Question

A point source of light is placed at a depth of h below the surface of water of refractive index $\mu$. A floating opaque disc is placed on the surface of water so that light from the source is not visible from the surface. The minimum diameter of the disc is

• A. $\frac{2h}{{({\mu }^2-1)}^{1/2}}$
• B. $2h{({\mu }^2-1)}^{1/2}$
• C. $\frac{h}{{2({\mu }^2-1)}^{1/2}}$
• D. $h{({\mu }^2-1)}^{1/2}$

Answer 1

Answer: (A)

$\frac{2h}{{({\mu }^2-1)}^{1/2}}$

The figure shows incidence from water at critical angle ${\theta }_c$ for the limiting case.

Now, $\sin {\theta }_c=\frac{1}{\mu }$

So that $\tan {\theta }_c=\frac{1}{({\mu }^2-1{)}^{1/2}}$

From figure, $\tan {\theta }_c=\frac{r}{h}$

Where $r$ is the radius of the disc.

Diameter of the disc $2r=2h\tan {\theta }_c=\frac{2h}{({\mu }^2-1{)}^{1/2}}$