Physics 21 Fall, 2004 Solution to HW-24 33 P29 A 4.5 cm tall object is placed 28 cm in front of a spherical mirror. It is desired to produce a virtual image that is erect and 3.5 cm tall. (a) What type of mirror should be used? (b) Where is the image located? (c) What is the focal length of the mirror? (d) What is the radius of curvature of the mirror? Use the magniFcation formula to Fnd the image position: m = − d i d o = − d i 28 = 3 . 5 4 . 5 ⇒ d i = − 21 . 8 , and then use the lens equation to determine f : 1 f = 1 d o + 1 d i = 1 28 + 1 − 21 . 8 = 1 − 98 . The image is behind the mirror ( d i < 0); the mirror is convex ( f< 0) with focal length − 98 cm and radius of curvature 2 f = − 196 cm. FC 1 2 3 object image 34 P11 (a) An object 37.5 cm in front of a certain lens is imaged 8.20 cm in front of the lens (on the same side as the object). What type of lens is this and what is its focal length? Is the image real or virtual? (b) If the image were located, instead, 46.0 cm in front of the lens, what type of lens would it be and what focal length would it have?
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