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 at 15 cm apart from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

Answer 1

Lens formula for convex lens,

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

$\frac{1}{v}-\frac{1}{-60}=\frac{1}{20}$

$v=30cm$

Image ($I_1$) formed by the convex lens acts as an object for the convex mirror.

Since the mirror and lens are separated by 15 cm, distance between $I_1$ and mirror is 15 cm.

i.e. $u=15$

For convex mirror,

$f=\frac{R}{2}=10cm$

From mirror equation,

$\frac{1}{v_2}+\frac{1}{u_2}=\frac{1}{f_2}$

$\frac{1}{v_2}+\frac{1}{15}=\frac{1}{10}$

$v_2=30cm$

Hence, image is formed 30 cm right of the convex mirror.

From the ray diagram, it can be observed that the image is virtual.