Question

If $p$ and $q$ are distance of object and real image from the principal focus of a concave mirror, then the relation between $p,q$ and $f$ is :

• A. $pq=\sqrt{f}$
• B. $pq=f$
• C. $pq=f^2$
• D. $pq=\frac{1}{f}$

Answer 1

Answer: (C)

$pq=f^2$

From the figure

$u=-(p+f)$

$v=-(q+f)$
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\frac{1}{-(p+f)}+\frac{1}{-(q+f)}=\frac{1}{-f}$
$\Rightarrow \frac{q+f+p+f}{(p+f)(q+f)}=\frac{1}{f}$
$\Rightarrow qf+2f^2+pf=pq+pf+qf+f^2$
$\Rightarrow pq=f^2$