A plano-convex lens μ = 3 2 has a radius of curvature R = 15 c m and is placed at a distance z from a concave lens of focal length 20 cm as shown. At what distance x 0 should a point object be placed

Question

A plano-convex lens μ = 3 2 has a radius of curvature R = 15 c m and is placed at a distance z from a concave lens of focal length 20 cm as shown. At what distance x 0 should a point object be placed from the plano-convex lens, so that position of the final image is independent of z ?

TestHub · 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.
$∴ \frac{1}{x_{0}} = \frac{1}{f_{1}} = (μ - 1) [\frac{1}{R_{1}} - \frac{1}{R_{2}}] = (\frac{3}{2} - 1) [\frac{1}{15} - \frac{1}{\infty}]$
$\Rightarrow x_{0} = 30 c m$

Physics - Geometrical Optics Question with Solution | TestHub

Options:

Doubts & Discussion