College Physics

Hugh D. Young Philip W. Adams

Chapter 24

Geometric Optics - all with Video Answers

Educators

Chapter Questions

Problem 1

A candle $4.85 \mathrm{~cm}$ tall is $39.2 \mathrm{~cm}$ to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?

Katie Mcalpine

Katie Mcalpine

Numerade Educator

Problem 2

Two plane mirrors form a $60^{\circ}$ wedge as shown in Figure $24.42 .$ A vertical ray of light reflects off the left side of the wedge. (a) How many times will the beam reflect from the wedge surfaces? (b) What is the final direction of the beam after the last reflection?

Vishal Gupta

Numerade Educator

Problem 3

An object is placed between two plane mirrors arranged at right angles to each other at a distance $d_{1}$ from the surface of one mirror and a distance $d_{2}$ from the surface of the other. (a) How many images are formed? Show the location of the images in a diagram. (b) Draw the paths of rays from the object to the eye of an observer.

Sheh Lit Chang

University of Washington

Problem 4

If you run away from a plane mirror at $2.40 \mathrm{~m} / \mathrm{s},$ at what speed does your image move away from you?

Vishal Gupta

Numerade Educator

Problem 5

A concave spherical mirror has a radius of curvature of $10.0 \mathrm{~cm}$. Calculate the location and size of the image formed of an $8.00-\mathrm{mm}-$ tall object whose distance from the mirror is (a) $15.0 \mathrm{~cm},$ (b) $10.0 \mathrm{~cm}$, (c) $2.50 \mathrm{~cm},$ and (d) $10.0 \mathrm{~m}$

Katie Mcalpine

Numerade Educator

Problem 6

Repeat the previous problem, except use a convex mirror with the same magnitude of focal length.

Farhanul Hasan

Numerade Educator

Problem 7

The diameter of Mars is $6794 \mathrm{~km}$, and its minimum distance from the earth is $5.58 \times 10^{7} \mathrm{~km} .$ (a) When Mars is at this distance, find the diameter of the image of Mars formed by a spherical, concave telescope mirror with a focal length of $1.75 \mathrm{~m}$. (b) Where is the image located?

Vishal Gupta

Numerade Educator

Problem 8

A concave mirror has a radius of curvature of $34.0 \mathrm{~cm} .$ (a) What is its focal length? (b) A ladybug $7.50 \mathrm{~mm}$ tall is located $22.0 \mathrm{~cm}$ from this mirror along the principal axis. Find the location and height of the image of the insect. (c) If the mirror is immersed in water (of refractive index 1.33 ), what is its focal length?

Farhanul Hasan

Numerade Educator

Problem 9

A mirror on the passenger side of your car is convex and has a radius of curvature with magnitude $18.0 \mathrm{~cm}$. (a) Another car is seen in this side mirror and is $13.0 \mathrm{~m}$ behind the mirror. If this car is $1.5 \mathrm{~m}$ tall, what is the height of its image? (b) The mirror has a warning attached that objects viewed in it are closer than they appear. Why is this so?

Vishal Gupta

Numerade Educator

Problem 10

Examining your image in a convex mirror whose radius of curvature is $25.0 \mathrm{~cm},$ you stand with the tip of your nose $10.0 \mathrm{~cm}$ from the surface of the mirror. (a) Where is the image of your nose located? What is its magnification? (b) Your ear is $10.0 \mathrm{~cm}$ behind the tip of your nose; where is the image of your ear located, and what is its magnification? Do your answers suggest reasons for your strange appearance in a convex mirror?

Farhanul Hasan

Numerade Educator

Problem 11

A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of $18.0 \mathrm{~cm}$. An image of the $1.5-\mathrm{cm}$ -tall coin is formed $6.00 \mathrm{~cm}$ behind the glass shell. Where is the coin located? Determine the size, orientation, and nature (real or virtual) of the image.

Katie Mcalpine

Numerade Educator

Problem 12

Consider a concave mirror that has a focal length $f$. In terms of $f$, determine the object distances that will produce a magnification of (a) $-1,(b)-2,$ and $(c)-3$.

Vishal Gupta

Numerade Educator

Problem 13

A spherical, concave shaving mirror has a radius of curvature of $32.0 \mathrm{~cm} .$ (a) What is the magnification of a person's face when it is $12.0 \mathrm{~cm}$ to the left of the vertex of the mirror? (b) Where is the image? Is the image real or virtual? (c) Draw a principal-ray diagram showing the formation of the image.

Jason Bane

Numerade Educator

Problem 14

An object $0.600 \mathrm{~cm}$ tall is placed $16.5 \mathrm{~cm}$ to the left of the vertex of a concave spherical mirror having a radius of curvature of $22.0 \mathrm{~cm}$. (a) Draw a principal-ray diagram showing the formation of the image. (b) Calculate the position, size, orientation (upright or inverted), and nature (real or virtual) of the image.

Vishal Gupta

Numerade Educator

Problem 15

Repeat the previous problem for the case in which the mirror is convex.

Katie Mcalpine

Numerade Educator

Problem 16

The thin glass shell shown in Figure 24.43 has a spherical shape with a radius of curvature of $12.0 \mathrm{~cm}$, and both of its surfaces can act as mirrors. A seed $3.30 \mathrm{~mm}$ high is placed $15.0 \mathrm{~cm}$ from the center of the mirror along the optic axis, as shown in the figure. (a) Calculate the location and height of the image of this seed. (b) Suppose now that the shell is reversed. Find the location and height of the seed's image.

Dading Chen

Numerade Educator

Problem 17

A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an upright image with a magnification of 2.00 when the mirror is $1.25 \mathrm{~cm}$ from a tooth. (Treat this problem as though the object and image lie along a straight line.) (a) What kind of mirror (concave or convex) is needed? Use a ray diagram to decide, without performing any calculations. (b) What must be the focal length and radius of curvature of this mirror? (c) Draw a principal-ray diagram to check your answer in part (b).

Vishal Gupta

Numerade Educator

Problem 18

The left end of a long glass rod $6.00 \mathrm{~cm}$ in diameter has a convex hemispherical surface $3.00 \mathrm{~cm}$ in radius. The refractive index of the glass is $1.60 .$ Determine the position of the image if an object is placed in air on the axis of the rod at the following distances to the left of the vertex of the curved end: (a) infinitely far, (b) $12.0 \mathrm{~cm},$ and (c) $2.00 \mathrm{~cm}$

Katie Mcalpine

Numerade Educator

Problem 19

The rod of the previous problem is immersed in a liquid. An object $90.0 \mathrm{~cm}$ from the vertex of the left end of the rod and on its axis is imaged at a point $1.60 \mathrm{~m}$ inside the rod. What is the refractive index of the liquid?

Farhanul Hasan

Numerade Educator

Problem 20

The left end of a long glass rod $8.00 \mathrm{~cm}$ in diameter and with an index of refraction of 1.60 is ground and polished to a convex hemispherical surface with a radius of $4.00 \mathrm{~cm} .$ An object in the form of an arrow $1.50 \mathrm{~mm}$ tall, at right angles to the axis of the rod, is located on the axis $24.0 \mathrm{~cm}$ to the left of the vertex of the convex surface. Find the position and height of the image of the arrow formed by paraxial rays incident on the convex surface. Is the image upright or inverted?

Ryan Kutayiah

Texas A&M University

Problem 21

A large aquarium has portholes of thin transparent plastic with a radius of curvature of $1.75 \mathrm{~m}$ and their convex sides facing into the water. A shark hovers in front of a porthole, sizing up the dinner prospects outside the tank. (a) If one of the shark's teeth is exactly $45.0 \mathrm{~cm}$ from the plastic, how far from the plastic does it appear to be to observers outside the tank? (You can ignore refraction due to the plastic.) (b) Does the shark appear to be right side up or upside down? (c) If the tooth has an actual length of $5.00 \mathrm{~cm}$, how long does it appear to the observers?

Vishal Gupta

Numerade Educator

Problem 22

The cornea of the eye has a radius of curvature of approximately $0.50 \mathrm{~cm},$ and the aqueous humor behind it has an index of refraction of $1.35 .$ The thickness of the cornea itself is small enough that we can ignore it. The depth of a typical human eye is around $25 \mathrm{~mm}$. (a) What would have to be the radius of curvature of the cornea so that it alone would focus the image of a distant mountain on the retina, which is at the back of the eye opposite the cornea? (b) If the cornea focused the mountain correctly on the retina as described in part (a), would it also focus the text from a computer screen on the retina if that screen were $25 \mathrm{~cm}$ in front of the eye? If not, where would it focus that text, in front of or behind the retina? (c) Given that the cornea has a radius of curvature of about $5.0 \mathrm{~mm},$ where does it actually focus the mountain? Is this in front of or behind the retina? Does this help you see why the eye needs help from a lens to complete the task of focusing?

Vishal Gupta

Numerade Educator

Problem 23

A speck of dirt is embedded $3.50 \mathrm{~cm}$ below the surface of a sheet of ice having a refractive index of $1.309 .$ What is the apparent depth of the speck, when viewed from directly above?

Katie Mcalpine

Numerade Educator

Problem 24

A skin diver is $2.0 \mathrm{~m}$ below the surface of a lake. A bird flies overhead $7.0 \mathrm{~m}$ above the surface of the lake. When the bird is directly overhead, how far above the diver does it appear to be?

Rashmi Sinha

Numerade Educator

Problem 25

A person is swimming $1.0 \mathrm{~m}$ beneath the surface of the water in a swimming pool. A child standing on the diving board drops a ball into the pool directly above the swimmer. The swimmer sees the ball dropped from a height of $3.0 \mathrm{~m}$ above the water. From what height was the ball actually dropped?

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 26

A converging lens with a focal length of $7.00 \mathrm{~cm}$ forms an image of a $4.00-\mathrm{mm}$ -tall real object that is to the left of the lens. The image is $1.30 \mathrm{~cm}$ tall and upright. Where are the object and image located? Is the image real or virtual?

Vishal Gupta

Numerade Educator

Problem 27

A converging lens with a focal length of $90.0 \mathrm{~cm}$ forms an image of a $3.20-\mathrm{cm}$ -tall real object that is to the left of the lens. The image is $4.50 \mathrm{~cm}$ tall and inverted. Where are the object and image located in relation to the lens? Is the image real or virtual?

Vishal Gupta

Numerade Educator

Problem 28

You are standing $0.50 \mathrm{~m}$ in front of a lens that projects an image of you onto a wall $2.0 \mathrm{~m}$ on the other side of the lens. (a) What is the focal length of the lens? (b) What is the magnification?

Vishal Gupta

Numerade Educator

Problem 29

Figure 24.44 shows an object and its image formed by a thin lens. (a) What is the focal length of the lens and what type of lens (converging or diverging) is it? (b) What is the height of the image? Is it real or virtual?

Vishal Gupta

Numerade Educator

Problem 30

Figure 24.45 shows an object and its image formed by a thin lens. (a) What is the focal length of the lens and what type of lens (converging or diverging) is it? (b) What is the height of the image? Is it real or virtual?

Farhanul Hasan

Numerade Educator

Problem 31

Figure 24.46 shows an object and its image formed by a thin lens. (a) What is the focal length of the lens and what type of lens (converging or diverging) is it? (b) What is the height of the image? Is it real or virtual?

Katie Mcalpine

Numerade Educator

Problem 32

The two surfaces of a plastic converging lens have equal radii of curvature of $22.0 \mathrm{~cm},$ and the lens has a focal length of $20.0 \mathrm{~cm} .$ Calculate the index of refraction of the plastic.

Katie Mcalpine

Numerade Educator

Problem 33

A lens has an index of refraction of 1.7 and a focal length of $12 \mathrm{~cm} .$ The front convex surface of a lens has a radius of curvature of $15 \mathrm{~cm} .$ Calculate the radius of curvature of the back convex surface of the lens.

Vishal Gupta

Numerade Educator

Problem 34

For each thin lens shown in Figure $24.47,$ calculate the location of the image of an object that is $18.0 \mathrm{~cm}$ to the left of the lens. The lens material has a refractive index of $1.50,$ and the radii of curvature shown are only the magnitudes.

Dominador Tan

Numerade Educator

Problem 35

The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in air is about $8.0 \mathrm{~mm},$ which also varies. We shall assume that the radii of curvature of its two surfaces have the same magnitude. (a) Find the radii of curvature of this lens. (b) If an object $16 \mathrm{~cm}$ tall were placed $30.0 \mathrm{~cm}$ from the eye lens, where would the lens focus it and how tall would the image be? Is this image real or virtual? Is it upright or inverted? (Note: The results obtained here are not strictly accurate because the lens is embedded in fluids having refractive indices different from that of air.)

Vishal Gupta

Numerade Educator

Problem 36

The cornea behaves as a thin lens of focal length approximately $1.8 \mathrm{~cm},$ although this varies a bit. The material of which it is made has an index of refraction of 1.38 , and its front surface is convex, with a radius of curvature of $5.0 \mathrm{~mm}$. (a) If this focal length is in air, what is the radius of curvature of the back side of the cornea? (b) The closest distance at which a typical person can focus on an object (called the near point) is about $25 \mathrm{~cm}$, although this varies considerably with age. Where would the cornea focus the image of an $8.0-\mathrm{mm}$ -tall object at the near point? (c) What is the height of the image in part (b)? Is this image real or virtual? Is it upright or inverted? (Note: The results obtained here are not strictly accurate because, on one side, the cornea has a fluid with a refractive index different from that of air.)

Vishal Gupta

Numerade Educator

Problem 37

An insect $3.75 \mathrm{~mm}$ tall is placed $22.5 \mathrm{~cm}$ to the left of a thin planoconvex lens. The left surface of this lens is flat, the right surface has a radius of curvature of magnitude $13.0 \mathrm{~cm},$ and the index of refraction of the lens material is $1.70 .$ (a) Calculate the location and size of the image this lens forms of the insect. Is it real or virtual? Upright or inverted? (b) Repeat part (a) if the lens is reversed.

Vishal Gupta

Numerade Educator

Problem 38

Two double-convex thin lenses each have surfaces with the same radius of curvature of magnitude $2.50 \mathrm{~cm} .$ However, lens 1 has a focal length of $f_{1}=2.5 \mathrm{~cm}$ and lens 2 has a focal length of $f_{2}=1.25 \mathrm{~cm} .$ Find the ratio of the indices of refraction of the two lenses, $n_{1} / n_{2}$.

Vishal Gupta

Numerade Educator

Problem 39

A converging meniscus lens (see Figure 24.30 ) with a refractive index of 1.52 has spherical surfaces whose radii are $7.00 \mathrm{~cm}$ and $4.00 \mathrm{~cm} .$ What is the position of the image if an object is placed $24.0 \mathrm{~cm}$ to the left of the lens? What is the magnification?

Sheh Lit Chang

University of Washington

Problem 40

A converging lens with a focal length of $12.0 \mathrm{~cm}$ forms a virtual image $8.00 \mathrm{~mm}$ tall, $17.0 \mathrm{~cm}$ to the right of the lens. Determine the position and size of the object. Is the image upright or inverted? Are the object and image on the same side or opposite sides of the lens?

Vishal Gupta

Numerade Educator

Problem 41

Combination of lenses, I. When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A $1.20-\mathrm{cm}-$ tall object is $50.0 \mathrm{~cm}$ to the left of a converging lens of focal length $40.0 \mathrm{~cm} .$ A second converging lens, this one having a focal length of $60.0 \mathrm{~cm},$ is located $300.0 \mathrm{~cm}$ to the right of the first lens along the same optic axis. (a) Find the location and height of the image (call it $I_{1}$ ) formed by the lens with a focal length of $40.0 \mathrm{~cm}$. (b) $I_{1}$. is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

Vishal Gupta

Numerade Educator

Problem 42

(a) You want to use a lens with a focal length of $35.0 \mathrm{~cm}$ to produce a real image of an object, with the image twice as long as the object itself. What kind of lens do you need, and where should the object be placed? (b) Suppose you want a virtual image of the same object, with the same magnification-what kind of lens do you need, and where should the object be placed?

Farhanul Hasan

Numerade Educator

Problem 43

Two thin lenses with a focal length of magnitude $12.0 \mathrm{~cm},$ the first diverging and the second converging, are located $9.00 \mathrm{~cm}$ apart. An object $2.50 \mathrm{~mm}$ tall is placed $20.0 \mathrm{~cm}$ to the left of the first (diverging) lens. (a) How far from this first lens is the final image formed? (b) Is the final image real or virtual? (c) What is the height of the final image? Is it upright or inverted? (Hint: See Problem 41.)

Vishal Gupta

Numerade Educator

Problem 44

A lens forms a real image that is $214 \mathrm{~cm}$ away from the object and $1 \frac{2}{3}$ times its length. What kind of lens is this, and what is its focal length?

Vishal Gupta

Numerade Educator

Problem 45

A converging lens has a focal length of $14.0 \mathrm{~cm} .$ For each of two objects located to the left of the lens, one at a distance of $18.0 \mathrm{~cm}$ and the other at a distance of $7.00 \mathrm{~cm},$ determine (a) the image position, (b) the magnification, (c) whether the image is real or virtual, and (d) whether the image is upright or inverted. Draw a principal-ray diagram in each case.

Vishal Gupta

Numerade Educator

Problem 46

A converging lens forms an image of an $8.00-\mathrm{mm}$ -tall real object. The image is $12.0 \mathrm{~cm}$ to the left of the lens, $3.40 \mathrm{~cm}$ tall, and upright. (a) What is the focal length of the lens? (b) Where is the object located? (c) Draw a principal-ray diagram for this situation.

Vishal Gupta

Numerade Educator

Problem 47

A diverging lens with a focal length of $-48.0 \mathrm{~cm}$ forms a virtual image $8.00 \mathrm{~mm}$ tall, $17.0 \mathrm{~cm}$ to the right of the lens. (a) Determine the position and size of the object. Is the image upright or inverted? Are the object and image on the same side or opposite sides of the lens? (b) Draw a principal-ray diagram for this situation.

Vishal Gupta

Numerade Educator

Problem 48

When an object is $16.0 \mathrm{~cm}$ from a lens, an image is formed $12.0 \mathrm{~cm}$ from the lens on the same side as the object. (a) What is the focal length of the lens? Is the lens converging or diverging? (b) If the object is $8.50 \mathrm{~mm}$ tall, how tall is the image? Is it upright or inverted? (c) Draw a principal-ray diagram.

Vishal Gupta

Numerade Educator

Problem 49

Figure 24.48 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is $2.0 \mathrm{~cm}$ along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions: (a) Using only the ray shown, decide what type of lens (converging or diverging) this is. (b) What is the focal length of the lens? (c) Locate the image by drawing the other two principal rays. (d) Calculate where the image should be, and compare this result with the graphical solution in part (c).

Vishal Gupta

Numerade Educator

Problem 50

Figure 24.49 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is $2.0 \mathrm{~cm}$ along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions: (a) Using only the ray shown, decide what type of lens (converging or diverging) this is. (b) What is the focal length of the lens? (c) Locate the image by drawing the other two principal rays. (d) Calculate where the image should be, and compare this result with the graphical solution in part (c).

Vishal Gupta

Numerade Educator

Problem 51

Figure 24.50 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is $2.0 \mathrm{~cm}$ along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following

Vishal Gupta

Numerade Educator

Problem 52

A layer of benzene $(n=1.50) 2.60 \mathrm{~cm}$ deep floats on water $(n=1.33)$ that is $6.50 \mathrm{~cm}$ deep. What is the apparent distance from the upper benzene surface to the bottom of the water layer when it is viewed at normal incidence?

Vishal Gupta

Numerade Educator

Problem 53

Where must you place an object in front of a concave mirror with focal length $f$ so that the image is upright and twice the size of the object? Where is the image?

Vishal Gupta

Numerade Educator

Problem 54

A physics student is given a set of converging lenses that have a range of focal lengths. The lab instructor asks her to position an object in front of each lens so that the image distance always has the same value, which is specified in the lab manual. The table gives the measured object distances and the corresponding focal lengths.
$$\begin{array}{ll}\hline f(\mathrm{~cm}) & d_{0}(\mathrm{~cm}) \\
\hline 5 & 10.1 \\
6 & 15.3 \\
7 & 22.8 \\
8 & 39.2 \\
9 & 90.5\end{array}$$
Make a plot of the inverse focal length as a function of the inverse object distance. Using a linear "best fit" to the data, determine the image distance that was specified in the lab manual.

James Kiss

Numerade Educator

Problem 55

A concave mirror is to form an image of the filament of a headlight lamp on a screen $8.00 \mathrm{~m}$ from the mirror. The filament is $6.00 \mathrm{~mm}$ tall, and the image is to be $36.0 \mathrm{~cm}$ tall. (a) How far in front of the vertex of the mirror should the filament be placed? (b) To what radius of curvature should you grind the mirror?

Farhanul Hasan

Numerade Educator

Problem 56

A lens has one convex surface of radius $6.00 \mathrm{~cm}$ and one concave surface of radius $10.0 \mathrm{~cm} .$ When an object is placed $35.0 \mathrm{~cm}$ from the lens, a real image is formed $50 \mathrm{~cm}$ from the lens. (a) What is the focal length of the lens? (b) What is the index of refraction of the lens?

Vishal Gupta

Numerade Educator

Problem 57

A 3.80-mm-tall object is $24.0 \mathrm{~cm}$ from the center of a silvered spherical glass Christmas tree ornament $6.00 \mathrm{~cm}$ in diameter. What are the position and height of its image?

Vishal Gupta

Numerade Educator

Problem 58

A lensmaker wants to make a magnifying glass from glass with $n=1.55$ and with a focal length of $20.0 \mathrm{~cm} .$ If the two surfaces of the lens are to have equal radii, what should that radius be?

Katie Mcalpine

Numerade Educator

Problem 59

An object is placed $18.0 \mathrm{~cm}$ from a screen. (a) At what two points between object and screen may a converging lens with a $3.00 \mathrm{~cm}$ focal length be placed to obtain an image on the screen? (b) What is the magnification of the image for each position of the lens?

Narayan Hari

Numerade Educator

Problem 60

In the text, Equations 24.4 and 24.7 were derived for the case of a concave mirror. Give a similar derivation for a convex mirror, and show that the same equations result if you use the sign convention established in the text.

Farhanul Hasan

Numerade Educator

Problem 61

A lens obeys Snell's law, bending light rays at each surface an amount determined by the index of refraction of the lens and the index of the medium in which the lens is located.
(a) Equation 24.20 assumes that the lens is surrounded by air. Consider instead a thin lens immersed in a liquid with refractive index $n_{\mathrm{liq}} .$ Prove that the focal length $f^{\prime}$ is then given by Equation 24.20 with $n$ replaced by $n / n_{\mathrm{liq}} .$ (b) A thin lens with index $n$ has focal length $f$ in vacuum. Use the result of part (a) to show that when this lens is immersed in a liquid of index $n_{\mathrm{liq}},$ it will have a new focal length given by
$$f^{\prime}=\left[\frac{n_{\mathrm{liq}}(n-1)}{n-n_{\mathrm{liq}}}\right] f.$$

Vishal Gupta

Numerade Educator

Problem 62

The focal length of a mirror can be determined entirely from the shape of the mirror. In contrast, to determine the focal length of a lens, we must know both the shape of the lens and its index of refraction - as well as the index of refraction of the surrounding medium. For instance, when a thin lens is immersed in a liquid, we must modify the thin-lens equation to take into account the refractive properties of the surrounding liquid:
$$\frac{1}{f}=\left(\frac{n}{n_{\mathrm{liq}}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right),$$
where $n_{\text {liq }}$ is the index of refraction of the liquid and $n$ is the index of refraction of the glass.

If you place a glass lens $(n=1.5),$ which has a focal length of $0.5 \mathrm{~m}$ in air, into a tank of water $(n=1.33),$ what will happen to its focal length?
A. Nothing will happen.
B. The focal length of the lens will be reduced.
C. The focal length of the lens will be increased.
D. There is not enough information to answer the question.

Vishal Gupta

Numerade Educator

Problem 63

The focal length of a mirror can be determined entirely from the shape of the mirror. In contrast, to determine the focal length of a lens, we must know both the shape of the lens and its index of refraction - as well as the index of refraction of the surrounding medium. For instance, when a thin lens is immersed in a liquid, we must modify the thin-lens equation to take into account the refractive properties of the surrounding liquid:
$$\frac{1}{f}=\left(\frac{n}{n_{\mathrm{liq}}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right),$$
where $n_{\text {liq }}$ is the index of refraction of the liquid and $n$ is the index of refraction of the glass.

If you place a concave glass lens into a tank of a liquid that has an index of refraction that is greater than that of the lens, what will happen?
A. The lens will no longer be able to create any images.
B. The focal length of the lens will become longer.
C. The focal length of the lens will become shorter.
D. The lens will become a converging lens.

Vishal Gupta

Numerade Educator

Problem 64

The focal length of a mirror can be determined entirely from the shape of the mirror. In contrast, to determine the focal length of a lens, we must know both the shape of the lens and its index of refraction - as well as the index of refraction of the surrounding medium. For instance, when a thin lens is immersed in a liquid, we must modify the thin-lens equation to take into account the refractive properties of the surrounding liquid:
$$\frac{1}{f}=\left(\frac{n}{n_{\mathrm{liq}}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right),$$
where $n_{\text {liq }}$ is the index of refraction of the liquid and $n$ is the index of refraction of the glass.

If you place a concave mirror with a focal length of $1 \mathrm{~m}$ into water, what will happen?
A. The mirror will no longer be able to focus light.
B. The focal length of the mirror will decrease.
C. The focal length of the mirror will increase.
D. Nothing will happen.

Vishal Gupta

Numerade Educator

Problem 65

The focal length of a mirror can be determined entirely from the shape of the mirror. In contrast, to determine the focal length of a lens, we must know both the shape of the lens and its index of refraction - as well as the index of refraction of the surrounding medium. For instance, when a thin lens is immersed in a liquid, we must modify the thin-lens equation to take into account the refractive properties of the surrounding liquid:
$$\frac{1}{f}=\left(\frac{n}{n_{\mathrm{liq}}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right),$$
where $n_{\text {liq }}$ is the index of refraction of the liquid and $n$ is the index of refraction of the glass.

In air, a particular person sees clearly when wearing eyeglasses that have glass lenses with a specific radius of curvature. To see clearly when scuba diving, this person wants to have her optometrist make new lenses that can be mounted in front of her scuba mask so that the lenses are surrounded by water. Which of the following is true if the new lenses are to have the same focal length in water as the original lenses do in air? The new lenses need to
A. have a larger radius of curvature compared to the original lenses.
B. have a smaller radius of curvature compared to the original lenses.
C. have the same radius of curvature as the original lenses.
D. be flat pieces of glass.

Vishal Gupta

Numerade Educator