Question

A right angles prism $({45}^o,{90}^o,{45}^o)$ of refractive index n has a plate of refractive index $(n_1<n)$ cemented to its diagonal face. The assembly is in air. A ray is incident on AB. Assuming $n=1.351$, The angle of incidence (in degrees rounded off to nearest integer) at AB is $12xx$, for which the refracted ray passes through the diagonal face undeviated. The value of $x$ is:

Answer 1

When refracted ray passes through the diagonal face undeflected, the incidence at diagonal face is perpendicular.
$r_2=0$ so $r_1+r_2={45}^o\Rightarrow r_1={45}^o$

Again, $\frac{sini}{sin{r}_1}=n\Rightarrow sini=nsin{r}_1=1.352sin{45}^o$

or $sini=1.3520020\frac{1}{\sqrt{2}}=0.956$

or $i=si{n}^{-1}\left(0.956\right)={72}^o{58}^{\prime }$