Question

A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart. A point object is placed 40 cm in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.

Answer 1

To find :$v$ for mirror

Solution: From lens formula

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

$\frac{1}{v}+\frac{1}{40}=\frac{1}{20}$

$\frac{1}{v}=\frac{1}{40}$

$v=40cm$

Hence $u^1$ for mirror =40-15$

$u^1=25cm$

So from mirror formula

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

$\frac{1}{v}+\frac{1}{25}=\frac{-1}{10}$

$\frac{1}{v}=\frac{-1}{25}-\frac{1}{10}$

$\frac{1}{v}=\frac{-7}{50}$

$v=\frac{-50}{7}cm$ from the mirror.