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

Answer 1

Answer: (A)

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.
$\therefore $ Diameter of the disc
$2r = 2h \,tan\,\theta_c = \frac{2h}{(\mu^2-1)^{1/2}}$