Question

A point source $S$ is placed at the bottom of a transparent block of height $10mm$ and refractive index $\mathrm{2.72.}$ It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter $11.54mm$ on top of the block. The refractive index of the liquid is

• A. $1.21$
• B. $1.30$
• C. $1.36$
• D. $1.42$

Answer 1

The correct option is C $1.36$

The disc is forming due to internal reflection when light travelling from a medium of high refractive index to a medium of low refractive index.

Radius of disc $=\frac{11.54}{2}=5.77mm$

The maximum angle at which light incidents surface is $\theta$

$\frac{{\mu }_{liquid}}{{\mu }_{block}}=\sin \theta$

$\tan \theta =0.57710$

$\theta ={30}^{\circ }$

$\sin \theta =\frac{1}{2}$

${\mu }_{liquid}=\frac{1}{2}.{\mu }_{block}$

${\mu }_{liquid}=\frac{1}{2}\times 2.72=1.36$