Convex mirrors are used in many stores to provide a wide angle of surveillance f

Question

Convex mirrors are used in many stores to provide a wide angle of surveillance 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 5.1 m from the mirror. The mirror has a radius of curvature equal to 1.1 m. Assume all rays are paraxial. (a) If a customer is 10 m from the mirror, how far from the mirror is his image? cm You currently have 7 submissions for this question. Only 15 submission ore allowed. You can make 8 more submissions for this question. (b) Is the image in front of or behind the mirror? behind the mirror in front of the mirror (c) If the customer is 2 m tall, how tall is his image? 10.4 cm

Explanation / Answer

(1)
do = 10 m
f = r/2 = - 1.1/2 = - 0.55 m

We know,
1/f = 1/di + 1/do
-1/0.55 = 1/di + 1/10
di = - 0.52 m
Distance of image from mirror, = 52 cm

(2)
Image is behind the mirror.

(3)
M = -di/do = hi/ho

-di/do = hi/ho
0.52/10 = hi/2
hi = 0.104 m
Height of image, hi = 10.4 cm

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