A plano-convex lens (μ = (3/2)) has a radius of curvature R=15 cm and is placed at a distance z from a concave lens of focal length 20 cm as shown. At what distance x0 should a point object be placed from the plano-convex lens, so that position of the final image is independent of z ?

Question

A plano-convex lens (μ = (3/2)) has a radius of curvature R=15 cm and is placed at a distance z from a concave lens of focal length 20 cm as shown. At what distance x0 should a point object be placed from the plano-convex lens, so that position of the final image is independent of z ? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-skflt3cekdpn.png" /> (A) 20 cm (B) 30 cm (C) 40 cm (D) 60 cm

Tardigrade Admin · Accepted Answer

The position of the final image will be independent of

z

, only if the rays of light are incident on the concave lens as a beam parallel to the principal axis. This will be possible only when the object is kept at focus of the plano-convex lens.

∴ \frac{1}{x _{0}} = \frac{1}{f _{1}} = (μ - 1) [\frac{1}{R _{1}} - \frac{1}{R _{2}}] = (\frac{3}{2} - 1) [\frac{1}{15} - \frac{1}{\infty}]

\Rightarrow x_{0} = 30 c m

$20 c m$

$30 c m$

$40 c m$

$60 c m$

Q. A plano-convex lens (μ=23​) has a radius of curvature R=15cm and is placed at a distance z from a concave lens of focal length 20cm as shown. At what distance x0​ should a point object be placed from the plano-convex lens, so that position of the final image is independent of z ?

20cm

30cm

40cm

60cm

$20 c m$

$30 c m$

$40 c m$

$60 c m$