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Unformatted text preview: Additional Example Problems From Chapter 23 Q1: Use Figure below to give a geometric proof that the virtual image formed by a plane mirror is the same distance behind the mirror as the object is in front of it. FIGURE: A geometric construction to locate the image of an object placed in front of a flat mirror. Because the triangles PQR and P'QR are identical, p = |Q| and h = h'. A: In the figure at the right, θ θ = ′ since they are vertical angles formed by two intersecting straight lines. Their complementary angles are also equal or α α = ′ . The right triangles PQR and P'QR have the common side QR and are then congruent by the angle-side-angle theorem. Thus, the corresponding sides PQ and P'Q are equal, or the image is as far behind the mirror as the object is in front of it. Q2: A dentist uses a mirror to examine a tooth. The tooth is 1.00 cm in front of the mirror, and the image is formed 10.0 cm behind the mirror. Determine (a) the mirror’s radius of curvature and (b) the magnification of the image. A: (a) Since the object is in front of the mirror, p . With the image behind the mirror, q < . The mirror equation gives the radius of curvature as 2 1 1 1 1 10-1 1.00 cm 10.0 cm 10.0 cm R p q = + =- = , or 10.0 cm 2 9 R = = 2.22 cm + (b) The magnification is ( 29 10.0 cm10....
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