Question

A narrow beam of monochromatic light, PQ, is incident normally on one face of an equiangular glass prism of refractive index 1.45. When the prism is immersed in a certain liquid, the ray make a grazing emergence along the other face. Find the refractive index of this liquid.

Answer 1

$e{\mu }_g=\frac{1}{sinc}$
$\angle A={60}^o$
$\angle A+\angle ARP={90}^o$
So, $\angle ARP={30}^o$
So, $\angle C={60}^o$
$e{\mu }_g=\frac{1}{sin60}=\frac{2}{\sqrt{3}}$
$g{\mu }_e=\sqrt{3/2}=0.866$
$a{\mu }_e=a{\mu }_g\times g{\mu }_e$
$=1.45\times 0.866=1.256$