope forms an image of a distant object at the focal point of the eyepiece, which has a focal length of $5.0 \mathrm{~cm}$. If the two lenses are $45.0 \mathrm{~cm}$ apart, what is the angular magnification?

Daniel Alva
Daniel Alva
Numerade Educator
01:07

Problem 52

A refracting telescope is used to view the Moon. The focal lengths of the objective and eyepiece are $+2.40 \mathrm{~m}$ and $+16.0 \mathrm{~cm}$, respectively. (a) What should be the distance between the lenses? (b) What is the diameter of the image produced by the objective? (c) What is the angular magnification?

Mayukh Banik
Mayukh Banik
Numerade Educator
10:17

Problem 53

The eyepiece of a Galilean telescope is a diverging lens. The focal points $F_{0}$ and $F_{\mathrm{e}}^{\prime}$ coincide. In one such telescope, the lenses are a distance $d=32 \mathrm{~cm}$ apart and the focal length of the objective is $36 \mathrm{~cm}$. A rhinoceros is viewed from a large distance. (a) What is the focal length of the eyepiece? (b) At what distance from the eyepiece is the final image? (c) Is the final image formed by the eyepiece real or virtual? Upright or inverted? (d) What is the angular magnification? [Hint: The angular magnification is $\beta / \alpha$.]

Daniel Alva
Daniel Alva
Numerade Educator
04:15

Problem 54

Good lenses used in cameras and other optical devices are actually compound lenses, made of five or more lenses put together to minimize distortions, including chromatic aberration. Suppose a converging lens with a focal length of $4.00 \mathrm{~cm}$ is placed right next to a diverging lens with focal length of $-20.0 \mathrm{~cm} .$ An object is placed $2.50 \mathrm{~m}$ to the left of this combination. (a) Where will the image be located? (b) Is the image real or virtual?

DM
Debra Mangion
Numerade Educator
05:47

Problem 55

Two converging lenses, separated by a distance of $50.0 \mathrm{~cm}$, are used in combination. The first lens, located to the left, has a focal length of $15.0 \mathrm{~cm}$. The second lens, located to the right, has a focal length of $12.0 \mathrm{~cm}$. An object, $3.00 \mathrm{~cm}$ high, is placed at a distance of $20.0 \mathrm{~cm}$ in front of the first lens. (a) Find the intermediate and final image distances relative to the corresponding lenses. (b) What is the total magnification? (c) What is the height of the final image?

Daniel Alva
Daniel Alva
Numerade Educator
01:00

Problem 56

A camera has a telephoto lens of $240-\mathrm{mm}$ focal length. The lens can be moved in and out a distance of $16 \mathrm{~mm}$ from the film plane by rotating the lens barrel. If the lens can focus objects at infinity, what is the closest object distance that can he focused?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:47

Problem 57

You have two lenses of focal length $25.0 \mathrm{~cm}$ (lens 1 ) and $5.0 \mathrm{~cm}$ (lens 2). (a) To build an astronomical telescope that gives an angular magnification of $5.0$, how should you use the lenses (which for objective and which for eyepiece)? Explain. (b) How far apart should they be?

Daniel Alva
Daniel Alva
Numerade Educator
01:23

Problem 58

The Ortiz family is viewing slides from their summer vacation trip to the Grand Canyon. Their slide projector has a projection lens of $10.0-\mathrm{cm}$ focal length and the screen is located $2.5 \mathrm{~m}$ from the projector.
(a) What is the distance between the slide and the projection lens?
(b) What is the magnification of the image?
(c) How wide is the image of a slide of width $36 \mathrm{~mm}$ on the screen? (See the figure with Problem 16.)

Mayukh Banik
Mayukh Banik
Numerade Educator
04:05

Problem 59

A slide projector, using slides of width $5.08 \mathrm{~cm}$, produces an image that is $2.00 \mathrm{~m}$ wide on a screen $3.50 \mathrm{~m}$ away. What is the focal length of the projector lens?

Daniel Alva
Daniel Alva
Numerade Educator
01:46

Problem 60

An object is placed $20.0 \mathrm{~cm}$ from a converging lens with focal length $15.0 \mathrm{~cm}$ (see the figure, not drawn to scale). A concave mirror with focal length $10.0 \mathrm{~cm}$ is located $75.0 \mathrm{~cm}$ to the right of the lens.
(a) Describe the final image -is it real or virtual? Upright or inverted?
(b) What is the location of the final image? (c) What is the total transverse magnification?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:08

Problem 61

Two lenses, of focal lengths $3.0 \mathrm{~cm}$ and $30.0 \mathrm{~cm}$, are used to build a small telescope. (a) Which lens should be the objective? (b) What is the angular magnification? (c) How far apart are the two lenses in the telescope?

Daniel Alva
Daniel Alva
Numerade Educator
00:43

Problem 62

(a) If Harry has a near point of $1.5 \mathrm{~m}$, what focal length contact lenses does he require? (b) What is the power of these lenses in diopters?

Mayukh Banik
Mayukh Banik
Numerade Educator
03:31

Problem 63

An astronomical telescope provides an angular magnification of 12 . The two converging lenses are $66 \mathrm{~cm}$ apart. Find the focal length of each of the lenses.

Daniel Alva
Daniel Alva
Numerade Educator
02:00

Problem 64

Two lenses, separated by a distance of $21.0 \mathrm{~cm}$, are used in combination. The first lens has a focal length of $+30.0 \mathrm{~cm} ;$ the second has a focal length of $-15.0 \mathrm{~cm}$. An object, $2.0 \mathrm{~mm}$ long, is placed $1.8 \mathrm{~cm}$ before the first lens. (a) What are the intermediate and final image distances relative to the corresponding lenses? (b) What is the total magnification? (c) What is the height of the final image?

Mayukh Banik
Mayukh Banik
Numerade Educator
07:30

Problem 65

A camera lens has a fixed focal length of magnitude $50.0 \mathrm{~mm}$. The camera is focused on a $1.0$ -m-tall child who is standing $3.0 \mathrm{~m}$ from the lens. (a) Should the image formed be real or virtual? Why? (b) Is the lens converging or diverging? Why? (c) What is the distance from the lens to the film? (d) How tall is the image on the film? (e) To focus the camera, the lens is moved away from or closer to the film. What is the total distance the lens must be able to move if the camera can take clear pictures of objects at distances anywhere from $1.00 \mathrm{~m}$ to infinity?

Daniel Alva
Daniel Alva
Numerade Educator
00:52

Problem 66

A camera with a $50.0$ -mm lens can focus on objects located from $1.5 \mathrm{~m}$ to an infinite distance away by adjusting the distance between the lens and the film. When the focus is changed from that for a distant mountain range to that for a flower bed at $1.5 \mathrm{~m}$, how far does the lens move with respect to the film?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:44

Problem 67

The area occupied by one frame on $35-\mathrm{mm}$ film is $24 \mathrm{~mm}$ by $36 \mathrm{~mm}$ -see the figure with Problem 16 . The focal length of the camera lens is $50.0 \mathrm{~mm}$. A picture is taken of a person $182 \mathrm{~cm}$ tall. What is the minimum distance from the camera for the person to stand so that the image fits on the film? Give two answers; one for each orientation of the camera.

Daniel Alva
Daniel Alva
Numerade Educator
01:34

Problem 68

A dissecting microscope is designed to have a large distance between the object and the objective lens. Suppose the focal length of the objective of a dissecting microscope is $5.0 \mathrm{~cm}$, the focal length of the eyepiece is $4.0 \mathrm{~cm}$, and the distance between the lenses is $32.0 \mathrm{~cm}$.
(a) What is the distance between the object and the objective lens? (b) What is the angular magnification?

Mayukh Banik
Mayukh Banik
Numerade Educator
05:23

Problem 69

A cub scout makes a simple microscope by placing two converging lenses of $+18 \mathrm{D}$ at opposite ends of a $28-\mathrm{cm}$ long tube.
(a) What is the tube length of the microscope?
(b) What is the angular magnification?
(c) How far should an object be placed from the objective lens?

DM
Debra Mangion
Numerade Educator
02:26

Problem 70

A convex lens of power $+12 \mathrm{D}$ is used as a magnifier to examine a wildflower. What is the angular magnification if the final image is at (a) infinity or (b) the near point of $25 \mathrm{~cm} ?$

Mayukh Banik
Mayukh Banik
Numerade Educator
01:57

Problem 71

A refracting telescope has an objective lens with a focal length of $2.20 \mathrm{~m}$ and an eyepiece with a focal length of $1.5 \mathrm{~cm}$. If you look through this telescope the wrong way, that is, with your eye placed at the objective lens, by what factor is the angular size of an observed object reduced?

Daniel Alva
Daniel Alva
Numerade Educator
01:24

Problem 72

Suppose the distance from the lens system of the eye (cornea + lens) to the retina is $18 \mathrm{~mm}$.
(a) What must the power of the lens be when looking at distant objects?
(b) What must the power of the lens be when looking at an object $20.0 \mathrm{~cm}$ from the eye?
(c) Suppose that the eye is farsighted; the person cannot see clearly objects that are closer than $1.0 \mathrm{~m}$. Find the power of the contact lens you would prescribe so that objects as close as $20.0 \mathrm{~cm}$ can be seen clearly.

Mayukh Banik
Mayukh Banik
Numerade Educator
07:25

Problem 73

An object is placed $7.00 \mathrm{~cm}$ to the left of a converging lens of focal length $3.00 \mathrm{~cm}$. A convex mirror with a radius of curvature of $4.00 \mathrm{~cm}$ is placed $12.00 \mathrm{~cm}$ to the right of the lens. (a) Where is the intermediate image formed by the lens? (b) Is the intermediate image real or virtual and is it upright or inverted with respect to the object? (c) What is the magnification of this image?
(d) Where is the image formed by the mirror? (e) Is the second image real or virtual and is it upright or inverted with respect to the original object? (f) What is the magnification due to the mirror? (g) What is the total magnification?

Daniel Alva
Daniel Alva
Numerade Educator
03:42

Problem 74

Refer to Problem $73 .$ Draw ray diagrams for the two images. Mark the focal points with dots and draw three rays to determine each image. [Hint: The second image is very small. so start with a fairlv large obiect.

Mayukh Banik
Mayukh Banik
Numerade Educator
07:01

Problem 75

Veronique is nearsighted; she cannot see clearly anything more than $6.00 \mathrm{~m}$ away without her contacts. One day she doesn't wear her contacts; rather, she wears an old pair of glasses prescribed when she could see clearly up to $8.00 \mathrm{~m}$ away. Assume the glasses are $2.0 \mathrm{~cm}$ from her eyes. What is the greatest distance an object can be placed so that she can see it clearly with these glasses?

Manish Jain
Manish Jain
Numerade Educator
03:17

Problem 76

A man requires reading glasses with $+2.0 \mathrm{D}$ power to read a book held $40.0 \mathrm{~cm}$ away with a relaxed eye. Assume the glasses are $2.0 \mathrm{~cm}$ from his eyes. (a) What is his uncorrected far point? (b) What refractive power lenses should he use for distance vision? (c) His uncorrected near point is $1.0 \mathrm{~m}$. What should the refractive powers of the two lenses in his bifocals be to give him clear vision from $25 \mathrm{~cm}$ to infinity?

Mayukh Banik
Mayukh Banik
Numerade Educator
05:09

Problem 77

A microscope has an eyepiece of focal length $2.00 \mathrm{~cm}$ and an objective of focal length $3.00 \mathrm{~cm}$. The eyepiece produces a virtual image at the viewer's near point $(25.0 \mathrm{~cm}$ from the eye). (a) How far from the eyepiece is the image formed by the objective? (b) If the lenses are $20.0 \mathrm{~cm}$ apart, what is the distance from the objective lens to the object being viewed? (c) What is the angular magnification?

Daniel Alva
Daniel Alva
Numerade Educator
08:54

Problem 78

An object is located at $x=0 .$ At $x=2.50 \mathrm{~cm}$ is a converging lens with a focal length of $2.00 \mathrm{~cm}$, at $x=16.5 \mathrm{~cm}$ is an unknown lens, and at $x=19.8 \mathrm{~cm}$ is another converging lens with focal length $4.00 \mathrm{~cm}$. An upright image is formed at $x=39.8 \mathrm{~cm} .$ For each lens, the object distance exceeds the focal length. The magnification of the system is $6.84$. (a) Is the unknown lens diverging or converging? (b) What is the focal length of the unknown lens? (c) Draw a ray diagram to confirm your answer.

Mayukh Banik
Mayukh Banik
Numerade Educator