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:

\(\Rightarrow\) Each incident ray will make an angle of \(45^{\circ}\) with the normal at face \(PR\).

\(\Rightarrow\) The wavelength corresponding to which the incidence angle is less than the critical angle, will pass through \(PR\). \(\Rightarrow \theta_{ C }=\) critical angle

\(\Rightarrow \theta_{c}=\sin ^{-1}\left(\frac{1}{\mu}\right)\)

\(\Rightarrow\) If \(\theta_{ C } \geq 45^{\circ}\)

the light ray will pass

\(\Rightarrow\left(\theta_{ C }\right)_{ Red }=\sin ^{-1}\left(\frac{1}{1.27}\right)=51.94^{\circ}\)

Red will pass.

\(\Rightarrow\left(\theta_{ C }\right)_{ Green }=\sin ^{-1}\left(\frac{1}{1.42}\right)=44.76^{\circ}\)

Green will not pass

\(\Rightarrow\left(\theta_{ C }\right)_{ Blue }=\sin ^{-1}\left(\frac{1}{1.49}\right)=42.15^{\circ}\)

Blue will not pass

\(\Rightarrow\) So only red will pass through \(PR.\)