Question

Two students in a physics laboratory each have a concave mirror with the same radius of curvature, 45 cm. Each student places an object in front of a mirror. The image in both mirrors is one and a half times the size of the object. However, when the students compare notes, they find that the object distances are not the same. What is the distance of the closer object?

Answer 1

its clear that, for same focal length, and image distance if the object distances is different then one object placed at distance less than focal. length in order to get virtual inage and other is placed somewhere between center of curvature and focal length.

as we need to find for closer ( virtual image) so we need to find it by magnification

m = 1.5 = v/u

v = 1.5 u

using mirror formula

1/f = 1/ v + 1/ u

- 1/22.5 = 1/1.5u - 1/u

u = 7.5 cm from mirror

=========

Comment in case any doubt, will reply for sure.. Goodluck