Question

A convex lens of focal length $20\text{cm}$ is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is $10\text{cm}$. A point object is placed on principal axis at a distance of $60\text{cm}$ from the convex lens. The image formed by combination, coincides the object itself. The focal length of the convex mirror is $\text{cm}$.

Answer 1

The given condition can be shown as below.


We have for lens
$u=-60\text{cm},f=20\text{cm}$
Therefore,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{-60}=\frac{1}{20}$
$\Rightarrow \frac{1}{v}=-\frac{1}{60}+\frac{1}{20}=\frac{-1+3}{60}=\frac{2}{60}\Rightarrow v=+30\text{cm}$
So, Radius of curvature of mirror $=30-10=20\text{cm}$
$\Rightarrow f_{mirror}=\frac{20}{2}=10\text{cm}$