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

Answer: 5

$\frac{1}{f}=(\mu -1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=\frac{1}{40}$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{(d-20)}-\frac{1}{(-80)}=\frac{1}{40}$
$\frac{1}{(d-20)}=\frac{2}{80}-\frac{1}{80}=\frac{1}{80}$
$d=25+80=105cm=21\times 5cm$
Hence $x=5cm$