Question

Use the mirror equation to show that an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.

Answer 1

From Mirror equation,

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

For concave mirror, $f=-|f|,u=-|u|$

$\frac{1}{v}=\frac{1}{|u|}-\frac{1}{|f|}$............(i)

It is given that $|f|<|u|<2|f|$

$\frac{1}{2|f|}<\frac{1}{|u|}<\frac{1}{|f|}$.........(ii)

Substituting the values from the eq (i) in the eq(ii)

$-\frac{1}{2|f|}<\frac{1}{v}<0$

Above equation shows that $v$ is negative. Hence,

$v<-2|f|$

Hence, image is formed at same side of mirror as the object at a distance greater than 2f.

Magnification is given by:

$m=\frac{-v}{u}<0$

Hence, image formed is real.