Question

A uniform, horizontal beam of light is incident upon a quarter cylinder of radius R $=$ 5cm, and has a refractive index 2/$\sqrt{3}$. A patch on the table for a distance 'x' from the cylinder is unilluminated. Find the value of 'x'?

Answer 1

Since the rays are normal to first surface there is no deviation.

At second surface

$\frac{{\mu }_1}{u}+\frac{{\mu }_2}{v}=\frac{{\mu }_1-{\mu }_2}{R}\frac{\frac{2}{\sqrt{3}}}{\infty }+\frac{1}{v}=\frac{\frac{2}{\sqrt{3}}-1}{5}v=\frac{5}{\frac{2}{\sqrt{3}}-1}=32.32cm$