Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

Chapter 26

The Refraction of Light: Lenses and Optical Instruments - all with Video Answers

Educators

RG

Chapter Questions

Problem 1

A plate glass window $(n=1.5)$ has a thickness of $4.0 \times 10^{-3} \mathrm{m} .$ How long does it take light to pass perpendicularly through the plate?

Adnan Gill

Adnan Gill

Numerade Educator

Problem 2

In an ultra-low-temperature experiment, a collection of sodium atoms enter a special state called a Bose-Einstein condensate in which the index of refraction is $1.57 \times 10^{7} .$ What is the speed of light in this condensate?

Adnan Gill

Numerade Educator

Problem 3

The refractive indices of materials $A$ and $B$ have a ratio of $n_{A} / n_{B}=1.33$ The speed of light in material $A$ is $1.25 \times 10^{8} \mathrm{m} / \mathrm{s} .$ What is the speed of light in material $B ?$

Adnan Gill

Numerade Educator

Problem 4

The frequency of a light wave is the same when the light travels in ethyl alcohol or in carbon disulfide. Find the ratio of the wavelength of the light in ethyl alcohol to that in carbon disulfide.

Adnan Gill

Numerade Educator

Problem 5

Light travels at a speed of $2.201 \times 10^{8} \mathrm{m} / \mathrm{s}$ in a certain substance. What substance from Table 26.1 could this be? For the speed of light in a vacuum use $2.998 \times 10^{8} \mathrm{m} / \mathrm{s} ;$ show your calculations.

Adnan Gill

Numerade Educator

Problem 6

Light has a wavelength of $340.0 \mathrm{nm}$ and a frequency of $5.403 \times 10^{14} \mathrm{Hz}$ when traveling through a certain substance. What substance from Table 26.1 could this be? Show your calculations.

Adnan Gill

Numerade Educator

Problem 7

In a certain time, light travels $6.20 \mathrm{km}$ in a vacuum. During the same time, light travels only $3.40 \mathrm{km}$ in a liquid. What is the refractive index of the liquid?

Adnan Gill

Numerade Educator

Problem 8

A flat sheet of ice has a thickness of $2.0 \mathrm{cm} .$ It is on top of a flat sheet of crystalline quartz that has a thickness of $1.1 \mathrm{cm} .$ Light strikes the ice perpendicularly and travels through it and then through the quartz. In the time it takes the light to travel through the two sheets, how far (in centimeters) would it have traveled in a vacuum?

Adnan Gill

Numerade Educator

Problem 9

The drawing shows four different situations in which a light ray is traveling from one medium into another. In some of the cases, the refraction is not shown correctly. For cases $(a),(b),$ and $(c),$ the angle of incidence is $55^{\circ} ;$ for case $(d),$ the angle of incidence is $0^{\circ} .$ Determine the angle of refraction in each case. If the drawing shows the refraction incorrectly, explain why it is incorrect.

Adnan Gill

Numerade Educator

Problem 10

A layer of oil $(n=1.45)$ floats on an unknown liquid. A ray of light originates in the oil and passes into the unknown liquid. The angle of incidence is $64.0^{\circ},$ and the angle of refraction is $53.0^{\circ} .$ What is the index of refraction of the unknown liquid?

Adnan Gill

Numerade Educator

Problem 11

A ray of light impinges from air onto a block of ice $(n=1.309)$ at a $60.0^{\circ}$ angle of incidence. Assuming that this angle remains the same, find the difference $\theta_{2, \text { ice }}-\theta_{2, \text { water }}$ in the angles of refraction when the ice turns to water $(n=1.333)$

Narendra Kumar

Numerade Educator

Problem 12

A narrow beam of light from a laser travels through air $(n=1.00)$ and strikes point $A$ on the surface of the water $(n=1.33)$ in a lake. The angle of incidence is $55^{\circ} .$ The depth of the lake is $3.0 \mathrm{m} .$ On the flat lake-bottom is point $\mathrm{B},$ directly below point $\mathrm{A}$. (a) If refraction did not occur, how far away from point $B$ would the laser beam strike the lake-bottom? (b) Considering refraction, how far away from point $B$ would the laser beam strike the lake-bottom?

Adnan Gill

Numerade Educator

Problem 13

The drawing shows a coin resting on the bottom of a beaker filled with an unknown liquid. A ray of light from the coin travels to the surface of the liquid and is refracted as it enters into the air. A person sees the ray as it skims just above the surface of the liquid. How fast is the light traveling in the liquid?

Adnan Gill

Numerade Educator

Problem 14

Amber $(n=1.546)$ is a transparent brown-yellow fossil resin. An insect, trapped and preserved within the amber, appears to be $2.5 \mathrm{cm}$ beneath the surface when viewed directly from above. How far below the surface is the insect actually located?

Adnan Gill

Numerade Educator

Problem 15

A beam of light is traveling in air and strikes a material. The angles of incidence and refraction are $63.0^{\circ}$ and $47.0^{\circ},$ respectively. Obtain the speed of light in the material.

RG

Ryan Griffith

Numerade Educator

Problem 16

The drawing shows a ray of light traveling through three materials whose surfaces are parallel to each other. The refracted rays (but not the reflected rays) are shown as the light passes through each material. A ray of light strikes the $a-b$ interface at a $50.0^{\circ}$ angle of incidence. The index of refraction of material $a$ is $n_{a}=1.20 .$ The angles of refraction in materials $b$ and $c$ are, respectively, $45.0^{\circ}$ and $56.7^{\circ} .$ Find the indices of refraction in these two media.

Adnan Gill

Numerade Educator

Problem 17

Light in a vacuum is incident on a transparent glass slab. The angle of incidence is $35.0^{\circ} .$ The slab is then immersed in a pool of liquid. When the angle of incidence for the light striking the slab is $20.3^{\circ},$ the angle of refraction for the light entering the slab is the same as when the slab was in a vacuum. What is the index of refraction of the liquid?

Adnan Gill

Numerade Educator

Problem 18

A stone held just beneath the surface of a swimming pool is released and sinks to the bottom at a constant speed of $0.48 \mathrm{m} / \mathrm{s} .$ What is the apparent speed of the stone, as viewed from directly above by an observer who is in air?

Suzanne W.

Numerade Educator

Problem 19

Review Conceptual Example 4 as background for this problem. A man in a boat is looking straight down at a fish in the water directly beneath him. The fish is looking straight up at the man. They are equidistant from the air-water interface. To the man, the fish appears to be $2.0 \mathrm{m}$ beneath his eyes. To the fish, how far above its eyes does the man appear to be?

Suzanne W.

Numerade Educator

Problem 20

The drawing shows a rectangular block of glass $(n=1.52)$ surrounded by liquid carbon disulfide $(n=1.63) .$ A ray of light is incident on the glass at point A with a $30.0^{\circ}$ angle of incidence. At what angle of refraction does the ray leave the glass at point $\mathrm{B} ?$

Sheh Lit Chang

University of Washington

Problem 21

In Figure $26.6,$ suppose that the angle of incidence is $\theta_{1}=30.0^{\circ}$, the thickness of the glass pane is $6.00 \mathrm{mm},$ and the refractive index of the glass is $n_{2}=1.52 .$ Find the amount (in $\mathrm{mm}$ ) by which the emergent ray is displaced relative to the incident ray.

Adnan Gill

Numerade Educator

Problem 22

The back wall of a home aquarium is a mirror that is a distance of $40.0 \mathrm{cm}$ away from the front wall. The walls of the tank are negligibly thin. A fish, swimming midway between the front and back walls, is being viewed by a person looking through the front wall. The index of refraction of air is $n_{\text {air }}=1.000$ and that of water is $n_{\text {water }}=1.333 .$ (a) Calculate the apparent distance between the fish and the front wall. (b) Calculate the apparent distance between the image of the fish and the front wall.

Suzanne W.

Numerade Educator

Problem 23

Refer to Figure $26.4 b$ and assume the observer is nearly above the submerged object. For this situation, derive the expression for the apparent depth: $d^{\prime}=d\left(n_{2} / n_{1}\right),$ Equation 26.3. (Hint: Use Snell's law of refraction and the fact that the angles of incidence and refraction are small, so $\tan \theta \approx \sin \theta .$ )

Sheh Lit Chang

University of Washington

Problem 24

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 25

A small logo is embedded in a thick block of crown glass $(n=1.52)$, $3.20 \mathrm{cm}$ beneath the top surface of the glass. The block is put under water, so there is $1.50 \mathrm{cm}$ of water above the top surface of the block. The logo is viewed from directly above by an observer in air. How far beneath the top surface of the water does the logo appear to be?

Adnan Gill

Numerade Educator

Problem 26

For the liquids in Table $26.1,$ determine the smallest critical angle for light that originates in one of them and travels toward the air-liquid interface.

Adnan Gill

Numerade Educator

Problem 27

A glass is half-full of water, with a layer of vegetable oil $(n=$ 1.47) floating on top. A ray of light traveling downward through the oil is incident on the water at an angle of $71.4^{\circ} .$ Determine the critical angle for the oil-water interface and decide whether the ray will penetrate into the water.

Suzanne W.

Numerade Educator

Problem 28

A point source of light is submerged $2.2 \mathrm{m}$ below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?

Adnan Gill

Numerade Educator

Problem 29

A ray of light is traveling in glass and strikes a glass-liquid interface. The angle of incidence is $58.0^{\circ},$ and the index of refraction of glass is $n=1.50 .$ (a) What must be the index of refraction of the liquid so that the direction of the light entering the liquid is not changed? (b) What is the largest index of refraction that the liquid can have, so that none of the light is transmitted into the liquid and all of it is reflected back into the glass?

Adnan Gill

Numerade Educator

Problem 30

The drawing shows three layers of different materials, with air above and below the layers. The interfaces between the layers are parallel. The index of refraction of each layer is given in the drawing. Identical rays of light are sent into the layers, and light zigzags through each layer, reflecting from the top and bottom surfaces. The index of refraction for air is $n_{\mathrm{air}}=1.00 .$ For each layer, the ray of light has an angle of incidence of $75.0^{\circ} .$ For the cases in which total internal refection is possible from either the top or bottom surface of a layer, determine the amount by which the angle of incidence exceeds the critical angle.

Suzanne W.

Numerade Educator

Problem 31

The drawing shows a crown glass slab with a rectangular cross section. As illustrated, a laser beam strikes the upper surface at an angle of $60.0^{\circ} .$ After reflecting from the upper surface, the beam reflects from the side and bottom surfaces. (a) If the glass is surrounded by air, determine where part of the beam first exits the glass, at point $A, B,$ or $C$. (b) Repeat part (a), assuming that the glass is surrounded by water instead of air.

Adnan Gill

Numerade Educator

Problem 32

The drawing shows three materials, $a, b,$ and $c .$ A ray of light strikes the $a-b$ interface at an angle that just barely exceeds its critical angle of $40.0^{\circ} .$ The reflected ray then strikes the $a-c$ interface at an angle of incidence that just barely exceeds its critical angle (which is not $40.0^{\circ}$ ). The index of refraction of material $a$ is $n_{a}=1.80 .$ Find the indices of refraction for the two other materials.

Adnan Gill

Numerade Educator

Problem 33

Multiple-Concept Example 7 provides helpful background for this problem. The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of $\theta_{1}=34^{\circ},$ enters the quartz, and travels to point $P .$ This slab is surrounded by a fluid with a refractive index $n .$ What is the maximum value of $n$ for which total internal reflection occurs at point $P ?$

Jaime Munoz

Numerade Educator

Problem 34

The drawing shows a ray of light traveling from point $A$ to point $B,$ a distance of $4.60 \mathrm{m}$ in a material that has an index of refraction $n_{1}$ At point $B$, the light encounters a different substance whose index of refraction is $n_{2}=1.63 .$ The light strikes the interface at the critical angle of $\theta_{\mathrm{c}}=$ $48.1^{\circ} .$ How much time does it take for the light to travel from $A$ to $B ?$

Adnan Gill

Numerade Educator

Problem 35

A layer of liquid $B$ floats on liquid $A$. A ray of light begins in liquid $A$ and undergoes total internal reflection at the interface between the liquids when the angle of incidence exceeds $36.5^{\circ} .$ When liquid $B$ is replaced with liquid $C,$ total internal reflection occurs for angles of incidence greater than $47.0^{\circ} .$ Find the ratio $n_{B} / n_{C}$ of the refractive indices of liquids $B$ and $C$.

Narayan Hari

Numerade Educator

Problem 36

For light that originates within a liquid and strikes the liquid-air in-terface, the critical angle is $39^{\circ} .$ What is Brewster's angle for this light?

Adnan Gill

Numerade Educator

Problem 37

Light is reflected from a glass coffee table. When the angle of incidence is $56.7^{\circ},$ the reflected light is completely polarized parallel to the surface of the glass. What is the index of refraction of the glass?

Adnan Gill

Numerade Educator

Problem 38

Light is incident from air onto the surface of a liquid. The angle of incidence is $53.0^{\circ},$ and the angle of refraction is $34.0^{\circ} .$ At what angle of incidence would the reflected light be $100 \%$ polarized?

Adnan Gill

Numerade Educator

Problem 39

When light strikes the surface between two materials from above, the Brewster angle is $65.0^{\circ} .$ What is the Brewster angle when the light encounters the same surface from below?

Narayan Hari

Numerade Educator

Problem 40

A laser is mounted in air, at a distance of $0.476 \mathrm{m}$ above the edge of a large, horizontal pane of crown glass, as shown in the drawing. The laser is aimed at the glass in such a way that the reflected beam is $100 \%$ polarized. Determine the distance $d$ between the edge of the pane and the point at which the laser beam is reflected.

Suzanne W.

Numerade Educator

Problem 41

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 42

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 43

A ray of sunlight is passing from diamond into crown glass; the angle of incidence is $35.00^{\circ} .$ The indices of refraction for the blue and red components of the ray are: blue $\left(n_{\text {diamond }}=2.444, n_{\text {crown glass }}=1.531\right),$ and red $\left(n_{\text {diamond }}=2.410, n_{\text {crown glass}}=1.520\right) .$ Determine the angle between the refracted blue and red rays in the crown glass.

Narayan Hari

Numerade Educator

Problem 44

Violet light and red light travel through air and strike a block of plastic at the same angle of incidence. The angle of refraction is $30.400^{\circ}$ for the violet light and $31.200^{\circ}$ for the red light. The index of refraction for violet light in plastic is greater than that for red light by $0.0400 .$ Delaying any rounding off of calculations until the very end, find the index of refraction for violet light in plastic.

Adnan Gill

Numerade Educator

Problem 45

A beam of sunlight encounters a plate of crown glass at a $45.00^{\circ}$ angle of incidence. Using the data in Table $26.2,$ find the angle between the violet ray and the red ray in the glass.

Adnan Gill

Numerade Educator

Problem 46

Horizontal rays of red light $(\lambda=660 \mathrm{nm},$ in vacuum) and violet light $(\lambda=410 \mathrm{nm},$ in vacuum) are incident on the flint-glass prism shown in the drawing. The indices of refraction for the red and violet light are $n_{\text {red }}=$ 1.662 and $n_{\text {violet }}=1.698 .$ The prism is surrounded by air. What is the angle of refraction for each ray as it emerges from the prism?

Adnan Gill

Numerade Educator

Problem 47

This problem relates to Figure $26.18,$ which illustrates the dispersion of light by a prism. The prism is made from glass, and its cross section is an equilateral triangle. The indices of refraction for the red and violet light are 1.662 and $1.698,$ respectively. The angle of incidence for both the red and the violet light is $60.0^{\circ} .$ Find the angles of refraction at which the red and violet rays emerge into the air from the prism.

Adnan Gill

Numerade Educator

Problem 48

The drawing shows a horizontal ray of white light incident perpendicularly on the vertical face of a prism (crown glass). The light enters the prism, and part of it undergoes refraction at the slanted face and emerges into the surrounding material. The rest of it is totally internally reflected and exits through the horizontal base of the prism. The colors of light that emerge from the slanted face may be chosen by altering the index of refraction of the material surrounding the prism. Find the required index of refraction of the surrounding material so that (a) only red light and (b) all colors except violet emerge from the slanted face.

Adnan Gill

Numerade Educator

Problem 49

An object is located $9.0 \mathrm{cm}$ in front of a converging lens $(f=$ $6.0 \mathrm{cm}$$ )$. Using an accurately drawn ray diagram, determine where the image is located.

Adnan Gill

Numerade Educator

Problem 50

The owner of a van installs a rear-window lens that has a focal length of $-0.300 \mathrm{m} .$ When the owner looks out through the lens at a person standing directly behind the van, the person appears to be just $0.240 \mathrm{m}$ from the back of the van, and appears to be $0.34 \mathrm{m}$ tall. (a) How far from the van is the person actually standing, and (b) how tall is the person?

Adnan Gill

Numerade Educator

Problem 51

A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and $150.0 \mathrm{mm} .$ A woman whose height is $1.60 \mathrm{m}$ stands $9.00 \mathrm{m}$ in front of the camera. What is the height (including sign) of her image on the image sensor, as produced by (a) the 35.0 -mm lens and (b) the 150.0 -mm lens?

Adnan Gill

Numerade Educator

Problem 52

When a diverging lens is held $13.0 \mathrm{cm}$ above a line of print, as in Figure $26.29,$ the image is $5.0 \mathrm{cm}$ beneath the lens. (a) Is the image real or virtual? (b) What is the focal length of the lens?

Adnan Gill

Numerade Educator

Problem 53

A slide projector has a converging lens whose focal length is $105.00 \mathrm{mm}$ (a) How far (in meters) from the lens must the screen be $10 \mathrm{c}-$ ated if a slide is placed $108.00 \mathrm{mm}$ from the lens? (b) If the slide measures $24.0 \mathrm{mm} \times 36.0 \mathrm{mm},$ what are the dimensions (in $\mathrm{mm}$ ) of its image?

Adnan Gill

Numerade Educator

Problem 54

(a) For a diverging lens $(f=-20.0 \mathrm{cm}),$ construct a ray diagram to scale and find the image distance for an object that is $20.0 \mathrm{cm}$ from the lens. (b) Determine the magnification of the lens from the diagram.

Adnan Gill

Numerade Educator

Problem 55

A tourist takes a picture of a mountain $14 \mathrm{km}$ away using a camera that has a lens with a focal length of $50 \mathrm{mm}$. She then takes a second picture when she is only $5.0 \mathrm{km}$ away. What is the ratio of the height of the mountain's image on the camera's image sensor for the second picture to its height on the image sensor for the first picture?

Suzanne W.

Numerade Educator

Problem 56

An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is onehalf the size of the object. The distance between the object and the image is $90.0 \mathrm{cm} .$ (a) How far from the lens is the object? (b) What is the focal length of the lens?

Adnan Gill

Numerade Educator

Problem 57

A converging lens has a focal length of $88.00 \mathrm{cm}$. An object $13.0 \mathrm{cm}$ tall is located $155.0 \mathrm{cm}$ in front of this lens. (a) What is the image distance? (b) Is the image real or virtual? (c) What is the image height? Be sure to include the proper algebraic sign.

Adnan Gill

Numerade Educator

Problem 58

The distance between an object and its image formed by a diverging lens is $49.0 \mathrm{cm} .$ The focal length of the lens is $-233.0 \mathrm{cm} .$ Find (a) the image distance and (b) the object distance.

Adnan Gill

Numerade Educator

Problem 59

The moon's diameter is $3.48 \times 10^{6} \mathrm{m},$ and its mean distance from the earth is $3.85 \times 10^{8} \mathrm{m} .$ The moon is being photographed by a camera whose lens has a focal length of $50.0 \mathrm{mm}$. (a) Find the diameter of the moon's image on the slide film. (b) When the slide is projected onto a screen that is $15.0 \mathrm{m}$ from the lens of the projector $(f=110.0 \mathrm{mm}),$ what is the diameter of the moon's image on the screen?

Adnan Gill

Numerade Educator

Problem 60

When a converging lens is used in a camera (as in Figure $26.26 b$ ), the film must be at a distance of $0.210 \mathrm{m}$ from the lens to record an image of an object that is $4.00 \mathrm{m}$ from the lens. The same lens and film are used in a projector (see Figure $26.27 b$ ), with the screen $0.500 \mathrm{m}$ from the lens. How far from the projector lens should the film be placed?

Narayan Hari

Numerade Educator

Problem 61

An object is $18 \mathrm{cm}$ in front of a diverging lens that has a focal length of $-12 \mathrm{cm} .$ How far in front of the lens should the object be placed so that the size of its image is reduced by a factor of $2.0 ?$

Adnan Gill

Numerade Educator

Problem 62

An object is placed in front of a converging lens in such a position that the lens $(f=12.0 \mathrm{cm})$ creates a real image located $21.0 \mathrm{cm}$ from the lens. Then, with the object remaining in place, the lens is replaced with another converging lens $(f=16.0 \mathrm{cm}) .$ A new, real image is formed. What is the image distance of this new image?

Adnan Gill

Numerade Educator

Problem 63

A converging lens $(f=25.0 \mathrm{cm})$ is used to project an image of an object onto a screen. The object and the screen are $125 \mathrm{cm}$ apart, and between them the lens can be placed at either of two locations. Find the two object distances.

Adnan Gill

Numerade Educator

Problem 64

Available in WileyPLUS.

Ajay Singhal

Numerade Educator

Problem 65

Two identical diverging lenses are separated by $16 \mathrm{cm} .$ The focal length of each lens is $-8.0 \mathrm{cm} .$ An object is located $4.0 \mathrm{cm}$ to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

Adnan Gill

Numerade Educator

Problem 66

Two systems are formed from a converging lens and a diverging lens, as shown in parts $a$ and $b$ of the drawing. (The point labeled " $F_{\text {coverging }}$ is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 at a distance of $10.00 \mathrm{cm}$ to the left of lens $1 .$ The focal lengths of the converging and diverging lenses are 15.00 and $-20.0 \mathrm{cm},$ respectively. The distance between the lenses is $50.0 \mathrm{cm} .$ Determine the final image distance for each system, measured with respect to lens 2 .

Suzanne W.

Numerade Educator

Problem 67

Two converging lenses are separated by $24.00 \mathrm{cm} .$ The focal length of each lens is $12.00 \mathrm{cm} .$ An object is placed $36.00 \mathrm{cm}$ to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

Adnan Gill

Numerade Educator

Problem 68

A converging lens $\left(f_{1}=24.0 \mathrm{cm}\right)$ is located $56.0 \mathrm{cm}$ to the left of a diverging lens $\left(f_{2}=-28.0 \mathrm{cm}\right) .$ An object is placed to the left of the converging lens, and the final image produced by the two-lens combination lies $20.7 \mathrm{cm}$ to the left of the diverging lens. How far is the object from the converging lens?

Adnan Gill

Numerade Educator

Problem 69

A converging lens $(f=12.0 \mathrm{cm})$ is located $30.0 \mathrm{cm}$ to the left of a diverging lens $(f=-6.00 \mathrm{cm}) .$ A postage stamp is placed $36.0 \mathrm{cm}$ to the left of the converging lens. (a) Locate the final image of the stamp relative to the diverging lens. (b) Find the overall magnification. (c) Is the final image real or virtual? With respect to the original object, is the final image (d) upright or inverted, and is it (e) larger or smaller?

Adnan Gill

Numerade Educator

Problem 70

A diverging lens $(f=-10.0 \mathrm{cm})$ is located $20.0 \mathrm{cm}$ to the left of a converging lens $(f=30.0 \mathrm{cm}) .$ A $3.00-\mathrm{cm}-$ tall object stands to the left of the diverging lens, exactly at its focal point.
(a) Determine the distance of the final image relative to the converging lens.
(b) What is the height of the final image (including the proper algebraic sign)?

Adnan Gill

Numerade Educator

Problem 71

An object is placed $20.0 \mathrm{cm}$ to the left of a diverging lens $(f=$ $-8.00 \mathrm{cm}$$) .$ A concave mirror $(f=12.0 \mathrm{cm})$ is placed $30.0 \mathrm{cm}$ to the right of the lens. (a) Find the final image distance, measured relative to the mirror. (b) Is the final image real or virtual? (c) Is the final image upright or inverted with respect to the original object?

Adnan Gill

Numerade Educator

Problem 72

Two converging lenses $\left(f_{1}=9.00 \mathrm{cm}\right.$ and $\left.f_{2}=6.00 \mathrm{cm}\right)$ are separated by $18.0 \mathrm{cm} .$ The lens on the left has the longer focal length. An object stands $12.0 \mathrm{cm}$ to the left of the left-hand lens in the combination. (a) Locate the final image relative to the lens on the right. (b) Obtain the overall magnification. (c) Is the final image real or virtual? With respect to the original object, (d) is the final image upright or inverted and (e) is it larger or smaller?

Adnan Gill

Numerade Educator

Problem 73

Visitors at a science museum are invited to sit in a chair to the right of a full-length diverging lens $\left(f_{1}=-3.00 \mathrm{m}\right)$ and observe a friend sitting in a second chair, $2.00 \mathrm{m}$ to the left of the lens. The visitor then presses a button and a converging lens $\left(f_{2}=+4.00 \mathrm{m}\right)$ rises from the floor to a position $1.60 \mathrm{m}$ to the right of the diverging lens, allowing the visitor to view the friend through both lenses at once. Find (a) the magnification of the friend when viewed through the diverging lens only and (b) the overall magnification of the friend when viewed through both lenses. Be sure to include the algebraic signs $(+$ or $-$ ) with your answers.

Adnan Gill

Numerade Educator

Problem 74

A student is reading material written on a blackboard. Her contact lenses have a refractive power of 57.50 diopters; the lens-to-retina distance is $1.750 \mathrm{cm} .$ (a) How far (in meters) is the blackboard from her eyes?
(b) If the material written on the blackboard is $5.00 \mathrm{cm}$ high, what is the size of the image on her retina?

Adnan Gill

Numerade Educator

Problem 75

A nearsighted person cannot read a sign that is more than $5.2 \mathrm{m}$ from his eyes. To deal with this problem, he wears contact lenses that do not correct his vision completely, but do allow him to read signs located up to distances of $12.0 \mathrm{m}$ from his eyes. What is the focal length of the contacts?

Narayan Hari

Numerade Educator

Problem 76

A woman can read the large print in a newspaper only when it is at a distance of $65 \mathrm{cm}$ or more from her eyes. (a) Is she nearsighted (myopic) or farsighted (hyperopic), and what kind of lens is used in her glasses to correct her eyesight? (b) What should be the refractive power (in diopters) of her glasses (worn $2.0 \mathrm{cm}$ from the eyes), so she can read the newspaper at a distance of $25 \mathrm{cm}$ from her eyes?

Adnan Gill

Numerade Educator

Problem 77

Your friend has a near point of $138 \mathrm{cm},$ and she wears contact lenses that have a focal length of $35.1 \mathrm{cm} .$ How close can she hold a magazine and still read it clearly?

Adnan Gill

Numerade Educator

Problem 78

A farsighted woman breaks her current eyeglasses and is using an old pair whose refractive power is 1.660 diopters. since these eyeglasses do not completely correct her vision, she must hold a newspaper $42.00 \mathrm{cm}$ from her eyes in order to read it. She wears the eyeglasses $2.00 \mathrm{cm}$ from her eyes. How far is her near point from her eyes?

Adnan Gill

Numerade Educator

Problem 79

A person has far points of $5.0 \mathrm{m}$ from the right eye and $6.5 \mathrm{m}$ from the left eye. Write a prescription for the refractive power of each corrective contact lens.

Adnan Gill

Numerade Educator

Problem 80

A farsighted man uses eyeglasses with a refractive power of 3.80 diopters. Wearing the glasses $0.025 \mathrm{m}$ from his eyes, he is able to read books held no closer than $0.280 \mathrm{m}$ from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters?

Adnan Gill

Numerade Educator

Problem 81

The far point of a nearsighted person is $6.0 \mathrm{m}$ from her eyes, and she wears contacts that enable her to see distant objects clearly. A tree is $18.0 \mathrm{m}$ away and $2.0 \mathrm{m}$ high. (a) When she looks through the contacts at the tree, what is its image distance? (b) How high is the image formed by the contacts?

Adnan Gill

Numerade Educator

Problem 82

The contacts worn by a farsighted person allow her to see objects clearly that are as close as $25.0 \mathrm{cm},$ even though her uncorrected near point is $79.0 \mathrm{cm}$ from her eyes. When she is looking at a poster, the contacts form an image of the poster at a distance of $217 \mathrm{cm}$ from her eyes. (a) How far away is the poster actually located? (b) If the poster is $0.350 \mathrm{m}$ tall, how tall is the image formed by the contacts?

Adnan Gill

Numerade Educator

Problem 83

A jeweler whose near point is $72 \mathrm{cm}$ from his eye uses a magnifying glass as in Figure $26.39 b$ to examine a watch. The watch is held $4.0 \mathrm{cm}$ from the magnifying glass. Find the angular magnification of the magnifying glass.

Narayan Hari

Numerade Educator

Problem 84

A spectator, seated in the left-field stands, is watching a baseball player who is $1.9 \mathrm{m}$ tall and is $75 \mathrm{m}$ away. On a $\mathrm{TV}$ screen, located $3.0 \mathrm{m}$ from a person watching the game at home, the image of this same player is $0.12 \mathrm{m}$ tall. Find the angular size of the player as seen by (a) the spectator watching the game live and (b) the TV viewer. (c) To whom does the player appear to be larger?

Adnan Gill

Numerade Educator

Problem 85

An engraver uses a magnifying glass $(f=9.50 \mathrm{cm})$ to examine some work, as in Figure $26.39 b .$ The image he sees is located $25.0 \mathrm{cm}$ from his eye, which is his near point. (a) What is the distance between the work and the magnifying glass? (b) What is the angular magnification of the magnifying glass?

Narayan Hari

Numerade Educator

Problem 86

The near point of a naked eye is $32 \mathrm{cm} .$ When an object is placed at the near point and viewed by the naked eye, it has an angular size of 0.060 rad. A magnifying glass has a focal length of $16 \mathrm{cm},$ and is held next to the eye. The enlarged image that is seen is located $64 \mathrm{cm}$ from the magnifying glass. Determine the angular size of the image.

Adnan Gill

Numerade Educator

Problem 87

An object has an angular size of 0.0150 rad when placed at the near point $(21.0 \mathrm{cm})$ of an eye. When the eye views this object using a magnifying glass, the largest possible angular size of the image is 0.0380 rad. What is the focal length of the magnifying glass?

Adnan Gill

Numerade Educator

Problem 88

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Ajay Singhal

Numerade Educator

Problem 89

A farsighted person can read printing as close as $25.0 \mathrm{cm}$ when she wears contacts that have a focal length of $45.4 \mathrm{cm} .$ One day, she forgets her contacts and uses a magnifying glass, as in Figure $26.39 b .$ Its maximum angular magnification is 7.50 for a young person with a normal near point of $25.0 \mathrm{cm} .$ What is the maximum angular magnification that the magnifying glass can provide for her?

Narayan Hari

Numerade Educator

Problem 90

A forensic pathologist is viewing heart muscle cells with a microscope that has two selectable objectives with refracting powers of 100 and 300 diopters. When he uses the 100 -diopter objective, the image of a cell subtends an angle of $3 \times 10^{-3}$ rad with the eye. What angle is subtended when he uses the 300 -diopter objective?

Adnan Gill

Numerade Educator

Problem 91

A compound microscope has a barrel whose length is $16.0 \mathrm{cm}$ and an eyepiece whose focal length is $1.4 \mathrm{cm} .$ The viewer has a near point located $25 \mathrm{cm}$ from his eyes. What focal length must the objective have so that the angular magnification of the microscope will be $-320 ?$

Adnan Gill

Numerade Educator

Problem 92

The distance between the lenses in a compound microscope is $18 \mathrm{cm} .$ The focal length of the objective is $1.5 \mathrm{cm} .$ If the microscope is to provide an angular magnification of -83 when used by a person with a normal near point $(25 \mathrm{cm}$ from the eye), what must be the focal length of the eyepiece?

Adnan Gill

Numerade Educator

Problem 93

The near point of a naked eye is $25 \mathrm{cm} .$ When placed at the near point and viewed by the naked eye, a tiny object would have an angular size of $5.2 \times 10^{-5}$ rad. When viewed through a compound microscope, however, it has an angular size of $-8.8 \times 10^{-3}$ rad. (The minus sign indicates that the image produced by the microscope is inverted.) The objective of the microscope has a focal length of $2.6 \mathrm{cm},$ and the distance between the objective and the eyepiece is $16 \mathrm{cm} .$ Find the focal length of the eyepiece.

Adnan Gill

Numerade Educator

Problem 94

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Ajay Singhal

Numerade Educator

Problem 95

In a compound microscope, the focal length of the objective is $3.50 \mathrm{cm}$ and that of the eyepiece is $6.50 \mathrm{cm}$. The distance between the lenses is $26.0 \mathrm{cm} .$ (a) What is the angular magnification of the microscope if the person using it has a near point of $35.0 \mathrm{cm} ?$ (b) If, as usual, the first image lies just inside the focal point of the eyepiece (see Figure 26.32 ), how far is the object from the objective? (c) What is the magnification (not the angular magnification) of the objective?

Adnan Gill

Numerade Educator

Problem 96

An astronomical telescope has an angular magnification of -132 . Its objective has a refractive power of 1.50 diopters. What is the refractive power of its eyepiece?

Adnan Gill

Numerade Educator

Problem 97

Mars subtends an angle of $8.0 \times 10^{-5} \mathrm{rad}$ at the unaided eye. An astronomical telescope has an eyepiece with a focal length of $0.032 \mathrm{m}$. When Mars is viewed using this telescope, it subtends an angle of $2.8 \times 10^{-3} \mathrm{rad}$ Find the focal length of the telescope's objective lens.

Adnan Gill

Numerade Educator

Problem 98

A telescope has an objective with a refractive power of 1.25 diopters and an eyepiece with a refractive power of 250 diopters. What is the angular magnification of the telescope?

Adnan Gill

Numerade Educator

Problem 99

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Ajay Singhal

Numerade Educator

Problem 100

An amateur astronomer decides to build a telescope from a discarded pair of eyeglasses. One of the lenses has a refractive power of 11 diopters, and the other has a refractive power of 1.3 diopters. (a) Which lens should be the objective? (b) How far apart should the lenses be separated? (c) What is the angular magnification of the telescope?

Adnan Gill

Numerade Educator

Problem 101

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Ajay Singhal

Numerade Educator

Problem 102

The lengths of three telescopes are $L_{\mathrm{A}}=455 \mathrm{mm}, L_{\mathrm{B}}=615 \mathrm{mm},$ and $L_{C}=824 \mathrm{mm} .$ The focal length of the eyepiece for each telescope is 3.00 mm. Find the angular magnification of each telescope.

Adnan Gill

Numerade Educator

Problem 103

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Ajay Singhal

Numerade Educator

Problem 104

An astronomical telescope is being used to examine a relatively close object that is only $114.00 \mathrm{m}$ away from the objective of the telescope. The objective and eyepiece have focal lengths of 1.500 and $0.070 \mathrm{m},$ respectively. Noting that the expression $M \approx-f_{\mathrm{o}} / f_{\mathrm{e}}$ is no longer applicable because the object is so close, use the thin-lens and magnification equations to find the angular magnification of this telescope. (Hint: See Figure 26.41 and note that the focal points $F_{\mathrm{o}}$ and $F_{\mathrm{e}}$ are so close together that the distance between them may be ignored.)

Adnan Gill

Numerade Educator

Problem 105

An object is located $30.0 \mathrm{cm}$ to the left of a converging lens whose focal length is $50.0 \mathrm{cm} .$ (a) Draw a ray diagram to scale and from it determine the image distance and the magnification.
(b) Use the thin-lens and magnification equations to verify your answers to part (a).

Adnan Gill

Numerade Educator

Problem 106

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Ajay Singhal

Numerade Educator

Problem 107

A glass block $(n=1.56)$ is immersed in a liquid. A ray of light within the glass hits a glass-liquid surface at a $75.0^{\circ}$ angle of incidence. Some of the light enters the liquid. What is the smallest possible refractive index for the liquid?

Adnan Gill

Numerade Educator

Problem 108

As an aid in understanding this problem, refer to Conceptual Example 4. A swimmer, who is looking up from under the water, sees a diving board directly above at an apparent height of $4.0 \mathrm{m}$ above the water. What is the actual height of the diving board above the water?

Adnan Gill

Numerade Educator

Problem 109

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Ajay Singhal

Numerade Educator

Problem 110

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Ajay Singhal

Numerade Educator

Problem 111

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Ajay Singhal

Numerade Educator

Problem 112

A camper is trying to start a fire by focusing sunlight onto a piece of paper. The diameter of the sun is $1.39 \times 10^{9} \mathrm{m},$ and its mean distance from the earth is $1.50 \times 10^{11} \mathrm{m} .$ The camper is using a converging lens whose focal length is $10.0 \mathrm{cm}$. (a) What is the area of the sun's image on the paper? (b) If $0.530 \mathrm{W}$ of sunlight passes through the lens, what is the intensity of the sunlight at the paper?

Adnan Gill

Numerade Educator

Problem 113

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Ajay Singhal

Numerade Educator

Problem 114

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Ajay Singhal

Numerade Educator

Problem 115

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Ajay Singhal

Numerade Educator

Problem 116

Red light $(n=1.520)$ and violet light $(n=1.538)$ traveling in air are incident on a slab of crown glass. Both colors enter the glass at the same angle of refraction. The red light has an angle of incidence of $30.00^{\circ} .$ What is the angle of incidence of the violet light?

Adnan Gill

Numerade Educator

Problem 117

A converging lens $(f=12.0 \mathrm{cm})$ is held $8.00 \mathrm{cm}$ in front of a newspaper that has a print size with a height of $2.00 \mathrm{mm}$. Find (a) the image distance (in $\mathrm{cm}$ ) and (b) the height (in $\mathrm{mm}$ ) of the magnified print.

Narayan Hari

Numerade Educator

Problem 118

To focus a camera on objects at different distances, the converging lens is moved toward or away from the image sensor, so a sharp image always falls on the sensor. A camera with a telephoto lens $(f=200.0 \mathrm{mm})$ is to be focused on an object located first at a distance of $3.5 \mathrm{m}$ and then at $50.0 \mathrm{m} .$ Over what distance must the lens be movable?

Adnan Gill

Numerade Educator

Problem 119

An office copier uses a lens to place an image of a document onto a rotating drum. The copy is made from this image.
(a) What kind of lens is used, converging or diverging? If the document and its copy are to have the same size, but are inverted with respect to one another,
(b) how far from the document is the lens located and (c) how far from the lens is the image located? Express your answers in terms of the focal length $f$ of the lens.

Adnan Gill

Numerade Educator

Problem 120

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Ajay Singhal

Numerade Educator

Problem 121

At age forty, a man requires contact lenses $(f=65.0 \mathrm{cm})$ to read a book held $25.0 \mathrm{cm}$ from his eyes. At age forty-five, while wearing these contacts he must now hold a book $29.0 \mathrm{cm}$ from his eyes. (a) By what distance has his near point changed? (b) What focal-length lenses does he require at age forty-five to read a book at $25.0 \mathrm{cm} ?$

Adnan Gill

Numerade Educator

Problem 122

An object is in front of a converging lens $(f=0.30 \mathrm{m})$. The magnification of the lens is $m=4.0 .$ (a) Relative to the lens, in what direction should the object be moved so that the magnification changes to $m=-4.0 ?$
(b) Through what distance should the object be moved?

Adnan Gill

Numerade Educator

Problem 123

The angular magnification of a telescope is 32800 times as large when you look through the correct end of the telescope as when you look through the wrong end. What is the angular magnification of the telescope?

Prabhat Tyagi

Numerade Educator

Problem 124

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Ajay Singhal

Numerade Educator

Problem 125

Bill is farsighted and has a near point located $125 \mathrm{cm}$ from his eyes. Anne is also farsighted, but her near point is $75.0 \mathrm{cm}$ from her eyes. Both have glasses that correct their vision to a normal near point $(25.0 \mathrm{cm}$ from the eyes), and both wear the glasses $2.0 \mathrm{cm}$ from the eyes. Relative to the eyes, what is the closest object that can be seen clearly (a) by Anne when she wears Bill's glasses and (b) by Bill when he wears Anne's glasses?

Aishwarya Krishnakumar

Aishwarya Krishnakumar

Numerade Educator

Problem 126

A ray of light is incident on a glass-water interface at the critical angle $\theta_{c}$ as the figure illustrates. The reflected light then passes through a liquid (immiscible with water) and into air. The indices of refraction for the four substances are given in the drawing. Concepts: (i) What determines the critical angle when the ray strikes the glass-water interface? (ii) When the light is incident at the glass-water interface at the critical angle, what is the angle of refraction, and how is the angle $\theta_{1}$ related to the critical angle?(iii) When the reflected ray strikes the glass-liquid interface, how is the angle of refraction $\theta_{3}$ related to the angle of incidence $\theta_{2} ?$ Note that the two materials have the same indices of refraction. (iv) When the ray passes from the liquid into the air, is the ray refracted? Explain. Calculation: Determine the angle of refraction $\theta_{5}$ for the ray as it passes into the air.

Sheh Lit Chang

University of Washington

Problem 127

In the figure, a converging lens $\left(f_{1}=+20.0 \mathrm{cm}\right)$ and a diverging lens $\left(f_{2}=-15.0 \mathrm{cm}\right)$ are separated by a distance of $10.0 \mathrm{cm} .$ An object with a height of $h_{\mathrm{ol}}=5.00 \mathrm{mm}$ is placed at a distance of $d_{\mathrm{ol}}=45.0 \mathrm{cm}$ to the left of the first (converging) lens. Concepts: (i) Is the image produced by the first (converging) lens real or virtual? (ii) As far as the second lens is concerned, what role does the image produced by the first lens play? (iii) Note in the figure that the image produced by the first lens is called the "first image," and it falls to the right of the second lens. This image acts as the object for the second lens. Normally, however, an object would lie to the left of the lens. How do we take into account that this object lies to the right of the diverging lens? (iv) How do we find the location of the image produced by the second lens when its object is a virtual object? Calculation: What are (a) the image distance $d_{i 1}$ and (b) the height $h_{i 1}$ of the image produced by the first lens?
(c) What is the object distance for the second (diverging) lens? Find (d) the image distance $d_{i 2}$ and (e) the height $h_{i 2}$ of the image produced by the second lens.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 128

An Optical Spectrometer. You and your team are tasked with characterizing an equilateral, triangular prism to be used in an optical specAn optical spectrometer contains a dispersive element (in this case, the prism) that separates an incoming beam of light into its constituent wavelengths (or colors), and a photocell that measures the intensity of each color (wavelength) by measuring the intensity of the dispersed light as a function of angle. The index of refraction of the prism material you are using depends on the wavelength as An incident beam of white light impinges on the surface (see drawing) at an angle of 45.0 degrees below the normal. The prism is in air $(n=1.000)$. Relative to the prism base (i.e., the horizontal in the drawing), at what angles do (a) red light $(\lambda=660.0 \mathrm{nm})$ and (b) violet light $(\lambda=410.0 \mathrm{nm})$ emerge on the opposite side? (c) What is the angular range of the full spectrum, from red to violet?

Keshav Singh

Numerade Educator

Problem 129

Emergency Replacement Glasses. One of your team members lost her glasses in a river. She is nearsighted and cannot see long distances without them. You are on an expedition to map a remote area in southern Argentina, and her long-distance vision is crucial to her role in the group. You can request a new pair of glasses for her that will be delivered with the next airdrop of supplies, but she does not know her lens prescription.
(a) Does she need a converging or diverging lens? (b) You do a simple eye test and estimate her far point to be $623.0 \mathrm{cm}$ from her eyes. Assuming she will wear her glasses $2.0 \mathrm{cm}$ in front of her eyes, what should be the focal length of her new lenses? (c) What should be the refractive power of her new lenses (in diopters)?

Hast Aggarwal

Numerade Educator