Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 118 | Concept Question The drawing shows four different situations in which a light ray is traveling from one medium into another. Without doing any calculations, but taking note of the relative sizes of the angles of incidence and refraction, decide which situations (if any) show a refraction that is physically possible. Provide a reason as to why the refraction is possible or impossible.
Problem For cases (a), (b), and (c), the angle of incidence is 55°; for case (d), the angle of incidence is 0°. For each case, determine the angle of refraction. Check to be sure that your answers are consistent with your answers to the Concept Question.

| 119 | Concept Question The drawing shows a ray of light traveling through three materials whose surfaces are parallel to each other. The refracted rays (but not the reflected rays) are shown as the light passes through each material. Taking into account the relative sizes of the angles of incidence and refraction, rank the materials according to their indices of refraction, greatest first. Provide reasons for your ranking.

Problem A ray of light strikes the a − b interface at a 50.0° angle of incidence. The index of refraction of material a is na = 1.20. The angles of refraction in materials b and c are, respectively, 45.0° and 56.7°. Find the indices of refraction in these two media. Verify that your answers are consistent with your answers to the Concept Question.

| 120 | Concept Question The drawing shows three materials, a, b, and c. A ray of light strikes the a − b interface at an angle of incidence that just barely exceeds its critical angle. The reflected ray then strikes the a − c interface at an angle of incidence that just barely exceeds its critical angle. Rank the three materials according to their indices of refraction, largest first.

Problem A ray of light is incident at the a − b interface with an angle of incidence that just barely exceeds the critical angle of . The index of refraction of material a is na = 1.80. Find the indices of refraction for the two other materials. Be sure your ranking of the indices is consistent with that determined in the Concept Question.

| 121 | Concept Question The drawing shows three layers of different materials, with air above and below the layers. The interfaces between the layers are parallel. The index of refraction of each layer is given in the drawing. Identical rays of light are sent into the layers, and each ray zigzags through the layer, reflecting from the top and bottom surfaces. Fill in the following table specifying a “yes” or “no” as to whether total internal reflection is possible from the top and bottom surfaces of each layer. Provide a reason for each of your answers.

Is total internal reflection possible?
Layer | Top surface of layer | Bottom surface of layer
a |  |
b |  |
c |  |

Problem For each layer, the ray of light has an angle of incidence of 75.0°. For the cases in which total internal reflection is possible from either the top or bottom surface of a layer, determine the amount by which the angle of incidence exceeds the critical angle.

| 122 | Concept Questions An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is one-half the size of the object. (a) What kind of lens, converging or diverging, is used to produce this image? (b) How is the height hi of the image related to the height ho of the object? Don’t forget to take into account the fact that the image is inverted relative to the object. (c) What is the ratio di/do of the image distance to the object distance?
Problem For the situation described in the Concept Questions, the distance between the object and the image is 90.0 cm. (a) How far from the lens is the object? (b) What is the focal length of the lens?

| 123 | Concept Question Two systems are formed from a converging lens and a diverging lens, as shown in parts a and b of the drawing. (The point labeled “Fconverging” is the focal point of the converging lens.) An object is placed inside the focal point of lens 1. Without doing any calculations, determine for each system whether the final image lies to the left or to the right of lens 2. Provide a reason for each answer.
Problem The focal lengths of the converging and diverging lenses are 15.00 and −20.0 cm, respectively. The distance between the lenses is 50.0 cm, and an object is placed 10.00 cm to the left of lens 1. Determine the final image distance for each system, measured with respect to lens 2. Check to be sure your answers are consistent with your answers to the Concept Question.

| 124 | Concept Questions The back wall of a home aquarium is a mirror that is a distance L away from the front wall. The walls of the tank are negligibly thin. A fish, swimming midway between the front and back walls, is being viewed by a person looking through the front wall. (a) Does the fish appear to be at a distance greater than, less than, or equal to from the front wall? (b) The mirror forms an image of the fish. How far from the front wall is this image located? Express your answer in terms of L. (c) Assume that your answer to Question (b) is a distance D. Does the image of the fish appear to be at a distance greater than, less than, or equal to D from the front wall? (d) Could the image of the fish appear to be in front of the mirror if the index of refraction of water were different than it actually is, and, if so, would the index of refraction have to be greater than or less than its actual value? Explain each of your answers.
Problem The distance between the back and front walls of the aquarium is 40.0 cm. (a) Calculate the apparent distance between the fish and the front wall. (b) Calculate the apparent distance between the image of the fish and the front wall. Verify that your answers are consistent with your answers to the Concept Questions.

| 125 | Concept Questions (a) For astronomical telescopes that have large angular magnifications, which lens has the greater focal length, the objective or the eyepiece? (b) How is the length L of the telescope related to the focal length fo of the objective and the focal length fe of the eyepiece? (c) Three astronomical telescopes have different lengths L, such that LA < LB < LC. They have identical eyepieces. Rank the angular magnifications (magnitudes only) of these telescopes in descending order (largest first). For each answer, give your reasoning.
Problem The lengths of the three telescopes are LA = 455 mm, LB = 615 mm, and LC = 824 mm. The focal length of the eyepieces is 3.00 mm for each telescope. Find the angular magnification of each telescope. Be sure that your answers are consistent with your answer to part (c) of the Concept Questions.

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