HW4+Sol - Winter 1996 HOMEWORK 4 with Solutions 1 Find the...

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Winter 1996 HOMEWORK 4 with Solutions 1. Find the image of the object for the single concave mirror system shown in Fig.1 (see next pages for worksheets) by: (a) measuring the radius R and calculating the focal length for the concave mirror, (b) drawing the focal point into the diagram, and (c) constructing the image of the object graphically with three rays. R = 10 cm, and f = R 2 = 5 cm Three rays: Incident Rays Reflected Rays 1 Parallel to the optical axis Through the focal point of the mirror (F) 2 Through the center of the mirror (C) Through the center of the mirror (C) 3 Through the focal point of the mirror (F) Parallel to the optical axis C Object Image F
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2. Regarding your own face as a real object, describe the image of your face which you see standing 4 feet from the center (and looking directly toward) a polished and well-reflecting brass ball 2 feet in diameter hanging in front of a pawn shop. Determine the image of your face both graphically and by calculation . By Calculation: Brass ball is equivalent to a CONVEX MIRROR ( f < 0) . Diameter = 2 · R = 2 ft R = 1 ft and f = – 0.5 ft You are standing at 4 ft from the center of the brass ball, but the distance s o of object from the mirror is measured from the vortex of mirror. s o = (4 – 1) = + 3 ft From the mirror equation, 1 f = 1 s o + 1 s i s i = { 1 –0.5 1 3 } -1 = –0.43 ft Since s i < 0, the image is virtural .
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