Convex mirrors are used in many stores to provide a wide angle of surveillance f
ID: 1586844 • Letter: C
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 5.4 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? (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?
Explanation / Answer
(a)
do = 10 m
f = - 1.1/2 = -0.55
di = ?
1/f = 1/di + 1/do
-1/0.55 = 1/di + 1/10
di = - 0.52 m
Distance of the image from the mirror, di = 52 cm
(b)
As the di value is -ve, The image is formed behind the mirror.
(c)
hi/ho = - di/do
hi/2 = - (-0.52)/(10)
hi = 0.104 m
Height of the image, hi = 10.4 cm