College Physics Explore and Apply

Eugenia Etkina; Alan Van Heuvelen; Gorazd Planinši?

Chapter 23

Mirrors and Lenses - all with Video Answers

Educators

Chapter Questions

Problem 1

You need to teach your friend how to draw rays to locate the images of objects produced by a plane mirror. Outline the steps that she needs to take.

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 2

Place a pencil in front of a plane mirror so that it is not parallel to the mirror. Draw an image that the mirror forms of the pencil and show using rays how the image is formed.

Vishal Gupta

Numerade Educator

Problem 3

Use geometry to prove that the virtual image of an object in a plane mirror is at exactly the same distance behind the mirror as the object is in front.

Vishal Gupta

Numerade Educator

Problem 4

You are $1.8 \mathrm{m}$ tall. Where should you place the top of a mirror on the wall so you can see the top of your head? Where should you stand with respect to the wall?

Vishal Gupta

Numerade Educator

Problem 5

Two people are standing in front of a rectangular plane mirror. Each of them claims that she sees her own image but not the image of the other person. Draw a ray diagram to find out if this is possible.

Vishal Gupta

Numerade Educator

Problem 6

Test an idea Describe an experiment that you can conduct to test that the image produced by a plane mirror is virtual.

Vishal Gupta

Numerade Educator

Problem 7

Describe in detail an experiment to find the image of a candle produced in a curved mirror. Draw pictures of the experimental setup and a ray diagram. Show on the ray diagram where your eye is.

Vishal Gupta

Numerade Educator

Problem 8

Explain with a ray diagram how (a) a concave mirror and (b) a convex mirror produce images of objects. Make sure that you explain the choice of rays and the location of your eye.

Vishal Gupta

Numerade Educator

Problem 9

Test an idea Describe an experiment to test the idea that a convex mirror never produces a real image of an object.

Vishal Gupta

Numerade Educator

Problem 10

Test an idea Describe an experiment to test the mirror equation. What are you going to measure? What are you going to calculate?

Vishal Gupta

Numerade Educator

Problem 11

Tablespoon mirror You look at yourself in the back (convex shape) of a shiny steel tablespoon. Describe and explain what you see as you bring the spoon closer to your face. Then turn the spoon around and repeat the steps.

Vishal Gupta

Numerade Educator

Problem 12

Use ray diagrams and the mirror equation to locate the position, orientation, and type of image of an object placed in front of a concave mirror of focal length $20 \mathrm{cm} .$ The object distance is (a) $200 \mathrm{cm},$ (b) $40 \mathrm{cm},$ and (c) $10 \mathrm{cm}$.

Vishal Gupta

Numerade Educator

Problem 13

Repeat Problem 23.12 for a convex mirror of focal length $-20 \mathrm{cm}$.

Vishal Gupta

Numerade Educator

Problem 14

Use ray diagrams and the mirror equation to locate the images of the following objects: (a) an object that is $10 \mathrm{cm}$ from a concave mirror of focal length $7 \mathrm{cm}$ and $(\mathrm{b})$ an object that is $10 \mathrm{cm}$ from a convex mirror of focal length $-7 \mathrm{cm}$.

Vishal Gupta

Numerade Educator

Problem 15

Sinking ships A legend says that Archimedes once saved his native town of Syracuse by burning the enemy's fleet with mirrors. Describe quantitatively the type of mirrors that Archimedes could have used to burn ships that were $150 \mathrm{m}$ away. Justify your answer.

Vishal Gupta

Numerade Educator

Problem 16

Fortune-teller A fortune-teller looks into a silver-surfaced crystal ball with a radius of $10 \mathrm{cm}$ and focal length of $-5 \mathrm{cm} .$ (a) If her eye is $30 \mathrm{cm}$ from the ball's surface, where is the image of her eye? (b) Estimate the size of that image.

Vishal Gupta

Numerade Educator

Problem 17

You view yourself in a large convex mirror of $-1.2-\mathrm{m}$ focal length from a distance of $3.0 \mathrm{m}$ (a) Locate your image. (b) If you are $1.7 \mathrm{m}$ tall, what is your image height?

Vishal Gupta

Numerade Educator

Problem 18

Seeing the Moon in a mirror The Moon's diameter is $3.5 \times 10^{3} \mathrm{km},$ and its distance from Earth is $3.8 \times 10^{5} \mathrm{km} .$ Determine the position and size of the image formed by the Hale Telescope reflecting mirror, which has a focal length of $+16.9 \mathrm{m}$.

Vishal Gupta

Numerade Educator

Problem 19

You view your face in a $+20-\mathrm{cm}$ focal length concave mirror. Where should your face be in order to form an image that is magnified by a factor of $1.5 ?$

Vishal Gupta

Numerade Educator

Problem 20

Buying a dental mirror A dentist wants to purchase a small mirror that will produce an upright image of magnification +4.0 when placed $1.6 \mathrm{cm}$ from a tooth. What mirror should she order? Say everything you can about he mirror.

Vishal Gupta

Numerade Educator

Problem 21

Using a dental mirror A dentist examines a tooth that is $1.0 \mathrm{cm}$ in front of the dental mirror. An image is formed $2.0 \mathrm{cm}$ behind the mirror. Say everything you can about the mirror and the image of the tooth.

Vishal Gupta

Numerade Educator

Problem 22

Spooky fish The glasshead barreleye (Rhynchohyalus natalensis) is a fish that lives in the oceans around the world at depths of 200 to $600 \mathrm{m} .$ This fish and the brownsnout spookfish are the only two vertebrates known to use mirror-like reflective surfaces to form the images in their eyes. These fish have eyes with reflective surfaces to observe regions below them and eyes with lenses to observe regions above and beside them. Figure $P 23.22$ is a sketch of the cross section of an eye that uses reflection and shows how the eye focuses parallel beams of light that enter the eye at two extreme angles. Use the dimensions in the figure to estimate the range of values for the radius of curvature of the reflective surface. You will need a ruler to solve this problem.

Prashant Bana

Numerade Educator

Problem 23

If you place a point-like light source on the axis of a convex lens, you obtain on the screen the pattern shown in Figure $P 23.23$ a. If you repeat the experiment with a concave lens, you obtain the pattern shown in Figure $\mathrm{P} 23.24 \mathrm{b} .$ Explain qualitatively how the patterns are formed, using ray diagrams. Note that there are no frames around the lenses.

Vishal Gupta

Numerade Educator

Problem 24

You have a convex lens and a candle. Describe in detail an experiment that you will perform to find the image of the candle that this lens produces. Draw pictures of the experimental setup and a ray diagram. Show on the ray diagram where your eye is.

Vishal Gupta

Numerade Educator

Problem 25

Explain how to draw ray diagrams to locate images produced by objects in front of convex and concave lenses. Focus on the choice of rays and how you know where and what type of image is produced.

Vishal Gupta

Numerade Educator

Problem 26

Draw ray diagrams to show how a convex lens can produce (a) a real image that is smaller than the object, (b) a real image larger than the object, and (c) a virtual image.

Vishal Gupta

Numerade Educator

Problem 27

Use a ruler to draw ray diagrams to locate the images of the following objects: (a) an object that is $30 \mathrm{cm}$ from a convex lens of $+10-\mathrm{cm}$ focal length, (b) an object that is $14 \mathrm{cm}$ from the same lens, and (c) an object that is $5 \mathrm{cm}$ from the same lens. (Choose a scale so that your drawing fills a significant portion of the width of a paper.) Measure the image locations on your drawings and indicate if they are real or virtual, upright or inverted.

Vishal Gupta

Numerade Educator

Problem 28

Repeat the procedure described in Problem 23.27 for the following lenses and objects: (a) an object that is $30 \mathrm{cm}$ from a concave lens of $-10-\mathrm{cm}$ focal length, (b) an object that is $14 \mathrm{cm}$ from the same lens, and (c) an object that is $5 \mathrm{cm}$ from the same lens.

Vishal Gupta

Numerade Educator

Problem 29

Repeat the procedure described in Problem 23.27 for the following lenses and objects: (a) an object that is $7 \mathrm{cm}$ from a convex lens of $+10-\mathrm{cm}$ focal length and (b) an object that is $7 \mathrm{cm}$ from a concave lens of $-10-\mathrm{cm}$ focal length.

Vishal Gupta

Numerade Educator

Problem 30

Repeat the procedure in Problem 23.27 for the following lenses and objects: (a) an object that is $20 \mathrm{cm}$ from a convex lens of $+10-\mathrm{cm}$ focal length, (b) an object that is $5 \mathrm{cm}$ from the same lens, (c) an object that is $20 \mathrm{cm}$ from a concave lens of $-10-\mathrm{cm}$ focal length, and (d) an object that is $5 \mathrm{cm}$ from the lens in part (c).

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 31

Partially covering lens Your friend thinks that if she covers one half of a convex lens she will only be able to see half of the object. Do you agree with her opinion? Why would she have such an opinion? Provide physics arguments. Design an experiment to test her idea.

Vishal Gupta

Numerade Educator

Problem 32

Use ray diagrams to locate the images of the following objects: (a) an object that is $10 \mathrm{cm}$ from a convex lens of $+15-\mathrm{cm}$ focal length and (b) an object that is $10 \mathrm{cm}$ from a concave lens of $-15-\mathrm{cm}$ focal length. (c) Calculate the image locations for parts (a) and (b) using the thin lens equation. Check for consistency.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 33

Use ray diagrams to locate the images of the following objects: (a) an object that is $6.0 \mathrm{cm}$ from a convex lens of $+4.0-\mathrm{cm}$ focal length and (b) an object that is $8.0 \mathrm{cm}$ from a diverging lens of $-4.0-\mathrm{cm}$ focal length. (c) Calculate the image locations for parts (a) and (b) using the thin lens equation. Check for consistency.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 34

Light passes through a narrow slit, and then through a lens and onto a screen. The slit is $20 \mathrm{cm}$ from the lens. The screen, when adjusted for a sharp image of the slit, is $15 \mathrm{cm}$ from the lens. What is the focal length of the lens?

Prabhu Ramji

Numerade Educator

Problem 35

Describe two experiments that you can perform to determine the focal length of a glass convex lens. Is it a converging or a diverging lens? How do you know?

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 36

Shaving/makeup mirror You wish to order a mirror for shaving or makeup. The mirror should produce an image that is upright and magnified by a factor of 2.0 when held $15 \mathrm{cm}$ from your face. What type and focal length mirror should you order?

Vishal Gupta

Numerade Educator

Problem 37

Dentist lamps Dentists use special lamps that consist of a concave mirror and a small, bright light source that is fixed on the principal axis of the mirror. When the light source is placed $5.0 \mathrm{cm}$ from the mirror, the reflected light is focused in a bright spot at distance $70.0 \mathrm{cm}$ from the mirror. Determine the radius of curvature of the mirror.

Vishal Gupta

Numerade Educator

Problem 38

A large concave mirror of focal length $3.0 \mathrm{m}$ stands $20 \mathrm{m}$ in front of you. Describe the changing appearance of your image as you move from $20 \mathrm{m}$ to $1.0 \mathrm{m}$ from the mirror. Indicate distances from the mirror where the change in appearance is dramatic.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 39

Two convex mirrors on the side of a van are shown in Figure P23.39. Estimate the ratio $f_{\text {upper }} / f_{\text {lower }}$ of the focal lengths of the mirrors. Explain the reasoning behind your estimate, stating what assumptions you had to make.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 40

Your friend gives you the following description of a method that apparently allows you to estimate the focal length of a concave lens: "Place a ruler on a table. Hold the lens above the ruler and parallel to the table so that you can simultaneously observe the image of the ruler (through the lens) and the part of the ruler that extends beyond the lens. Move the lens up and down until the width of the image of the ruler is half the width of the ruler that extends beyond the lens. The distance between the lens and the ruler is equal to the focal distance of the lens." Do you agree that this method gives you the focal length of the concave lens? Explain using a ray diagram.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 41

Camera You are using a camera with a lens of focal length $6.0 \mathrm{cm}$ to take a picture of a painting located $3.0 \mathrm{m}$ from the camera lens. Where should the image sensor be positioned in relation to the lens in order to capture the image?

Vishal Gupta

Numerade Educator

Problem 42

Camera A camera with an $8.0-\mathrm{cm}$ focal length lens is used to photograph a person who is $2.0 \mathrm{m}$ tall. The height of the image on the image sensor must be no greater than $3.5 \mathrm{cm}$. (a) Calculate the closest distance the person can stand to the lens. (b) For this object distance, how far should the image sensor be located from the lens?

Vishal Gupta

Numerade Educator

Problem 43

Video projector An LCD video projector (LCD stands for liquid-crystal display ) produces real, inverted, enlarged images of a small LCD picture on a screen (the display picture is upside down in the projector). If the display is located $12.6 \mathrm{cm}$ from the $12.0-\mathrm{cm}$ focal length lens of the projector, what are (a) the distance between the screen and the lens and (b) the height of the image of a person on the screen who is $2.0 \mathrm{cm}$ tall on the display?

Vishal Gupta

Numerade Educator

Problem 44

Photo of carpenter ant You take a picture of a carpenter ant with an old fashioned camera with a lens $18 \mathrm{cm}$ from the film. How far from the 4.0-cm focal length convex camera lens should the ant be located so you see a sharp image of the ant on the film?

Vishal Gupta

Numerade Educator

Problem 45

Photo of secret document A secret agent uses a camera with a $5.0-\mathrm{cm}$ focal length lens to photograph a document whose height is $10 \mathrm{cm} .$ At what distance from the lens should the agent hold the document so that an image $2.5 \mathrm{cm}$ high is produced on the image sensor? [Note: The real image is inverted.]

Vishal Gupta

Numerade Educator

Problem 46

Photo of landscape To photograph a landscape $2.0 \mathrm{km}$ wide from a height of $5.0 \mathrm{km},$ Joe uses an aerial camera with a lens of $0.40-\mathrm{m}$ focal length. What is the width of the image on the detector surface?

Vishal Gupta

Numerade Educator

Problem 47

Make a rough graph of image distance versus object distance for a convex lens of a known focal length as the object distance varies from infinity to zero.

Vishal Gupta

Numerade Educator

Problem 48

Make a rough graph of linear magnification versus object distance for a convex lens of $20-\mathrm{cm}$ focal length as the object distance varies from infinity to zero. Indicate in which regions the image is real and in which regions it is virtual.

Vishal Gupta

Numerade Educator

Problem 49

Repeat Problem 23.48 for a concave lens of $-20-\mathrm{cm}$ focal length.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 50

Eye The image distance for the lens of a person's eye is $2.10 \mathrm{cm}$. Determine the focal length of the eye's lens system for an object (a) at infinity, (b) $500 \mathrm{cm}$ from the eye, and (c) $25 \mathrm{cm}$ from the eye.

Vishal Gupta

Numerade Educator

Problem 51

Lens-retina distance Fish and amphibians accommodate their eyes to see objects at different distances by altering the distance from the lens system to the retina (to learn more about this, see the Reading Passage at the end of this chapter). If the lens system has a focal length of $2.10 \mathrm{cm},$ what is the lens-retina distance needed to view objects at (a) infinity, (b) $300 \mathrm{cm},$ and (c) $25 \mathrm{cm} ?$

Vishal Gupta

Numerade Educator

Problem 52

Nearsighted and farsighted (a) A woman can produce sharp images on her retina only of objects that are from $150 \mathrm{cm}$ to $25 \mathrm{cm}$ from her eyes. Indicate the type of vision problem she has and determine the focal length of eyeglass lenses that will correct her problem. (b) Repeat part (a) for a man who can produce sharp images on his retina only of objects that are $3.0 \mathrm{m}$ or more from his eyes. He would like to be able to read a book held $30 \mathrm{cm}$ from his eyes.

Vishal Gupta

Numerade Educator

Problem 53

Prescribe glasses A man who can produce sharp images on his retina only of objects that lie from $80 \mathrm{cm}$ to $240 \mathrm{cm}$ from his eyes needs bifocal lenses. (a) Determine the desired focal length of the upper half of the glasses used to see distant objects. (b) Determine the focal length of the lower half used to read a paper held $25 \mathrm{cm}$ from his eyes.

Vishal Gupta

Numerade Educator

Problem 54

Correcting vision A woman who produces sharp images on her retina only of objects that lie from 100 to $300 \mathrm{cm}$ from her eyes needs bifocal lenses. (a) Determine the desired power of the upper half of the glasses used to see distant objects. (b) Determine the power of the lower half used to read a book held $30 \mathrm{cm}$ from her eyes.

Vishal Gupta

Numerade Educator

Problem 55

Where are the far and near points? (a) A woman wears glasses of $50-\mathrm{cm}$ focal length while reading. What eye defect is being corrected and what approximately are the near and far points of her unaided eye? (b) Repeat part (a) for a man whose glasses have a -350 -cm focal length. He wears the glasses while driving a car.

Vishal Gupta

Numerade Educator

Problem 56

Age-related vision changes A 35 -year-old patent clerk needs glasses of 50-cm focal length to read patent applications that he holds $25 \mathrm{cm}$ from his eyes. Five years later, he notices that while wearing the same glasses, he has to hold the patent applications $40 \mathrm{cm}$ from his eyes to see them clearly. What should be the focal length of new glasses so that he can read again at $25 \mathrm{cm} ?$

SG

Soumitra Ganguly

Numerade Educator

Problem 57

Looking at an aphid You examine an aphid on a plant leaf with a magnifying glass of $+6.0-\mathrm{cm}$ focal length. You hold the glass so that the final virtual image is $40 \mathrm{cm}$ from the lens. If you assume that your near point is at $30 \mathrm{cm},$ then what is the angular magnification? How will the magnification change if you are farsighted? Nearsighted?

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 58

Reading with a magnifying glass You examine the fine print in a legal contract with a magnifying glass of focal length $5.0 \mathrm{cm}$. (a) How far from the lens should you hold the print to see a final virtual image $30 \mathrm{cm}$ from the lens (at the eye's near point)? (b) Determine the angular magnification of the magnifying glass.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 59

Seeing an image with a magnifying glass A person has a near point of $150 \mathrm{cm} .$ (a) What is the nearest distance at which she needs to hold a magnifying glass of $5.0-\mathrm{cm}$ focal length from print on a page and still have an image formed beyond her near point? (b) Determine the angular magnification for an image at her near point.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 60

Stamp collector A stamp collector is viewing a stamp through a magnifying glass of $5.0-\mathrm{cm}$ focal length. Determine the object distance for virtual images formed at (a) negative infinity, (b) $-200 \mathrm{cm},$ and $(\mathrm{c})-25 \mathrm{cm} .$ (d) Determine the angular magnification in each case.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 61

You place a $+20-\mathrm{cm}$ focal length convex lens at a distance of $30 \mathrm{cm}$ in front of another convex lens of focal length $+4.0 \mathrm{cm} .$ Then you place a candle $100 \mathrm{cm}$ in front of the first lens. Find (a) the location of the final image of the candle, (b) its orientation, and (c) whether it is real or virtual.

Vishal Gupta

Numerade Educator

Problem 62

You place a $+25-\mathrm{cm}$ focal length convex lens at a distance of $50 \mathrm{cm}$ in front of a concave lens with a focal length of $-40 \mathrm{cm} .$ Then you place a small lightbulb $(2 \mathrm{cm}$ tall $) 30 \mathrm{cm}$ in front of the convex lens. Determine (a) the location of the final image, (b) its orientation, and (c) whether it is real or virtual.

Vishal Gupta

Numerade Educator

Problem 63

You place a candle $10 \mathrm{cm}$ in front of a convex lens of focal length $+4.0 \mathrm{cm} .$ Then you place a second convex lens, also of focal length $+4.0 \mathrm{cm},$ at a distance of $12 \mathrm{cm}$ from the first lens. (a) Use a ray diagram to locate the final image (keep the scale). (b) Using measurements on your ray diagram, estimate the linear magnification of the object. Be sure to show your rays and/or estimation technique for each step. Do not use equations!

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 64

Repeat Problem 23.63 for an object located $6.0 \mathrm{cm}$ from a convex lens of focal length $3.0 \mathrm{cm}$ separated by $11 \mathrm{cm}$ from another convex lens of focal length $1.0 \mathrm{cm}$.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 65

You measure the focal length of a concave lens by first forming a real image of a light source using a convex lens. The image is formed on a screen $20 \mathrm{cm}$ from the lens. You then place the concave lens halfway between the convex lens and the screen. To obtain a sharp image, you need to move the screen $15 \mathrm{cm}$ farther away from the lenses. How does this experiment help you determine the focal length of the concave lens? What is the focal length?

Vishal Gupta

Numerade Educator

Problem 66

Telescope A telescope consists of a $+4.0-\mathrm{cm}$ focal length objective lens and a $+0.80-\mathrm{cm}$ focal length eyepiece that are separated by $4.78 \mathrm{cm} .$ Determine (a) the location and (b) the height of the final image for an object that is $1.0 \mathrm{m}$ tall and is $100 \mathrm{m}$ from the objective lens.

Vishal Gupta

Numerade Educator

Problem 67

Yerkes telescope The world's largest telescope made only from lenses (with no mirrors) is located at the Yerkes Observatory near Chicago. Its objective lens is $1.0 \mathrm{m}$ in diameter and has a focal length of $+18.9 \mathrm{m} .$ The eyepiece has a focal length of $+7.5 \mathrm{cm} .$ The objective lens and eyepiece are separated by $18.970 \mathrm{m}$ (a) What is the location of the final image of a Moon crater $3.8 \times 10^{5} \mathrm{km}$ from Earth? (b) If the crater has a diameter of $2.0 \mathrm{km},$ what is the size of its final image? (c) Determine the angular magnification of the telescope by comparing the angular size of the image as seen through the telescope and the object as seen by the unaided eye.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 68

Telescope A telescope consisting of a +3.0 -cm objective lens and a $+0.60-\mathrm{cm}$ eyepiece is used to view an object that is $20 \mathrm{m}$ from the objective lens. (a) What must be the distance between the objective lens and eyepiece to produce a final virtual image $100 \mathrm{cm}$ to the left of the eyepiece? (b) What is the total angular magnification?

Vishal Gupta

Numerade Educator

Problem 69

Design a telescope You are marooned on a tropical island. Design a telescope from a cardboard map tube and the lenses of your eyeglasses. One lens has a $+1.0-\mathrm{m}$ focal length and the other has a $+0.30-\mathrm{m}$ focal length. The telescope should allow you to view an animal $100 \mathrm{m}$ from the objective with the final image being formed $1.0 \mathrm{m}$ from the eyepiece. Indicate the location of the lenses and the expected angular magnification.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 70

Microscope A microscope has a $+0.50-\mathrm{cm}$ objective lens and $a+3.0-\mathrm{cm}$ eyepiece that is $20 \mathrm{cm}$ from the objective lens. (a) Where should the object be located to form a final virtual image $100 \mathrm{cm}$ to the left of the eyepiece? (b) What is the total angular magnification of the microscope, assuming a near point of $25 \mathrm{cm} ?$

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 71

Dissecting microscope A dissecting microscope is designed with a larger than normal distance between the object and the objective lens. The microscope has an objective lens of $+5.0-\mathrm{cm}$ focal length and an eyepiece of $+2.0-\mathrm{cm}$ focal length. The lenses are separated by $15 \mathrm{cm} .$ The final virtual image is located $100 \mathrm{cm}$ to the left of the eyepiece. (a) Determine the distance of the object from the objective lens. (b) Determine the total angular magnification.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 72

Microscope A microscope has an objective lens of focal length $+0.80 \mathrm{cm}$ and an eyepiece of focal length $+2.0 \mathrm{cm} .$ An object is placed $0.90 \mathrm{cm}$ in front of the objective lens. The final virtual image is $100 \mathrm{cm}$ from the eyepiece at the position of minimum eyestrain. (a) Determine the separation of the lenses. (b) Determine the total angular magnification.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 73

Microscope Determine the lens separation and object location for a microscope made from an objective lens of focal length $+1.0 \mathrm{cm}$ and an eyepiece of focal length $+4.0 \mathrm{cm} .$ Arrange the lenses so that a final virtual image is formed $100 \mathrm{cm}$ to the left of the eyepiece and so that the angular magnification is -260 for a person with a near point of $25 \mathrm{cm}$.

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 74

Paul needs to determine the diameter of the wire used to make the filament of an incandescent lightbulb. He decides to project a magnified image of the filament onto a screen using a lens. (a) Describe Paul's experimental setup in words and with a sketch. (b) What additional data (other than those that can be obtained from the image on the screen) does Paul need to determine the diameter of the wire?

David Collins

Numerade Educator

Problem 75

Figure $P 23.75$ shows three cases of the primary axis of a lens (the lens is not shown) and the location of a shining object and its image. In each case, find the location and the type of the lens (convex or concave) that could produce the image and find the focal points of the lens.

Vishal Gupta

Numerade Educator

Problem 76

Jeopardy problem The equations below describe a process that involves one lens. Determine the unknown quantities and write a word description of an optics situation that is consistent with the equations.
$$
\begin{array}{l}
\frac{1}{4.0 \mathrm{m}}+\frac{1}{s^{\prime}}=\frac{1}{0.10 \mathrm{m}} \\
h^{\prime}=-\left(\frac{s^{\prime}}{4.0 \mathrm{m}}\right)(1.6 \mathrm{m})
\end{array}
$$

Vishal Gupta

Numerade Educator

Problem 77

Jeopardy problem The equations below describe a process involving more than one lens. Determine the unknown quantities and write a word description of an optics situation that is consistent with the equations.
$$
\begin{array}{l}
\frac{1}{100 \mathrm{m}}+\frac{1}{s_{1}^{\prime}}=\frac{1}{0.10 \mathrm{m}} \\
s_{2}=(0.14 \mathrm{m})-s_{1}^{\prime} \\
\frac{1}{s_{2}}+\frac{1}{s_{2}^{\prime}}=\frac{1}{0.042 \mathrm{m}}
\end{array}
$$

Vishal Gupta

Numerade Educator