Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
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Chapter 35, Problem 32P
(a)
To determine
The proof for the expression
(b)
To determine
The height of the container.
(c)
To determine
The range of magnitude of
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As shown in Figure P35.73, a light ray is incident normal to one face of a 30°-60°-90° block of flint glass (a prism) that is immersed in water.
(a) Determine the exit angle θ3 of the ray.(b) A substance is dissolved in the water to increase the index of refraction n2. At what value of n2 does total internal reflection cease at point P?
Figure P23.28 shows a curved surface separating a material with index of refraction n1 from a material with index n2 . The surface forms an image I of object o. The ray shown in red passes through the surface along a radial line. Its angles of incidence and refraction are both zero, so its direction does not change at the surface. For the ray shown in blue, the direction changes according to n1 sin θ1 = n2 sin02 . For paraxial rays, we assume θ1 and θ2 are small, so we may write n1 tan θ1 = n2 tan θ2. The magnification is defined as M =h′/h. Prove that the magnification is given by M = −n1 q/n2p.
Figure P23.28 shows a curved surface separating a materialwith index of refraction n1 from a material with index n2.The surface forms an image I of object O. The ray shown inred passes through the surface along a radial line. Its angles ofincidence and refraction are both zero, so its direction does notchange at the surface. For the ray shown in blue, the directionchanges according to n1 sin Θ1 = n2 sin Θ2. For paraxial rays, weassume Θ1 and Θ2 are small, so we may write n1 tan Θ1 = n2 tan Θ2.The magnification is defined as M = h'/h. Prove that the magnificationis given by M = -n1q/n2p.
Chapter 35 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 35.4 - Prob. 35.1QQCh. 35.5 - If beam is the incoming beam in Figure 34.10b,...Ch. 35.5 - Light passes from a material with index of...Ch. 35.7 - Prob. 35.4QQCh. 35.8 - Prob. 35.5QQCh. 35 - Prob. 1OQCh. 35 - Prob. 2OQCh. 35 - Prob. 3OQCh. 35 - Prob. 4OQCh. 35 - Prob. 5OQ
Ch. 35 - Prob. 6OQCh. 35 - Prob. 7OQCh. 35 - Prob. 8OQCh. 35 - Prob. 9OQCh. 35 - Prob. 10OQCh. 35 - Prob. 11OQCh. 35 - Prob. 12OQCh. 35 - Prob. 13OQCh. 35 - Prob. 14OQCh. 35 - Prob. 15OQCh. 35 - Prob. 1CQCh. 35 - Prob. 2CQCh. 35 - Prob. 3CQCh. 35 - Prob. 4CQCh. 35 - Prob. 5CQCh. 35 - Prob. 6CQCh. 35 - Prob. 7CQCh. 35 - Prob. 8CQCh. 35 - Prob. 9CQCh. 35 - Prob. 10CQCh. 35 - Prob. 11CQCh. 35 - (a) Under what conditions is a mirage formed?...Ch. 35 - Prob. 13CQCh. 35 - Prob. 14CQCh. 35 - Prob. 15CQCh. 35 - Prob. 16CQCh. 35 - Prob. 17CQCh. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - In an experiment to measure the speed of light...Ch. 35 - As a result of his observations, Ole Roemer...Ch. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10PCh. 35 - Prob. 11PCh. 35 - A ray of light strikes a flat block of glass (n =...Ch. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - When you look through a window, by what time...Ch. 35 - Two flat, rectangular mirrors, both perpendicular...Ch. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - A submarine is 300 m horizontally from the shore...Ch. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 39PCh. 35 - Prob. 40PCh. 35 - Prob. 41PCh. 35 - Prob. 42PCh. 35 - Prob. 43PCh. 35 - Prob. 44PCh. 35 - Assume a transparent rod of diameter d = 2.00 m...Ch. 35 - Consider a light ray traveling between air and a...Ch. 35 - Prob. 47PCh. 35 - Prob. 48PCh. 35 - Prob. 49PCh. 35 - Prob. 50PCh. 35 - Prob. 51APCh. 35 - Prob. 52APCh. 35 - Prob. 53APCh. 35 - Prob. 54APCh. 35 - Prob. 55APCh. 35 - Prob. 56APCh. 35 - Prob. 57APCh. 35 - Prob. 58APCh. 35 - Prob. 59APCh. 35 - A light ray enters the atmosphere of a planet and...Ch. 35 - Prob. 61APCh. 35 - Prob. 62APCh. 35 - Prob. 63APCh. 35 - Prob. 64APCh. 35 - Prob. 65APCh. 35 - Prob. 66APCh. 35 - Prob. 67APCh. 35 - Prob. 68APCh. 35 - Prob. 69APCh. 35 - Prob. 70APCh. 35 - Prob. 71APCh. 35 - Prob. 72APCh. 35 - Prob. 73APCh. 35 - Prob. 74APCh. 35 - Prob. 75APCh. 35 - Prob. 76APCh. 35 - Prob. 77APCh. 35 - Prob. 78APCh. 35 - Prob. 79APCh. 35 - Prob. 80APCh. 35 - Prob. 81CPCh. 35 - Prob. 82CPCh. 35 - Prob. 83CPCh. 35 - Prob. 84CPCh. 35 - Prob. 85CPCh. 35 - Prob. 86CPCh. 35 - Prob. 87CP
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- In Figure P35.30, a thin converging lens of focal length 14.0 cm forms an image of the square abed, which is he = hb = 10.0 cm high and lies between distances of pd = 20.0 cm and pa = 30.0 cm from the lens. Let a, b, c. and d represent the respective corners of the image. Let qa represent the image distance for points a and b, qd represent the image distance for points c and d, hb, represent the distance from point b to the axis, and hc represent the height of c. (a) Find qa, qd, hb, and hc. (b) Make a sketch of the image. (c) The area of the object is 100 cm2. By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a and d, for which the object distance is p. Let h represent the distance from the axis to the point at the edge of the image between b and c at image distance q. Demonstrate that h=10.0q(114.01q) where h and q are in centimeters. (d) Explain why the geometric area of the image is given by qaqdhdq (e) Carry out the integration to find the area of the image. Figure P35.30arrow_forwardA floating strawberry illusion is achieved with two parabolic mirrors, each having a focal length 7.50 cm, facing each other as shown in Figure P33.58. If a strawberry is placed on the lower mirror, an image of the strawberry is formed at the small opening at the center of the top mirror, 7.50 cm above the lowest point of the bottom mirror. The position of the eye in Figure P35.58a corresponds to the view of the apparatus in Figure P35.58b. Consider the light path marked A. Notice that this light path is blocked by the upper mirror so that the strawberry itself is not directly observable. The light path marked B corresponds to the eye viewing the image of the strawberry that is formed at the opening at the top of the apparatus. (a) Show that the final image is formed at that location and describe its characteristics. (b) A very startling effect is to shine a flashlight beam on this image. Even al a glancing angle, the incoming light beam is seemingly reflected from the image! Explain. Figure P35.58arrow_forwardHow many times will the incident beam in Figure P34.33 (page 922) be reflected by each of the parallel mirrors? Figure P34.33arrow_forward
- Figure P36.95 shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of 9.00 cm and 11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. Assume the focal points F1 and F2 of the lens are 5.00 cm from the center of the lens, (a) Determine the index of refraction of the lens material. The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine (b) the position of the filial image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.arrow_forwardFigure P38.43 shows a concave meniscus lens. If |r1| = 8.50 cm and |r2| = 6.50 cm, find the focal length and determine whether the lens is converging or diverging. The lens is made of glass with index of refraction n = 1.55. CHECK and THINK: How do your answers change if the object is placed on the right side of the lens? FIGURE P38.43arrow_forwardTwo converging lenses having focal lengths of f1 = 10.0 cm and f2 = 20.0 cm are placed a distance d = 50.0 cm apart as shown in Figure P35.48. The image due to light passing through both lenses is to be located between the lenses at the position x = 31.0 cm indicated. (a) At what value of p should the object be positioned to the left of the first lens? (b) What is the magnification of the final image? (c) Is the final image upright or inverted? (d) Is the final image real or virtual?arrow_forward
- A person looking into an empty container is able to see the far edge of the container's bottom, as shown in Figure P22.23a. The height of the container is h, and its width is d. When the container is com- pletely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the container's bottom, as shown in Figure P22.23b. (a) Show that the ratio h/d is given by 4 - n² (b) Assuming the container has a width of 8.00 cm and is filled with water, use the expression above to find the height of the container. b. Figure P22.23arrow_forwardA block of crown glass is immersed in water as in the figure below. A light ray is incident on the top face at an angle of θ1= 41° with the normal and exits the block at point P. Find the angle of refraction θ2 of the light ray leaving the block at P. 80.2° 41° 43.3° 68.9°arrow_forwardFigure P22.59 shows the path of a beam of light through severallayers with different indices of refraction. (a) If Θ1 = 30.0°,what is the angle Θ2 of the emerging beam? (b) What must the incident angle Θ1 be to have total internal reflection at thesurface between the medium with n = 1.20 and the mediumwith n = 1.00?arrow_forward
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