College Physics 2013

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.

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.

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.

You are 1.8 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?

What is the smallest size plane mirror a 190-cm-tall person should buy to see himself if he mounts the mirror on a vertical wall?

Two people are standing in front of a 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.

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

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.

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.

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

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

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.

Partially covered mirror Your friend thinks that if he covers half of a concave mirror, he will see half of himself in it. Do you agree with his opinion? Support your opinion with a ray diagram. Why would he have such an opinion? Design an experiment to test whether he is correct.

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 cm. The object distance is (a) 200 cm, (b) 40 cm, and (c) 10 cm.

Repeat Problem 14 for a convex mirror of focal length -20 cm.

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

Sinking ships A legend says that Archimedes once saved his native town of Syracuse by burning the enemy’s fleet with a mirror. Describe quantitatively the type of mirror that Archimedes could have used to burn ships that were 150 m away. Justify your answer.

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

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

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 $+16.9 \mathrm{m} .$

You view your face in a +20-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?

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 cm from a tooth. What mirror should she order? Say everything you can about the mirror.

Using a dental mirror A dentist examines a tooth that is 1.0 cm in front of the dental mirror. An image is formed 8.0 cm behind the mirror. Say everything you can about the mirror and the image of the tooth.

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.

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.

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.

Use a ruler to draw ray diagrams to locate the images of the following objects: (a) an object that is 30 cm from a convex lens of +10-cm focal length, (b) an object that is 14 cm from the same lens, and (c) an object that is 5 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.

Repeat the procedure described in Problem 27 for the following lenses and objects: (a) an object that is 30 cm from a concave lens of -10-cm focal length, (b) an object that is 14 cm from the same lens, and (c) an object that is 5 cm from the same lens.

Repeat the procedure described in Problem 27 for the following lenses and objects: (a) an object that is 7 cm from a convex lens of +10-cm focal length and (b) an object that is 7 cm from a concave lens of –10-cm focal length.

Repeat the procedure in Problem 27 for the following lenses and objects: (a) an object that is 20 cm from a convex lens of +10-cm focal length, (b) an object that is 5 cm from the same lens, (c) an object that is 20 cm from a concave lens of -10-cm focal length, and (d) an object that is 5 cm from the lens in part (c).

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.

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

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

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

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?

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 cm from your face. What type and focal length mirror should you order?

Face in concave mirror You view your face in a concave mirror of focal length 20 cm and wish it to be magnified by a factor of 1.5. What should you do?

Clothing store mirror A cylindrical mirror in a clothing store causes the customer’s width to have a linear magnification of +0.85 when the customer stands 2.5 m from the mirror. Determine everything you can about the mirror.

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

Mirrors for truck Two mirrors (one plane and one convex) at the side of a truck are shown in Figure P22.40. Estimate the focal length of the curved mirror. Explain the reasoning behind your estimate.

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

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

Slide projector A slide projector produces real, inverted, enlarged images of the slides on a screen (slides are put upside down in the projector). If a slide is located 12.6 cm from the 12.0-cm focal length lens of a projector, (a) what should be the distance between the screen and the lens? (b) What is the height of the image of a person on the screen who is 2.0 cm tall on the slide?

Photo of carpenter ant You take a picture of a carpenter ant with an old fashioned camera with a lens 18 cm from the film. At what places can the 4.0-cm focal length convex camera lens be located so you see a sharp image of the ant on the film?

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

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

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.

Make a rough graph of linear magnification versus object distance for a convex lens of 20-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.

Repeat Problem 48 for a concave lens of - 20-cm focal length.

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

Lens-retina distance Assume that the eye accommodates to objects at different distances by altering the distance from the lens system to the retina. If the lens system has a focal length of 2.10 cm, what is the lens-retina distance needed to view objects at (a) infinity, (b) 300 cm, and (c) 25 cm?

Nearsighted and farsighted (a) A woman can produce sharp images on her retina only of objects that are from 150 cm to 25 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 m or more from his eyes. He would like to be able to read a book held 30 cm from his eyes.

Prescribe glasses A man who can produce sharp images on his retina only of objects that lie from 80 cm to 240 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 cm from his eyes.

Correcting vision A woman who produces sharp images on her retina only of objects that lie from 100 to 300 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 cm from her eyes.

Where are the far and near points? (a) A woman wears glasses of 50-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.

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 cm from his eyes. Five years later, he notices that while wearing the same glasses, he has to hold the patent applications 40 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 cm?

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

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

Seeing an image with a magnifying glass A person has a near point of 150 cm. (a) What is the nearest distance at which she needs to hold a magnifying glass of 5.0-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.

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

You place a +20-cm focal length convex lens at a distance of 30 cm in front of another convex lens of focal length +4.0 cm. Then you place a candle 100 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.

You place a +25-cm focal length convex lens at a distance of 50 cm in front of a concave lens with a focal length of -40 cm. Then you place a small lightbulb (2 cm tall) 30 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.

You place a candle 10 cm in front of a convex lens of focal length +4.0 cm. Then you place a second convex lens, also of focal length +4.0 cm, at a distance of 12 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!

Repeat Problem 63 for an object located 6.0 cm from a convex lens of focal length 3 cm separated by 11 cm from another convex lens of focal length 1 cm.

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 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 cm further away from the lenses. How does this experiment help you determine the focal length of the concave lens? What is the focal length?

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

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 m in diameter and has a focal length of +18.9 m. The eyepiece has a focal length of +7.5 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.

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

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-m focal length and the other has a +0.30-cm focal length. The telescope should allow you to view an animal 100 m from the objective with the final image being formed 1.0 m from the eyepiece. Indicate the location of the lenses and the expected angular magnification.

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

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-cm focal length and an eyepiece of +2.0-cm focal length. The lenses are separated by 15 cm. The final virtual image is located 100 cm to the left of the eyepiece. (a) Determine the distance of the object from the objective lens. (b) Determine the total angular magnification.

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

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

Figure P22.74 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. Then draw a ray diagram to help justify each choice.

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.
$$
\begin{aligned} \frac{1}{4.0 \mathrm{m}}+\frac{1}{s^{\prime}} &=\frac{1}{0.10 \mathrm{m}} \\ h^{\prime} &=-\left(\frac{s^{\prime}}{4.0 \mathrm{m}}\right)(1.6 \mathrm{m}) \end{aligned}
$$

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.
$$
\begin{array}{c}{\frac{1}{100 \mathrm{m}}+\frac{1}{s_{1}^{\prime}}=\frac{1}{0.10 \mathrm{m}}} \\ {s_{2}=(0.14 \mathrm{m})-s_{1}^{\prime}} \\ {\frac{1}{s_{2}}+\frac{1}{s_{2}^{\prime}}=\frac{1}{0.042 \mathrm{m}}}\end{array}
$$

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.
$$
\begin{array}{c}{\frac{1}{0.14 \mathrm{m}}+\frac{1}{s_{1}^{\prime}}=\frac{1}{0.10 \mathrm{m}}} \\ {s_{2}=(0.395 \mathrm{m})-s_{1}^{\prime}} \\ {\frac{1}{s_{2}}+\frac{1}{s_{2}^{\prime}}=\frac{1}{0.050 \mathrm{m}}}\end{array}
$$

Design a system that will allow you to project the picture from your neighbors’ TV set onto the wall of their living area that can be seen from your porch. They’d love to sit on your porch and watch TV while you barbeque. Design such a system and discuss its limitations.

Two-lens camera A two-lens camera (see Figure P22.79) has one lens with focal length +15.0 cm located 12 cm from the film and a second lens of focal length +13.0 cm a variable distance d of 5.0 to 10.0 cm from the film. Determine the range of distances at which you can photograph objects and achieve sharp images on the film.

You have a small spherically shaped bottle made of plastic that is so thin that we can disregard its effects for optical processes. Show that the bottle works as a converging lens when filled with water, but when the same bottle is empty, closed, and submerged in water, it becomes a diverging lens. If you have access to the appropriate materials, test your ray diagram experimentally.

Your eyeball is 2.10 cm from the cornea to the retina. You look at a sign on the freeway that is effectively an infinite distance away. The image for the sign is 1.96 cm from the cornea within the eye. Which answer below is closest to the focal length of the cornea-lens system?
$\begin{array}{llll}{\text { (a) }+1.96 \mathrm{cm}} & {\text { (b) }+2.10 \mathrm{cm}} & {\text { (c) }+2.26 \mathrm{cm}}\end{array}$ (d) $+2.42 \mathrm{cm} \quad(\mathrm{e})+27.90 \mathrm{cm}$

In Problem 81, what should the cornea-lens focal length be in order to form a sharp image on the retina of the sign?
(a) $+1.96 \mathrm{cm} \quad(\mathrm{b})+2.10 \mathrm{cm} \quad(\mathrm{c})+2.26 \mathrm{cm}$ $(\mathrm{d})+2.42 \mathrm{cm} \quad(\mathrm{e})+27.90 \mathrm{cm}$

What is one surgical way to correct nearsighted vision?
(a) Reduce the curvature of the cornea, thus reducing the focal length of the eye’s optics system.
(b) Increase the curvature of the cornea, thus increasing the focal length of the eye’s optics system.
(c) Increase the iris opening to allow more light to enter.
(d) Use the ciliary muscle to increase the thickness of the lens.

Your eyeball is 2.10 cm from the cornea to the retina. A book held 30 cm from your eyes produces an image 2.26 cm from the entrance to the image location. Which answer below is closest to the focal length of the cornea-lens system?
(a) $+1.96 \mathrm{cm} \quad(\mathrm{b})+2.10 \mathrm{cm} \quad(\mathrm{c})+2.26 \mathrm{cm}$ (d) $+2.42 \mathrm{cm} \quad(\mathrm{e})+27.90 \mathrm{cm}$

In Problem 84, what should the cornea-lens focal length be in order to form a sharp image of the book on the retina?
(a) $+1.96 \mathrm{cm} \quad(\mathrm{b})+2.10 \mathrm{cm} \quad$ (c) $+2.26 \mathrm{cm}$ (d) $+2.42 \mathrm{cm} \quad(\mathrm{e})+27.90 \mathrm{cm}$

What is one surgical way to correct the farsighted vision of the person in the last two problems?
(a) Reduce the curvature of the cornea, thus increasing the focal length of the eyes optics system.
(b) Increase the curvature of the cornea, thus reducing the focal length of the eyes optics system.
(c) Open the iris wider to allow more light to enter.
(d) Cause the ciliary muscle to stretch the lens so it becomes thinner.

Why is the fish eye in Figure 22.36 black?
(a) The lens is black.
(b) No light reflects out from behind the lens.
(c) The fluid behind the lens is black.
(d) The retina is black.

Which of the following is the same for the fish eye and the human eye?
(a) The muscles attached to the lens change their shape.
(b) The corneas help focus the light.
(c) The lenses have a spherical shape.
(d) The irises help focus the light.

Which ray in Figure P22.89 best represents the path of the incident light through the fisheye lens?
(a) I
(b) II
(c) III
(d) IV
(e) V

Which of the following statements regarding the fish eye and the human eye is not true?
(a) They both have a cornea.
(b) They both have an iris.
(c) They both have a lens.
(d) They both rely on the cornea and the lens for image formation.

How can the the peephole lens in a hotel door have an approximately 180 view?
(a) The light moves straight through the lens into eye.
(b) Light from about 90 from the straight-ahead direction is refracted into the observer’s eye if very close to the lens.
(c) Light from about 90 from the straight-ahead direction is refracted into the observer’s eye if looking at the lens from inside the room.
(d) The outside hall is illuminated so reflected light from the objects inside the 180angle goes into the lens.
(e) b and d.