Question

A convex lens of focal length $20cm$ is placed coaxially with a concave mirror of focal length $10cm$ at a distance of $50cm$ apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination.

Answer 1

Since rays are coming from infinity

For first image

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

$f=20cm$

$u>2f$ therefore infinity

$\frac{1}{v}=\frac{1}{20}$

$v=20cm$

for second mirror is placed it can be

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

$u=-30cm=$ infinity since greater than 2f

$f=-10cm$

therefore

$\frac{1}{v}=\frac{1}{-10}+\frac{1}{30}$

$v=-15cm$

again applying the lens formula for the lenses

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

$u=-35cm$

$f=20cm$

$v=46.6cm$ to the left of the lens.