Question

Three rays (R, G, B) are incident on PQ... Refractive indices are 1.27, 1.42 and 1.49. The colour of the ray(s) emerging out of the face PR is: 

• A. blue and green
• B. blue
• C. green
• D. red

Hint:

The higher the refractive index, the lower the critical angle, making TIR more likely for Blue/Violet light than for Red light.

Answer 1

The Correct Option is D

Step 1: At face PR, the angle of incidence \(i\) is 45°.
Step 2: Total Internal Reflection (TIR) occurs if \(i>\theta_c\), which means \(\sin i>\sin \theta_c \implies \sin 45^\circ>\frac{1}{\mu} \implies \frac{1}{\sqrt{2}}>\frac{1}{\mu} \implies \mu>\sqrt{2} \approx 1.414\).
Step 3: Compare given \(\mu\) values with 1.414:
Blue (\(\mu = 1.49\)): \(1.49>1.414\) \(\rightarrow\) TIR occurs (Does not emerge).
Green (\(\mu = 1.42\)): \(1.42>1.414\) \(\rightarrow\) TIR occurs (Does not emerge).
Red (\(\mu = 1.27\)): \(1.27<1.414\) \(\rightarrow\) No TIR.

Step 4: Only the red ray refracts and emerges from face PR.