b
Assuming that the right angled prism is an isoceles prism, so the other angles will be \(45^{\circ}\) each.

\(\Rightarrow\) 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 \(PR.\)