## Question

Two objects *A* and *B*, when placed in turn in front of a concave mirror of focal length 7.5 cm give images of equal size. If *A* is two times the size of*B* and is placed at a distance of 15cm from the mirror, find the distance of*B* from the mirror

### Solution

11.25 cm

For a mirror (concave or convex)

We have

And magnification

For object A: *u* = – 15cm, f = – 7.5 cm

If *y*_{1} is the size of the object *A* and *y*_{2} the size of the image, then the magnification is

For object B: size of object B = y_{1}/2 (given) and size of the image of B = – *y*_{1} (inverted)

or *c* = 2*u*

from mirror formula, we have

or

The object B is a distance of **11.25 cm** in front the mirror.

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