Question

A bulb is placed at a depth of $2\sqrt{7}m$ in water and a floating opaque disc is placed over the bulb so that the bulb is not visible from the surface. The radius of the disc should be at least $({\mu }_{water}=4/3)$ (Note, centre of disc is on the vertical line above the bulb) :

• A. $42m$
• B. $6m$
• C. $2\sqrt{21}m$
• D. $12m$

Answer 1

The correct option is C $2\sqrt{21}m$

Light should get internally reflected from the periphery.
For total internal reflection $\sin \theta =\frac{1}{\mu }$
$\frac{R}{\sqrt{R^2+(2\sqrt{7}{)}^2}}=\frac{1}{\frac{4}{3}}=\frac{3}{4}$
$⟹\frac{R^2}{R^2+28}=\frac{3}{4}$
$4R^2=3R^2+84$
$R^2=84$
$R=2\sqrt{21}$