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Solutions to Homework Questions 9

Physics 112 **Homework** 9 (solutions) (2004 Fall) **Solutions** **to** **Homework** **Questions** 9 Chapt23, Problem-1: Does your bathroom mirror show you older or younger than your actual age? Compute an order-of-magnitude estimate for the age difference, based on data that you specify. Solution: If you stand 40 cm in front of the mirror, the time required for light scattered from your face **to** travel **to** the mirror and back **to** your eye is 2 d 2 ( 0.40 m ) !t = = c 3.0 "10 8 ms = 2.7 "10 #9 s . Thus, the image you observe shows you ~10 !9 s younger than your current age. Chapt23, Problem-8: A dentist uses a mirror **to** examine a **to**oth. The **to**oth 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. Solution: (a) Since the object is in front of the mirror, p > 0 . With the image behind the mirror, q < 0 . The mirror equation gives the radius of curvature as 2 1 1 = + R p q = 1 1.00 cm ! 1 10 -1 = 10.0 cm 10.0 cm , ! 10.0 cm $ or R = 2# & = + 2.22 cm " 9 % (b) The magnification is M = ! q p ( ) !10.0 cm = ! 1.00 cm = +10.0 Chapt23, Problem-13: A concave makeup mirror is designed so that a person 25 cm in front of it sees an upright image magnified by a fac**to**r of 2. What is the radius of curvature of the mirror? Solution: The image is upright, so M > 0 and we have M = ! q =+2.0, or q =! 2.0 p =! 2.0 ( 25 cm )= !50 cm p The radius of curvature is then found **to** be 2 1 1 = + R p q = 1 25 cm ! 1 2 !1 = , or 50 cm 50 cm ! 0.50 m $ R = 2# " +1 & = 1.0 m % 1

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