Question

A plano convex lens $(\mu =\frac{3}{2})$ has radius of curvature R = 10 cm, and is placed at a distance of ‘b’ from a concave lens of focal length 20 cm as shown in the figure.
At what distance ‘a’ should a point object be placed from plano
convex lens, so that position of the final image is independent of ‘b’?

• A. 40 cm
• B. 60 cm
• C. 30 cm
• D. 20 cm

Answer 1

The correct option is D 20 cm

​The position of final image is independent of b only when the rays are incident parallel to principal axis on concave lens, which is possible only when the object is kept at focus of plano convex lens.
$\therefore \frac{1}{a}=\frac{1}{f_1}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
$=(\frac{3}{2}-1)(\frac{1}{10}-\frac{1}{\infty })$
$\Rightarrow a=20cm$.