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 5.9 m from the mirror. The mirror has a radius of curvature equal to 1.4 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
(b) Is the image in front of or behind the mirror?

behind the mirrorin

front of the mirror

(c) If the customer is 2 m tall, how tall is his image?

cm

Explanation / Answer

given

R = 1.4 m

a) we know,

focal length of mirror, f = -R/2 = -1.4/2 = -0.7 m

object distance, u = 10 m

let v is the image distance.

apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/(-0.7) - 1/10

v = -0.654 m

= -65.4 cm

here "-" sign indicaes the image is virtual

b) behind the mirror

c) magnification, m = -v/u

= -(-0.654)/10

= 0.0654

image height = m*object height

= 0.0654*2

= 0.13 m

= 13 cm

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