Question

An object is placed in front of a mirror with focal length 25cm. What must the object distance be in order that the magnification of a virtual image is 3?

Answer 1

Let the required object distance be x.

As the magnification is 3, so, image is enlarged and also it is virtual according to question, so, mirror is concave.

Thus, focal length, f = - 25 cm,

Object distance, u = - x

As virtual object forms behind the mirror, so, image distance, v, is positive.

Now, magnification, m = - v/u

Or,     -3u = v

Or, v = -3*(-x) = 3x

By mirror equation, 1/v + 1/u = 1/f

Or, 1/3x - 1/x = - 1/25

Or, (1-3)/3x = - 1/25

Or, - 2/3x = - 1/25

Or, x = 50/3

So, required object distance = (50/3) = 16.67 cm

In front of the mirror.