Question

A thick plane-convex lens made of crown glass (refractive index 1.5) has thickness of 3 cm at its centre. The radius of curvature of the spherical surface is 5 cm.

An link mark made at the centre of its plane face, when viewed normal through the curved face, appears to be at a distance x from the curved face. Then, x is equal to 

A. 2cm B. 2.1cm C. 2.3cm D. 2.5cm

Answer 1

Given: 

Radius of curvature, R=-5 cm 

Object distance, u=-3 cm 

The refractive indices n₁=1.5 (glass), n₂=1.0(air)

We have, \(\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\) (The Lensmaker's formula)

\(\frac{1}{v}-\frac{1.5}{-3}=\frac{1-1.5}{-5}\)

\(\frac{1}{v}-\frac{0.5}{5}=\frac{1.5}{3}=-\frac{2}{5}\)

v = -2.5 cm

Then the image will appear at distance of 2.5 cm from the plane surface of the mirror 

Hence D is the correct option.