Physics - Geometrical Optics Question with Solution | TestHub

Equivalent power of combination is

$P_{eff}=2P_{lens}+P_{mirror}$...(i)

$\because P_{mirror }=0$for plane mirror and$P_{lens}=\frac{1}{f}$

Also combination behaves as a mirror. So.$P_{eff}=\frac{1}{f_{mirror}}$

In equation (i)

$-\frac{1}{f_{mirror }}=\frac{2}{f}\Rightarrow f_{mirror}=-\frac{f}{2}$

By mirror formula

$\frac{1}{f_{mirror }}=\frac{1}{u}+\frac{1}{v}$

Here$u= -a, v=-\frac{a}{3}, f_{mirror}= -\frac{f}{2}$

$\Rightarrow -\frac{2}{f}=\frac{1}{-a}+\frac{3}{-a}=\frac{-4}{a}$

$\Rightarrow \frac{-2}{f}=\frac{-4}{a}\Rightarrow a=2f$