Additional Problems

| 97 | ssm An object is located 9.0 cm in front of a converging lens (f = 6.0 cm). Using an accurately drawn ray diagram, determine where the image is located.

| 98 | The near point of a naked eye is 25 cm. When placed at the near point and viewed by the naked eye, a tiny object would have an angular size of rad. When viewed through a compound microscope, however, it has an angular size of rad. (The minus sign indicates that the image produced by the microscope is inverted.) The objective of the microscope has a focal length of 2.6 cm, and the distance between the objective and the eyepiece is 16 cm. Find the focal length of the eyepiece.

| 99 | ssm The drawing shows a crown glass slab with a rectangular cross section. As illustrated, a laser beam strikes the upper surface at an angle of 60.0°. After reflecting from the upper surface, the beam reflects from the side and bottom surfaces. (a) If the glass is surrounded by air, determine where part of the beam first exits the glass, at point A, B, or C. (b) Repeat part (a), assuming that the glass is surrounded by water.

| 100 | As an aid in understanding this problem, refer to Conceptual Example 4. A swimmer, who is looking up from under the water, sees a diving board directly above at an apparent height of 4.0 m above the water. What is the actual height of the diving board?

| 101 | ssm A nearsighted person has a far point that is located only 220 cm from his eyes. Determine the focal length of contact lenses that will enable him to see distant objects clearly.

| 102 | A person working on the transmission of a car accidentally drops a bolt into a tray of oil. The oil is 5.00 cm deep. The bolt appears to be 3.40 cm beneath the surface of the oil, when viewed from directly above. What is the index of refraction of the oil?

| 103 | ssm An object is located 30.0 cm to the left of a converging lens whose focal length is 50.0 cm. (a) Draw a ray diagram to scale and from it determine the image distance and the magnification, (b) Use the thin-lens and magnification equations to verify your answers to part (a).

| 104 | A slide projector has a converging lens whose focal length is 105.00 mm. (a) How far (in meters) from the lens must the screen be located if a slide is placed 108.00 mm from the lens? (b) If the slide measures , what are the dimensions (in mm) of its image?

| 105 | ssm The drawing shows a coin resting on the bottom of a beaker filled with an unknown liquid. A ray of light from the coin travels to the surface of the liquid and is refracted as it enters into the air. A person sees the ray as it skims just above the surface of the liquid. How fast is the light traveling in the liquid?

| 106 | The near point of a naked eye is 32 cm. When an object is placed at the near point and viewed by the naked eye, it has an angular size of 0.060 rad. A magnifying glass has a focal length of 16 cm, and is held next to the eye. The enlarged image that is seen is located 64 cm from the magnifying glass. Determine the angular size of the image.

| 107 | A nearsighted person cannot read a sign that is more than 5.2 m from his eyes. To deal with this problem, he wears contact lenses that do not correct his vision completely, but do allow him to read signs located up to distances of 12.0 m from his eyes. What is the focal length of the contacts?

| 108 | Refer to Conceptual Example 8 as an aid in understanding this problem. The drawing shows a ray of light traveling through a gas (n = 1.00), a solid (n = 1.55), and a liquid (n = 1.55). At what angle does the light enter the liquid?

| 109 | A camper is trying to start a fire by focusing sunlight onto a piece of paper. The diameter of the sun is , and its mean distance from the earth is . The camper is using a converging lens whose focal length is 10.0 cm. (a) What is the area of the sun’s image on the paper? (b) If 0.530 W of sunlight pass through the lens, what is the intensity of the sunlight at the paper?

| 110 | (a) For a diverging lens (f = −20.0 cm), construct a ray diagram to scale and find the image distance for an object that is 20.0 cm from the lens. (b) Determine the magnification of the lens from the diagram.

* | 111 | ssm An office copier uses a lens to place an image of a document onto a rotating drum. The copy is made from this image. (a) What kind of lens is used? If the document and its copy are to have the same size, but are inverted with respect to one another, (b) how far from the document is the lens located and (c) how far from the lens is the image located? Express your answers in terms of the focal length f of the lens.

* | 112 | A stamp collector is viewing a stamp with a magnifying glass held next to her eye. Her near point is 25 cm from her eye. (a) What is the refractive power of a magnifying glass that has an angular magnification of 6.0 when the image of the stamp is located at the near point? (b) What is the angular magnification when the image of the stamp is 45 cm from the eye?

* | 113 | ssm At age forty, a certain man requires contact lenses (f = 65.0 cm) to read a book held 25.0 cm from his eyes. At age forty-five, while wearing these contacts he must now hold a book 29.0 cm from his eyes. (a) By what distance has his near point changed? (b) What focal length lenses does he require at age forty-five to read a book at 25.0 cm?

* | 114 | An object is in front of a converging lens (f = 0.30 m). The magnification of the lens is m = 4.0. (a) Relative to the lens, in what direction should the object be moved so that the magnification changes to m = −4.0? (b) Through what distance should the object be moved?

** | 115 | ssm The angular magnification of a telescope is 32 800 times as large when you look through the correct end of the telescope as when you look through the wrong end. What is the angular magnification of the telescope?

** | 116 | The equation

is called the Gaussian form of the thin-lens equation. The drawing shows the variables do, di, and f. The drawing also shows the distances x and x′, which are, respectively, the distance from the object to the focal point on the left of the lens and the distance from the focal point on the right of the lens to the image. An equivalent form of the thin-lens equation, involving x, x′, and f, is called the Newtonian form. Show that the Newtonian form of the thin-lens equation can be written as .

** | 117 | The far point of a nearsighted person is 6.0 m from her eyes, and she wears contacts that enable her to see distant objects clearly. A tree is 18.0 m away and 2.0 m high. (a) When she looks through the contacts at the tree, what is its image distance? (b) How high is the image formed by the contacts?

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