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

The correct option is A $\frac{2h}{({\mu }^2-1{)}^{1/2}}$

The figure shows incidence from water at a 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 $=2htan{\theta }_c,d=\frac{2h}{({\mu }^2-1{)}^{1/2}}$