Question

Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '$1$' and '$2$' are 1.35 and 1.45 respectively. Trace the path of these rays after entering through the prism.

Answer 1

Critical angle of ray '$1$':

$sin\left(c_1\right)=\frac{1}{{\mu }_1}=\frac{1}{1.35}$

$\Rightarrow c_1=si{n}^{-1}\left(\frac{1}{1.35}\right)={47.79}^{\circ }$

Similarly, critical angle of ray '$2$':

$sin\left(c_2\right)=\frac{1}{{\mu }_2}=\frac{1}{1.45}$

$\Rightarrow c_2=si{n}^{-1}\left(\frac{1}{1.45}\right)={43.6}^{\circ }$

Ray '$1$' and '$2$' will fall on the side AC at an angle of incidence '$i$' of ${45}^{\circ }$. Critical angle of ray '$1$' is greater than '$i$', so it will get refracted from the prism. Critical angle of ray '$2$' is less than that of '$i$', so it will undergo total internal reflection.