Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 34, Problem 129P
The equation 1/p 1/i = 2/r for spherical mirrors is an approximation that is valid if the image is formed by rays that make only small angles with the central axis. In reality, many of the angles are large, which smears the image a little. You can determine how much. Refer to Fig. 34-22 and consider a ray that leaves a point source (the object) on the central axis and that makes an angle α with that axis.
First, find the point of intersection of the ray with the mirror. If the coordinates of this intersection point are x and y and the origin is placed at the center of curvature, then y = (x + p – r) tan α and x2 + y2 + r2, where p is the object distance and r is the mirror’s radius of curvature. Next, use tan β = y/x to find the angle β at the point of intersection, and then use α + γ = 2 β to find the value of γ. Finally, use the relation tan γ = y/(x + i – r) to find the distance i of the image.
(a) Suppose r = 12 cm and p = 20 cm. For each of the following values of α, find the position of the image — that is, the position of the point where the reflected ray crosses the central axis: 0.500, 0.100, 0.0100 rad. Compare the results with those obtained with the equation 1/p + 1/i = 2/r. (b) Repeat the calculations for p = 4.00 cm.
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Chapter 34 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 34 - Figure 34-25 shows a fish and a fish stalker in...Ch. 34 - In Fig. 34-26, stick figure O stands in front of a...Ch. 34 - Figure 34-27 is an overhead view of a mirror maze...Ch. 34 - A penguin waddles along the central axis of a...Ch. 34 - When a T. rex pursues a jeep in the movie Jurassic...Ch. 34 - An object is placed against the center of a...Ch. 34 - The table details six variations of the basic...Ch. 34 - An object is placed against the center of a...Ch. 34 - Figure 34-30 shows four thin lenses, all of the...Ch. 34 - In Fig. 34-26, stick figure O stands in front of a...
Ch. 34 - Figure 34-31 shows a coordinate system in front of...Ch. 34 - You look through a camera towards an image of a...Ch. 34 - ILW A moth at about eye level is 10 cm in front of...Ch. 34 - In Fig. 34-32, an isotropic point source of light...Ch. 34 - Figure 34-33 shows an overhead view of a corridor...Ch. 34 - SSM WWW Figure 34-34 shows a small lightbulb...Ch. 34 - An object is moved along the central axis of a...Ch. 34 - A concave shaving mirror has a radius of curvature...Ch. 34 - An object is placed against the center of a...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 9 through 16 GO 12 SSM 9, 11, 13 Spherical...Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - 17 through 29 GO 22SSM 23, 29 More mirrors. Object...Ch. 34 - 17 through 29 GO 22 SSM 23, 29 More mirrors....Ch. 34 - GO Figure 34-37 gives the lateral magnification m...Ch. 34 - a A luminous point is moving at speed vo towards a...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - 32 through 38 GO 37, 38 SSM 33, 35 Spherical...Ch. 34 - In Fig. 34-38, a beam of parallel light rays from...Ch. 34 - A glass sphere has radius R = 5.0 cm and index of...Ch. 34 - A lens is made of glass having an index of...Ch. 34 - Figure 34-40 gives the lateral magnification m of...Ch. 34 - A movie camera with a single lens of focal length...Ch. 34 - An object is placed against the center of a thin...Ch. 34 - You produce an image of the Sun on a screen, using...Ch. 34 - An object is placed against the center of a thin...Ch. 34 - SSM WWW A double-convex lens is to be made of...Ch. 34 - An object is moved along the central axis of a...Ch. 34 - SSM An illuminated slide is held 44 cm from a...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 50 through 57 GO 55, 57 SSM 53 Thin lenses. Object...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - 58 through 67 GO 61 SSM 59 Lenses with given...Ch. 34 - In Fig. 34-44, a real inverted image I of an...Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 69 through 79 GO 76, 78 SSM 75, 77 More lenses....Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - 80 through 87 GO 80, 87 SSM WWW 83 Two-lens...Ch. 34 - If the angular magnification of an astronomical...Ch. 34 - SSM In a microscope of the type shown in the Fig....Ch. 34 - Figure 34-46a shows the basic structure of an old...Ch. 34 - SSM Figure 34-47a shows the basic structure of a...Ch. 34 - An object is 10.0 mm from the objective of a...Ch. 34 - Someone with a near point Pn of 25 cm views a...Ch. 34 - An object is placed against the center of a...Ch. 34 - 95 through 100 GO 95, 96, 99 Three-lens systems....Ch. 34 - 95 through 100 GO 95, 96, 99 Three-lens systems....Ch. 34 - 95 through 100 GO 95, 96, 99 Three-lens systems....Ch. 34 - 95 through 100 GO 95, 96, 99 Three-lens systems....Ch. 34 - 95 through 100 GO 95, 96, 99 Three-lens systems....Ch. 34 - 95 through 100 GO 95, 96, 99 Three-lens systems....Ch. 34 - SSM The formula 1/p 1/i = 1/f is called the...Ch. 34 - Figure 34-50a is an overhead view of two vertical...Ch. 34 - SSM Two thin lenses of focal lengths f1 and f2 are...Ch. 34 - Two plane mirrors are placed parallel to each...Ch. 34 - In Fig. 34-51, a box is somewhere at the left, on...Ch. 34 - In Fig. 34-52, an object is placed in front of a...Ch. 34 - SSM A fruit fly of height H sits in front of lens...Ch. 34 - You grind the lenses shown in Fig. 34-53 from flat...Ch. 34 - In Fig. 34-54, a fish watcher at point P watches a...Ch. 34 - A goldfish in a spherical fish bowl of radius R is...Ch. 34 - Figure 34-56 shows a beam expander made with two...Ch. 34 - You look down at a coin that lies at the bottom of...Ch. 34 - A pinhole camera has the hole a distance 12 cm...Ch. 34 - Light travels from point A to point B via...Ch. 34 - A point object is 10 cm away from a plane mirror,...Ch. 34 - Show that the distance between an object and its...Ch. 34 - A luminous object and a screen are a fixed...Ch. 34 - An eraser of height 1.0 cm is placed 10.0 cm in...Ch. 34 - A peanut is placed 40 cm in front of a two-lens...Ch. 34 - A coin is placed 20 cm in front of a two-lens...Ch. 34 - An object is 20 cm to the left of a thin diverging...Ch. 34 - In Fig 34-58 a pinecone is at distance p1 = 1.0 m...Ch. 34 - One end of a long glass rod n = 1.5 is a convex...Ch. 34 - A short straight object of length L lies along the...Ch. 34 - Prove that if a plane mirror is rotated through an...Ch. 34 - An object is 30.0 cm from a spherical mirror,...Ch. 34 - A concave mirror has a radius of curvature of 24...Ch. 34 - A pepper seed is placed in front of a lens. The...Ch. 34 - The equation 1/p 1/i = 2/r for spherical mirrors...Ch. 34 - A small cup of green tea is positioned on the...Ch. 34 - A 20-mm-thick layer of water n = 1.33 floats on a...Ch. 34 - A millipede sits 1.0 m in front of the nearest...Ch. 34 - a Show that if the object O in Fig. 34-19c is...Ch. 34 - Isaac Newton, having convinced himself erroneously...Ch. 34 - A narrow beam of parallel light rays is incident...Ch. 34 - A corner reflector, much used in optical,...Ch. 34 - A cheese enchilada is 4.00 cm in front of a...Ch. 34 - A grasshopper hops to a point on the central axis...Ch. 34 - In Fig. 34-60, a sand grain is 3.00 cm from thin...Ch. 34 - Suppose the farthest distance a person can see...Ch. 34 - A simple magnifier of focal length f is placed...
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