Question

How far should an object be placed from the pole of a converging mirror of focal length 20 cm to form a real image of the size exactly $\frac{1}{4}$th the size of the object?

Answer 1

Step 1, Given data

Focal length of a concave mirror, $f=-20cm$

Step 2, Finding the object distance

Let object distance be $u$ and image distance be $v$.

Magnification is, $m=\frac{-v}{u}$ = -1/4 (for real image m is negative)

Therefore,$v=\frac{u}{4}$

Now, from mirror formula we have,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Putting all the values

$\frac{-1}{20}=\frac{4}{u}+\frac{1}{u}$

After solving

u = - 100 cm

Hence the object should be placed 100 cm from the mirror.