Three rays of light, namely red $(R)$, green $(G)$ and blue $(B)$ are incident on the face $PQ$ of a right angled prism $PQR$ as shown in figure.
The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face $PR$ is:
Answer: (B) red
The rays enter $PQ$ normally and strike $PR$ at an angle of incidence of $45^\circ$ (isosceles right-angled prism). A ray emerges only if $45^\circ$ is less than the critical angle, i.e. $\sin45^\circ < \dfrac1n$, or $n < \sqrt2 \approx 1.414$.
Red: $n = 1.27 < 1.414$, emerges. Green ($1.42$) and blue ($1.49$) are totally internally reflected. Only red emerges from $PR$.
Solution by Sreeraj P, M.Sc Physics