(a) Two plane mirrors make an angle of The light from a

Can a virtual image be photographed? If so, give an example. If not, explain why.

Suppose the and axes of a coordinate system are painted different colors. One photograph is taken of the coordinate system and another is taken of its image in a plane mirror. Is it possible to tell that one of the photographs is of a mirror image? Or could both photographs be of the real coordinate system from different angles? x, y, z 3-D

True or False (a) The virtual image formed by a concave mirror is always smaller than the object. (b) A concave mirror always forms a virtual image. (c) A convex mirror never forms a real image of a real object. (d) A concave mirror never forms an enlarged real image of an object.

An ant is crawling along the axis of a concave mirror that has radius of curvature At what object distances, if any, will the mirror produce (a) an upright image, (b) a virtual image, (c) an image smaller than the object, and (d) an image larger than the object?

An ant is crawling along the axis of a convex mirror that has radius of curvature At what object distances, if any, will the mirror produce (a) an upright image, (b) a virtual image, (c) an image smaller than the object, and (d) an image larger than the object?

Convex mirrors are often used for rearview mirrors on cars and trucks to give a wide-angle view. Warning, objects are closer than they appear is written below the mirrors. Yet, according to a ray diagram, the image distance for distant objects is much shorter than the object distance. Why then do they appear more distant?

As an ant on the axis of a concave mirror crawls from a great distance to the focal point of a concave mirror, the image of the ant moves (a) from a great distance toward the focal point and is always real, (b) from the focal point to a great distance from the mirror and is always real, (c) from the focal point to the center of curvature of the mirror and is always real, (d) from the focal point to a great distance from the mirror and changes from a real image to a virtual image.

A kingfisher bird that is perched on a branch a few feet above the water is viewed by a scuba diver submerged beneath the surface of the water directly below the bird. Does the bird appear to the diver to be closer to or farther from the surface than the actual bird? Explain your answer using a ray diagram.

An object is placed on the axis of a diverging lens whose focal length has a magnitude of The distance from the object to the lens is The image is (a) real, inverted, and diminished, (b) real, inverted, and enlarged, (c) virtual, inverted, and diminished, (d) virtual, upright, and diminished, (e) virtual, upright, and enlarged.

If an object is placed between the focal point of a converging lens and the optical center of the lens, the image is (a) real, inverted, and enlarged, (b) virtual, upright, and diminished, (c) virtual, upright, and enlarged, (d) real, inverted, and diminished.

A converging lens is made of glass that has an index of refraction of 1.6. When the lens is in air, its focal length is When the lens is immersed in water, its focal length (a) is greater than (b) is between zero and (c) is equal to (d) has a negative value.

True or false: (a) A virtual image cannot be displayed on a screen. (b) A negative image distance implies that the image is virtual. (c) All rays parallel to the axis of a spherical mirror are reflected through a single point. (d) A diverging lens cannot form a real image from a real object. (e) The image distance for a converging lens is always positive.

BIOLOGICAL APPLICATION Both the human eye and the digital camera work by forming real images on light-sensitive surfaces. The eye forms a real image on the retina and the camera forms a real image on a CCD array. Explain the difference between the ways in which these two systems accommodate. That is, the difference between how an eye adjusts and how a camera adjusts (or can be adjusted) to form a focused image for objects at both large and short distances from the camera.

BIOLOGICAL APPLICATION If an object is in front of the naked eye of a farsighted person, an image (a) would be formed behind the retina if it were not for the fact that that the light is blocked (by the back of the eyeball) and the corrective contact lens should be convex, (b) would be formed behind the retina if it were not for the fact that that the light is blocked (by the back of the eyeball) and the corrective contact lens should be concave, (c) is formed in front of the retina and the corrective contact lens should be convex, (d) is formed in front of the retina and the corrective contact lens should be concave.

Explain the following statement: A microscope is an object magnifier, but a telescope is an angle magnifier. Hint: Take a look at the ray diagram for each magnifier and use it to explain the difference in adjectives.

Estimate the location and size of the image of your face when you hold a shiny new tablespoon a foot in front of your face and with the convex side toward you.

Estimate the focal length of the mirror produced by the surface of the water in the reflection pool in front of the Lincoln Memorial on a still night.

Estimate the maximum value that could be obtained for the magnifying power of a simple magnifier, using Equation 32-20. Hint: Think about the smallest focal length lens that could be made from glass and still be used as a magnifier.

The image of the object point in Figure 32-57 is viewed by an eye, as shown. Draw two rays from the object point that reflect from the mirror and enter the eye. If the object point and the mirror are fixed in their locations, indicate the range of locations where the eye can be positioned and still see the image of the object point.

You are tall and want to be able to see your full image in a vertical plane mirror. (a) What is the minimum height of the mirror that will meet your needs? (b) How far above the floor should the bottom of mirror in (a) be placed, assuming that the top of your head is above your eye level? Use a ray diagram to explain your answer.

(a) Two plane mirrors make an angle of The light from a point object that is arbitrarily positioned in front of the mirrors produces images at three locations. For each image location, draw two rays from the object that, after one or two reflections, appear to come from the image location. (b) Two plane mirrors make an angle of with each other. Draw a sketch to show the location of all the images formed of an object on the bisector of the angle between the mirrors. (c) Repeat Part (b) for an angle of

Show that the mirror equation (Equation 32-4 where yields the correct image distance and magnification for a plane mirror.

When two plane mirrors are parallel, such as on opposite walls in a barber shop, multiple images arise because each image in one mirror serves as an object for the other mirror. An object is placed between parallel mirrors separated by The object is in front of the left mirror and in front of the right mirror. (a) Find the distance from the left mirror to the first four images in that mirror. (b) Find the distance from the right mirror to the first four images in that mirror. (c) Explain why each more distant image becomes fainter and fainter.

A concave mirror has a radius of curvature equal to Use ray diagrams to locate the image, if it exists, for an object near the axis at distances of (a) (b) (c) and (d) from the mirror. For each case, state whether the image is real or virtual; upright or inverted; and enlarged, reduced, or the same size as the object.

(a) Use the mirror equation (Equation 32-4 where to calculate the image distances for the object distances and mirror of Problem 24. (b) Calculate the magnification for each given object distance. SSM

A convex mirror has a radius of curvature that has a magnitude equal to Use ray diagrams to locate the image, if it exists, for an object near the axis at distances of (a) (b) (c) (d) and (e) from the mirror. For each case, state whether the image is real or virtual; upright or inverted; and enlarged, reduced, or the same size as the object.

(a) Use the mirror equation (Equation 32-4 where to calculate the image distances for the object distances and mirror of Problem 26. (b) Calculate the magnification for each given object distance.

Use the mirror equation (Equation 32-4 where to prove that a convex mirror cannot form a real image of a real object, no matter where the object is placed.

A dentist wants a small mirror that will produce an upright image that has a magnification of 5.5 when the mirror is located from a tooth. (a) Should the mirror be concave or convex? (b) What should the radius of curvature of the mirror be?

CONTEXT-RICH Convex mirrors are used in many stores to provide a wide angle of surveillance for a reasonable mirror size. Your summer job is at a local convenience store that uses the mirror shown in Figure 32-58. This setup allows you (or the clerk) to survey the entire store when you are from the mirror. The mirror has a radius of curvature equal to Assume all rays are paraxial. (a) If a customer is from the mirror, how far from the mirror is his image? (b) Is the image in front of or behind the mirror? (c) If the customer is 2.0 m tall, how tall is his image?

A certain telescope uses a concave spherical mirror that has a radius equal to Find the location and diameter of the image of the moon formed by this mirror. The moon has a diameter of and is from Earth.

A piece of a thin spherical shell that has a radius of curvature of is silvered on both sides. The concave side of the piece forms a real image from the piece. The piece is then turned around so that its convex side faces the object. The piece is moved so that the image is now from the piece on the concave side. (a) How far was the piece moved? (b)Was it moved toward the object or away from the object?

Two light rays parallel to the optic axis of a concave mirror strike that mirror as shown in Figure 32-59. The mirror has a radius of curvature equal to They then strike a small spherical mirror that is from the large mirror. The light rays finally meet at the vertex of the large mirror. Note: The small mirror is shown as planar, so as not to give away the answer, but it is not actually planar. (a) What is the radius of curvature of the small mirror? (b) Is that mirror convex or concave? Explain your answer.

A very long glass rod has one end ground and polished to a convex spherical surface that has a radius. The glass material has an index of refraction of 1.68. (a) A point object in air is on the axis of the rod and from the spherical surface. Find the location of the image and state whether the image is real or virtual. (b) Repeat Part (a) for a point object in air, on the axis, and from the spherical surface. Draw a ray diagram for each case.

A fish is from the front surface of a spherical fish bowl of radius (a) How far behind the surface of the bowl does the fish appear to someone viewing the fish from in front of the bowl? (b) By what distance does the fishs apparent location change (relative to the front surface of the bowl) when it swims away to from the front surface?

A very long glass rod has one end ground and polished to a concave spherical surface that has a radius. The glass material has an index of refraction of 1.68. A point object in air is on the axis of the rod and from the spherical surface. Find the location of the image and state whether the image is real or virtual. Draw a ray diagram.

Repeat Problem 34 for when the glass rod and the object are immersed in water, and (a) the object is 6.00 cm from the spherical surface, and (b) the object is 12.0 cm from the spherical surface.

Repeat Problem 36 for when the glass rod and the object are immersed in water and the object is 20 cm from the spherical surface.

A rod that is long is made of glass that has an index of refraction equal to 1.60. The rod has its ends ground to convex spherical surfaces that have radii equal to and An object is in air on the long axis of the rod from the end that has the radius. (a) Find the image distance due to refraction at the surface. (b) Find the position of the final image due to refraction at both surfaces. (c) Is the final image real or virtual?

Repeat Problem 39 for an object in air on the axis of the glass rod from the end that has the radius.

A double concave lens that has an index of refraction equal to 1.45 has radii whose magnitudes are equal to and An object is located to the left of the lens. Find (a) the focal length of the lens, (b) the location of the image, and (c) the magnification of the image. (d) Is the image real or virtual? Is the image upright or inverted? SSM

The following thin lenses are made of glass that has an index of refraction equal to 1.60. Make a sketch of each lens and find each focal length in air: (a) and (b) and and (c) and

The following four thin lenses are made of glass that has an index of refraction of 1.5. The radii given are magnitudes. Make a sketch of each lens and find each focal length in air: (a) doubleconvex that has radii of curvature equal to and (b) plano-convex that has a radius of curvature equal to (c) double concave that has radii of curvature equal to and (d) plano-concave that has a radius of curvature equal to

Find the focal length of a glass lens that has an index of refraction equal to 1.62, a concave surface that has a radius of curvature of magnitude and a convex surface that has a radius of curvature of magnitude

(a) An object that is high is placed in front of a thin lens that has a power equal to Draw a ray diagram to find the position and the size of the image and check your results using the thin-lens equation. (b) Repeat Part (a) if the object is placed in front of the lens. (c) Repeat Part (a) for an object placed in front of a thin lens that has a power equal to

The lens-makers equation has three design parameters. They consist of the index of refraction of the lens and the radii of curvature for its two surfaces. Thus, there are many ways to design a lens that has a particular focal length in air. Use the lens-makers equation to design three different thin converging lenses, each having a focal length of and each made from glass that has an index of refraction of 1.60. Sketch each of your designs.

Repeat Problem 46, but for a diverging lens that has a focal length in air of the same magnitude.

(a) What is meant by a negative object distance? Describe a specific situation in which a negative object distance can occur. (b) Find the image distance and the magnification for a thin lens in air when the object distance is and the lens is a converging lens that has a focal length of Describe the imageis it virtual or real, upright or inverted? (c) Repeat Part (b) if the object distance is, instead, and the lens is diverging and has a focal length (magnitude) of

Two converging lenses, each having a focal length equal to are separated by An object is to the left of the first lens. (a) Find the position of the final image using both a ray diagram and the thin-lens equation. (b) Is the final image real or virtual? Is the final image upright or inverted? (c) What is the overall lateral magnification?

Repeat Problem 49, but with the second lens replaced by a diverging lens that has a focal length equal to

(a) Show that to obtain a magnification of magnitude using a converging thin lens of focal length the object distance must be equal to . (b) You want to use a digital camera which has a lens whose focal length is to take a picture of a person tall. How far from the camera lens should you have that person stand so that the image size on the light-receiving sensors of your camera is

SPREADSHEET A converging lens has a focal length of (a) Using a spreadsheet program or graphing calculator, plot the image distance as a function of the object distance, for object distances ranging from to where is the focal length. (b) On the same graph used in Part (a), but using a different y axis, plot the magnification of the lens as a function of the object distance. (c) What type of image is produced for this range of object distancesreal or virtual, upright or inverted? (d) Discuss the significance of any asymptotic limits your graphs have.

SPREADSHEET A converging lens has a focal length of (a) Using a spreadsheet program or graphing calculator, plot the image distance as a function of the object distance, for object distances ranging from to where is the focal length. (b) On the same graph used in Part (a), but using a different axis, plot the magnification of the lens as a function of the object distance. (c) What type of image is produced for this range of object distances real or virtual, upright or inverted? (d) Discuss the significance of any asymptotic limits your graphs have.

An object is in front of a converging lens that has a focal length equal to A second converging lens that also has a focal length equal to is located in back of the first. (a) Find the location of the final image and describe its properties (for example, real and inverted) and (b) draw a ray diagram to corroborate your answers to Part (a).

An object is in front of a converging lens that has a focal length equal to A diverging lens that has a focal length whose magnitude is equal to is located in back of the first. (a) Find the location of the final image and describe its properties (for example, real and inverted) and (b) draw a ray diagram to corroborate your answers to Part (a).

In a convenient form of the thin-lens equation used by Newton, the object and image distances and are measured from the focal points and and not from the center of the lens. (a) Indicate and on a sketch of a lens and show that if and the thin-lens equation (Equation 32-12) can be rewritten as (b) Show that the lateral magnification is given by

In Bessels method for finding the focal length f of a lens, an object and a screen are separated by distance where It is then possible to place the lens at either of two locations, both between the object and the screen, so that there is an image of the object on the screen, in one case magnified and in the other case reduced. Show that if the distance between those two lens locations is then the focal length is given by Hint: Refer to Figure 32-60.

ENGINEERING APPLICATION, CONTEXT-RICH You are working for an optician during the summer. The optician needs to measure an unknown focal length and you suggest using Bessels method (see Problem 57), which you used during a physics lab. You set the object-to-image distance at The lens position is adjusted to get a sharp image on the screen. A second sharp image is found when the lens is moved a distance of from its first location. (a) Sketch the ray diagram for the two locations. (b) Find the focal length of the lens using Bessels method. (c) What are the two locations of the lens with respect to the object? (d) What are the magnifications of the images when the lens is in the two locations?

An object is to the left of a lens that has a focal length of A second lens, which has a focal length of is to the right of the first lens. (a) Find the distance between the object and the final image formed by the second lens. (b) What is the overall magnification? (c) Is the final image real or virtual? Is the final image upright or inverted?

Chromatic aberration is a common defect of (a) concave and convex lenses, (b) concave lenses only, (c) concave and convex mirrors, (d) all lenses and mirrors.

ENGINEERING APPLICATION Discuss some of the reasons why most telescopes that are used by astronomers are reflecting rather than refracting telescopes.

A symmetric double-convex lens has radii of curvature equal to It is made from glass that has an index of refraction equal to 1.530 for blue light and equal to 1.470 for red light. Find the focal length of this lens for (a) red light and (b) blue light.

BIOLOGICAL APPLICATION Find the change in the focal length of the eye when an object originally at is brought to from the eye.

BIOLOGICAL APPLICATION A farsighted person requires lenses that have powers equal to to read comfortably from a book that is from his eyes. What is that persons near point without the lenses?

BIOLOGICAL APPLICATION If two point objects close together are to be seen as two distinct objects, the images must fall on the retina on two different cones that are not adjacent. That is, there must be an unactivated cone between them. The separation of the cones is about Model the eye as a uniform sphere that has a refractive index of 1.34. (a) What is the smallest angle the two points can subtend? (See Figure 32-61.) (b) How close together can two points be if they are 20.0 m from the eye? SSM

BIOLOGICAL APPLICATION Suppose the eye were designed like a camera that has a lens of fixed focal length equal to that could move toward or away from the retina, has air on both sides of the lens, and has no cornea. Approximately how far would the lens have to move to focus the image of an object from the eye onto the retina? Hint: Find the distance from the retina to the image behind it for an object at Note: Problems 67 through 69 refer to the model of the eye shown in Figure 32-62.

BIOLOGICAL APPLICATION A simple model for the eye is a lens that has a variable power located a fixed distance in front of a screen, with the space between the lens and the screen filled by air. This eye can focus for all values of object distance such that where the subscriptson the variables refer to near point and far point, respectively. This eye is said to be normal if it can focus on very distant objects. (a) Show that for a normal eye of this type, the required minimum value of is given by (b) Show that the maximum value of is given by (c) The difference between the maximum and minimum powers, symbolized by is defined as and is called the accommodation. Find the minimum power and accommodation for this model eye that has a screen distance of a far point distance of infinity, and a near point distance of

BIOLOGICAL APPLICATION (This problem refers to the model eye described in Problem 67.) In an eye that exhibits nearsightedness, the eye cannot focus on distant objects. (a) Show that for a nearsighted model eye capable of focusing out to a maximum distance the minimum value of the power is greater than that of a normal eye (that has a far point at infinity) and is given by (b) To correct for nearsightedness, a contact lens may be placed directly in front of the lens of the model eye. What power contact lens would be needed to correct the vision of a nearsighted model eye that has a far-point distance of

BIOLOGICAL APPLICATION (This problem refers to the model eye described in Problem 67.) In an eye that exhibits farsightedness, the eye may be able to focus on distant objects but cannot focus on close objects. (a) Show that for a farsighted model eye capable of focusing only as close as a distance the maximum value of the power is given by (b) Show that, compared to a model eye capable of focusing as close as a distance (where the maximum power of the farsighted lens is too small by (c) What power contact lens would be needed to correct the vision of a farsighted model eye, with so that the eye may focus on objects as close as 15 cm?

BIOLOGICAL APPLICATION A person who has a near point of needs to read from a computer screen that is only from her eye. (a) Find the focal length of the lenses in reading glasses that will produce an image of the screen at a distance of from her eye. (b) What is the power of the lenses?

BIOLOGICAL APPLICATION A nearsighted person cannot focus clearly on objects that are more distant than from her eye. What power lenses are required for her to see distant objects clearly?

BIOLOGICAL APPLICATION Because the index of refraction of the lens of the eye is not very different from that of the surrounding material, most of the refraction takes place at the cornea, where the index changes abruptly from 1.00 (air) to approximately 1.38. (a) Modeling the cornea, aqueous humor, lens and vitreous humor as a transparent homogeneous solid sphere that has an index of refraction of 1.38, calculate the spheres radius if it focuses parallel light on the retina a distance away. (b) Do you expect your result to be larger or smaller than the actual radius of the cornea? Explain your answer.

BIOLOGICAL APPLICATION The near point of a certain persons eyes is Reading glasses are prescribed so that he can read a book at from his eye. The glasses are from the eye. What diopter lenses should be used in the glasses?

BIOLOGICAL APPLICATION At age 45, a person is fitted for reading glasses that have a power equal to in order to read at By the time she reaches the age of 55, she discovers herself holding her newspaper at a distance of in order to see it clearly with her glasses on. (a) Where was her near point at age 45? (b) Where is her near point at age 55? (c) What power is now required for the lenses of her reading glasses so that she can again read at Assume the glasses are placed from her eyes.

What is the magnifying power of a lens that has a focal length equal to when the image is viewed at infinity by a person whose near point is at

Alens that has a focal length equal to is used as a simple magnifier by one person whose near point is and by another person whose near point is (a) What is the effective magnifying power of the lens for each person? (b) Compare the sizes of the images on the retinas when each person looks at the same object with the magnifier.

In your botany class, you examine a leaf using a convex lens as a simple magnifier. What is the angular magnification of the leaf if the image formed by the lens is (a) at infinity and (b) at

Your laboratory microscope objective has a focal length of 17.0 mm.It forms an image of a tiny specimen at from its second focal point. (a) How far from the objective is the specimen located? (b) What is the magnifying power for you if your near point distance is and the focal length of the eyepiece is 51.0 mm?

A microscope has an objective that has a focal length equal to The eyepiece provides an angular magnification of 10 for a person whose near point distance is The tube length is (a) What is the lateral magnification of the objective? (b) What is the magnifying power of the microscope?

A crude, symmetric handheld microscope consists of two lenses fastened at the ends of a tube long. (a) What is the tube length of this microscope? (b) What is the lateral magnification of the objective? (c) What is the magnifying power of the microscope? (d) How far from the objective should the object be placed?

A compound microscope has an objective lens that has a power of and an eyepiece that has a power of The lenses are separated by Assuming that the final image formed by the microscope is from the eye, what is the magnifying power?

A microscope has a magnifying power of 600. The eyepiece has an angular magnification of 15.0. The objective lens is from the eyepiece. Calculate (a) the focal length of the eyepiece, (b) the location of the object so that it is in focus for a normal relaxed eye, and (c) the focal length of the objective lens.

You have a simple telescope that has an objective which has a focal length of and an eyepiece which has a focal length of 5.00 cm. You are using it to look at the moon, which subtends an angle of about (a) What is the diameter of the image formed by the objective? (b) What angle is subtended by the image formed at infinity by the eyepiece? (c) What is the magnifying power of your telescope?

The objective lens of the refracting telescope at the Yerkes Observatory has a focal length of The moon subtends an angle of about When the telescope is used to look at the moon, what is the diameter of the image of the moon formed by the objective?

The diameter mirror of the reflecting telescope at Mt. Palomar has a focal length of (a) By what factor is the light-gathering power increased over the diameter refracting lens of the Yerkes Observatory telescope? (b) If the focal length of the eyepiece is what is the magnifying power of the telescope?

An astronomical telescope has a magnifying power of 7.0. The two lenses are apart. Find the focal length of each lens.

Adisadvantage of the astronomical telescope for terrestrial use (for example, at a football game) is that the image is inverted. A Galilean telescope uses a converging lens as its objective, but a diverging lens as its eyepiece. The image formed by the objective is at the second focal point of the eyepiece (the focal point on the refractedlight side of the eyepiece), so that the final image is virtual, upright, and at infinity. (a) Show that the magnifying power is given by where is the focal length of the objective and is that of the eyepiece (which is negative). (b) Draw a ray diagram to show that the final image is indeed virtual, upright, and at infinity.

A Galilean telescope (see Problem 87) is designed so that the final image is at the near point, which is (rather than at infinity). The focal length of the objective is and the focal length of the eyepiece is (a) If the object distance is where is the image of the objective? (b) What is the object distance for the eyepiece so that the final image is at the near point? (c) How far apart are the lenses? (d) If the object height is what is the height of the final image? What is the angular magnification?

If you look into the wrong end of a telescope, that is, into the objective, you will see distant objects reduced in angular size. For a refracting telescope that has an objective with a focal length equal to and an eyepiece with a focal length equal to by what factor is the angular size of the object changed?

To focus a camera, the distance between the lens and the image-sensing surface is varied. A wide-angle lens of a camera has a focal length of By how much must the lens move to change from focusing on an object at infinity to an object at a distance of in front of the camera?

A converging lens that has a focal length equal to is used to obtain an image that is twice the height of the object. Find the object and image distances if (a) the image is to be upright and (b) the image is to be inverted. Draw a ray diagram for each case.

You are given two converging lenses that have focal lengths of and (a) Show how the lenses should be arranged to form a telescope. State which lens to use as the objective, which lens to use as the eyepiece, how far apart to place the lenses, and what angular magnification you expect. (b) Draw a ray diagram to show how rays from a distant object are refracted by the two lenses.

(a) Show how the same two lenses in Problem 92 should be arranged to form a compound microscope that has a tube length of State which lens to use as the objective, which lens to use as the eyepiece, how far apart to place the lenses, and what overall magnification you expect to get, assuming the user has a near point of (b) Draw a ray diagram to show how rays from a close object are refracted by the lenses.

CONTEXT-RICH On a vacation, you are scuba diving and using a diving mask that has a face plate that bulges outward with a radius of curvature of As a result, a convex spherical surface exists between the water and the air in the mask. A fish swims by you in front of your mask. (a) How far in front of the mask does the fish appear to be? (b) What is the lateral magnification of the image of the fish?

A digital camera has a rectangular array of CCDs (light sensors) that is by It is used to take a picture of a person tall so that the image just fills the height of the CCD array. How far should the person stand from the camera if the focal length of the lens is

A camera that has interchangeable lenses is used to take a picture of a hawk that has a wingspan of The hawk is away. What would be the ideal focal length of the lens used so that the image of the wings just fills the width of the light-sensitive area of the camera, which is

An object is placed in front of a lens that has a focal length equal to A second lens that has a focal length equal to is placed in back of the first lens. (a) Find the position of the final image. (b) What is the magnification of the image? (c) Sketch a ray diagram showing the final image.

(a) Show that if is the focal length of a thin lens in air, its focal length in water is given by where is the index of refraction of water, is that of the lens material and is that of air. (b) Calculate the focal length in air and in water of a double concave lens that has an index of refraction of 1.50 and radii of magnitudes and

While parked in your car, you see a jogger in your rear view mirror, which is convex and has a radius of curvature whose magnitude is equal to The jogger is from the mirror and is approaching at How fast is the image of the jogger moving relative to the mirror?

A layer of water floats on top of a layer of carbon tetrachloride in a tank. How far below the top surface of the water does the bottom of the tank appear, according to an observer looking down from above at normal incidence?

An object is in front of a thin converging lens that has a focal length equal to A concave mirror that has a radius equal to is in back of the lens. (a) Find the position of the final image formed by the mirrorlens combination. (b) Is the image real or virtual? Is the image upright or inverted? (c) On a diagram, show where your eye must be to see this image.

When a bright light source is placed in front of a lens, there is an upright image from the lens. There is also a faint inverted image from the lens on the incident-light side due to reflection from the front surface of the lens. When the lens is turned around, this weaker, inverted image is in front of the lens. Find the index of refraction of the lens.

A concave mirror that has a radius of curvature equal to is oriented with its axis vertical. The mirror is filled with water that has an index of refraction equal to 1.33 and a maximum depth of At what height above the vertex of the mirror must an object be placed so that its image is at the same position as the object?

The concave side of a lens has a radius of curvature that has a magnitude equal to and the convex side of the lens has a radius of curvature that has a magnitude equal to The focal length of the lens in air is When the lens is placed in a liquid that has an unknown index of refraction, the focal length increases to What is the index of refraction of the liquid?

A solid glass ball of radius has an index of refraction equal to 1.500. The right half of the ball is silvered so that it acts as a concave mirror (Figure 32-63). Find the position of the final image formed for an object located at (a) and (b) to the left of the center of the ball.

(a) Show that a small change in the index of refraction of a lens material produces a small change in the focal length given approximately by (b) Use this result to estimate the focal length of a thin lens for blue light, for which if the focal length for red light, for which is

The lateral magnification of a spherical mirror or a thin lens is given by Show that for objects of small horizontal extent, the longitudinal magnification is approximately Hint: Show that ds_>ds _ _s_2>s2.