Find focal length of convex mirror While shopping in a groce

Find focal length of convex mirror

While shopping in a grocery store you look up at a convex security mirror. You notice that your image is about one-fourth of your height. By estimating your distance to be 2.0 meters in front of the mirror, determine the focal length of the mirror.

Solution

Given

h_i=0.25h_o

Magnification

M =h_i/h_o =-d_i/d_o

0.25h_o/h_o =-d_i/2

d_i=-0.5 m

from thin lens formula

1/f =1/d_i + 1/d_o

1/f =-1/0.5 + 1/2

f=-0.67 m

For Convex mirror ,focal length is f=0.67 m