Question

A right angled prism $({45}^o-{90}^o-{45}^o)$ of refractive index $n$ has a plate of refractive index $n_1(n_1<n)$ cemented to its diagonal face.
The assembly is in air. A ray is incident on $AB$.
(a) Calculate the angle of incidence at $AB$ for which the ray strikes the diagonal face at the critical angle.
(b) Assuming $n=1.352$, calculate the angle of incident at $AB$ for which the refracted ray passes through the diagonal face undeviated.

Answer 1

(a) If the ray strikes the diagonal face at the critical angle
$\therefore n\sin C=n_1\sin {90}^o$
$C={\sin }^{-1}\left(\frac{n_1}{n}\right)$
and $\angle r={45}^o-C$
For face $AB1\sin i=n\sin r$
$\therefore i={\sin }^{-1}\left[n\sin ({45}^o-{\sin }^{-1}\left(n_1/n_2\right))\right]$
(b) If the ray passes through the diagonal face un deviated
$\therefore r={45}^o$
$\therefore i\sin i=n.\sin {45}^o$
$i={\sin }^{-1}\left(\frac{1.352}{\sqrt{2}}\right)={72.9}^o$.