Beams of Red, Green and Blue light are incident normally on a right angled prism. The refractive indices are given as \( \mu_R = 1.39 \), \( \mu_G = 1.44 \) and \( \mu_B = 1.47 \). Then the colour which emerges out of face AC will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → only Red
The beams fall normally on face AB, so they enter without bending and meet the hypotenuse AC at an angle of incidence of \( 45^\circ \) (the angle A of the prism). A ray escapes through AC only if this angle is less than the critical angle \( C \), where \( \sin C = 1/\mu \); otherwise it undergoes total internal reflection.
The condition for total internal reflection at \( 45^\circ \) is \( \sin45^\circ \gt \frac{1}{\mu} \), that is:
\( \mu \gt \frac{1}{\sin45^\circ} = \sqrt{2} = 1.414 \)
Red: \( \mu_R = 1.39 \lt 1.414 \), so \( C \approx 46^\circ \gt 45^\circ \). Red is not totally reflected and emerges through AC.
Green: \( \mu_G = 1.44 \gt 1.414 \), so \( C \approx 44^\circ \lt 45^\circ \). Green is totally reflected.
Blue: \( \mu_B = 1.47 \gt 1.414 \), so \( C \approx 43^\circ \lt 45^\circ \). Blue is totally reflected.
Only red light emerges out of face AC.