Geometry of the prism

From the figure, the prism is a right-angled isosceles prism, so the acute angles are $45^\circ$ each.

The rays are incident normally on face $PQ$, so they enter the prism without deviation and travel horizontally inside the prism until they strike face $PR$.

Angle of incidence at face $PR$

Since face $PR$ is inclined at $45^\circ$ to the horizontal, the normal to $PR$ is also at $45^\circ$ to the horizontal.

Therefore, the angle of incidence for each ray at face $PR$ is $i = 45^\circ.$

Condition for emergence or total internal reflection

A ray will emerge from the prism if $i < C,$ where $C$ is the critical angle, given by $\sin C = \frac{1}{\mu}.$

If $i > C$, then total internal reflection occurs.

Find critical angle for each colour

(i) Red: $\mu_R = 1.27$

$\sin C_R = \frac{1}{1.27} = 0.7874$ $C_R = \sin^{-1}(0.7874) \approx 52^\circ.$

Since $45^\circ < 52^\circ,$ the red ray emerges.

(ii) Green: $\mu_G = 1.42$

$\sin C_G = \frac{1}{1.42} = 0.7042$ $C_G = \sin^{-1}(0.7042) \approx 44.8^\circ.$

Since $45^\circ > 44.8^\circ,$ the green ray undergoes total internal reflection.

(iii) Blue: $\mu_B = 1.49$

$\sin C_B = \frac{1}{1.49} = 0.6711$ $C_B = \sin^{-1}(0.6711) \approx 42.2^\circ.$

Since $45^\circ > 42.2^\circ,$ the blue ray also undergoes total internal reflection.

Conclusion

Only the red ray emerges out of face $PR$.

Hence the correct option is: $\boxed{\text{D: red}}$

Comparison with stored answer

Stored correct answer: $\boxed{\text{D}}$

My derived answer is also $\boxed{\text{D}}$, so they agree.