0 EP2-HW26-Long Convex mirrors are used in many stores to provide a wide angle o

Question

0 EP2-HW26-Long Convex mirrors are used in many stores to provide a wide angle of lance for a reasonable mirror size. Your summer job is at a local convenience store that uses the mirror shown in the figure below. This setup allows you (or the clerk) to survey the entire store when you are 4.3 m from the mirror. The mirror has a radius of curvature equal to 1.5 m. Assume all rays are paraxial. 10 m (a) If a customer is 10 m from the mirror, how far from the mirror is his image? cm (b) Is the image in front of or behind the mirror? behind the mirror O in front of the mirror (c) If the customer is 2 m tall, how tall is his image? cm 6

Explanation / Answer

distance of customer from mirror p = 10 m

radius of curvature R = -1.5 m

image distance q = ?

from mirror equation

1/p + 1/q = 2/R

1/10 + 1/q = -2/1.5

image distance q = -0.698 m

image distance = 69.8 cm = 70 cm ( rounded 2 significant figures)

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(b)

image distance is negative .so the image is behind the mirror

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(c)

magnification m = hi/ho = q/p

height of image hi = ho*q/p

hi = 2*0.7/10 = 0.14 m = 14 cm <<<<-------ANSWER

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