Question

An object is placed at a distance of $15$ cm from a convex lens of focal length $10$ cm. On the other side of the lens, a convex mirror is placed at its focus such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is :

Answer 1

For the lens,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}=\frac{1}{10}-\frac{1}{15}$

Thus, $v=30cm$

Now, for the mirror, this image acts as the object.

$u=30-10=20cm$

Also, $v=-25cm$
Hence,

$\frac{-1}{25}+\frac{1}{20}=\frac{1}{f}$

$f=100cm$