A plano-convex glass lens (μ g=3/2) of radius of curvature R=20 text cm is placed at a distance a from a concave lens of focal length 40 cm. What should be the distance b of a point object O from plano-convex lens so that the position of final image is independent of a ?

Question

A plano-convex glass lens (μ g=3/2) of radius of curvature R=20 text cm is placed at a distance a from a concave lens of focal length 40 cm. What should be the distance b of a point object O from plano-convex lens so that the position of final image is independent of a ? (A) 20 cm (B) 60 cm (C) 40 cm (D) 30 cm

Tardigrade Admin · Accepted Answer

Focal length of the plano-convex lens is

\frac{1}{f} = (μ_{0} - 1) (\frac{1}{20} - \frac{1}{\infty})

= (\frac{3}{2} - 1) (\frac{1}{20}) = \frac{1}{2} \times \frac{1}{20}

\Rightarrow

t = 40 c m

If point object O is placed at a distance of 40 cm from the plano-convex lens, rays become parallel and final image is formed at second focus or 40 cm from concave lens which is independent of a.

Q. A plano-convex glass lens (μg​=3/2) of radius of curvature R=20cm is placed at a distance a from a concave lens of focal length 40cm. What should be the distance b of a point object O from plano-convex lens so that the position of final image is independent of a ?

20 cm

60 cm

40 cm

30 cm

Q. A plano-convex glass lens $(μ_{g} = 3/2)$ of radius of curvature $R = 20 c m$ is placed at a distance a from a concave lens of focal length $40 c m$ . What should be the distance $b$ of a point object $O$ from plano-convex lens so that the position of final image is independent of $a$ ?