Question

An object is placed in front of a convex mirror, and the size of the image is three-fourth that of the object. What is the ratio (d_o/f) of the object distance to the focal length of the mirror?

Answer 1

magnification, m = hi / ho = -(di/do)

hi = image height, ho =object height , di = image distance, do = object distance

- di/ do = 3/4

di = - 0.75do

using mirror equation,
for convex mirro, f is negative.

1/(-f) = 1/do + 1/di   = 1/do + (1/-0.75do)

1/f = 0.333/d0

do/f = 0.333 Or 1/3