Question

In diagram below, final image formed after two refractions through the lens and one reflection from the mirror coincides with object $O$. Refractive index of the material of the lens is $\mu=3 / 2$. The value of $d$ (in $cm$ ) is

Answer 1

$\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)=\frac{1}{40}$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{(d-20)}-\frac{1}{(-80)}=\frac{1}{40}$
$\frac{1}{(d-20)}=\frac{2}{80}-\frac{1}{80}=\frac{1}{80}$
$d=25+80=105\, cm =21 \times 5\, cm$
Hence $x=5\, cm$