E2HWCH32 - Chapter 32 Optical Images 27 (a) Use the mirror...

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Chapter 32 Optical Images 27 • ( a ) Use the mirror equation (Equation 32-4 where f = r /2) to calculate the image distances for the object distances and mirror of Problem 26. ( b ) Calculate the magnification for each given object distance. Picture the Problem In describing the images, we must indicate where they are located, how large they are in relationship to the object, whether they are real or virtual, and whether they are upright or inverted. The object distance s , the image distance s , and the focal length of a mirror are related according to where and r is the radius of curvature of the mirror. In this problem, f = - 12 cm because r is negative for a convex mirror. ( a ) Solve the mirror equation for s : When s = 55 cm: When s = 24 cm: When s = 12 cm: When s = 8.0 cm:
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( b ) The lateral magnification is given by: When s = 55 cm, the lateral magnification of the image is: When s = 24 cm, the lateral magnification of the image is: When s = 12 cm, the lateral magnification of the image is: When s = 8.0 cm, the lateral magnification of the image is: Remarks: These results are in excellent agreement with those obtained graphically in Problem 26. 31 •• A certain telescope uses a concave spherical mirror that has a radius equal to 8.0 m. Find the location and diameter of the image of the moon formed by this mirror. The moon has a diameter of 3.5 × 10 6 m and is 3.8 × 10 8 m from Earth. Picture the Problem We can use the mirror equation to locate the image formed in this mirror and the expression for the lateral magnification of the mirror to find the diameter of the image. Solve the mirror equation for the location of the image of the
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Because : Substitute numerical values and evaluate s : Express the lateral magnification of the mirror: Substitute numerical values and evaluate y : The 3.7-cm-diameter image is 4.0 m in front of the mirror. 43 • 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 ) double-convex that has radii of curvature equal to 15 cm and 26 cm, ( b ) plano-convex that has a radius of curvature equal to 15 cm, ( c ) double concave that has radii of curvature equal to 15 cm, and ( d ) plano-concave that has a radius of curvature equal to 26 cm. Picture the Problem We can use the lens-maker’s equation to find the focal length of each of the lenses. The lens-maker’s equation is:
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E2HWCH32 - Chapter 32 Optical Images 27 (a) Use the mirror...

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