Question

A shopper standing 3.25 m from a convex security mirror sees his image with a magnification of 0.26.

a) What is his image distance in meters, measured from the surface of the mirror, given that the object distance is positive?

b) What is the focal length of the mirror, in meters?

c) What is its radius of curvature in meters?

Answer 1

a)

The magnification due to a convex mirror is given by (-V/U)

Where V is the image distance ( measured from the mirror) and U is the object distance (measured from the mirror).

Here we need to consider the sign convention, while measuring distances, that is we take positive in the direction of propagation of light.

Since the magnification is positive, hence image distance and object distance must be measured in two directions from the mirror, that means if the object in front of the mirror, then the image will be behind the mirror.

Therefore,

V/3.25 = 0.26

V = 0.845m behind the mirror.

b) now to calculate focus (f) of the mirror, we use mirror formula,

1/f = 1/U + 1/V

1/f = 1/(-3.25) + 1/0.845

f = 0.876m ( behind the mirror)

c) the focus of a mirror is half the radius of curvature (R) of the mirror,

Therefore, R = 2*f = 2*0.876 = 1.75m