Arrange the speed of light in ascending order for the following cases of media wherein for the same angle of incidence, the angle of refraction in them are as given below:
(A) 22.5°
(B) 60°
(C) 45°
(D) 30°
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (D), (C), (B)
By Snell's law, for light entering each medium from the same first medium at the same angle i,
\( \displaystyle \frac{\sin i}{\sin r} = \frac{v_1}{v_2} \)
With i and \( v_1 \) fixed, \( v_2 \propto \sin r \). So the smaller the angle of refraction, the slower the light in that medium.
\( \text{(A)}: \sin 22.5^\circ \approx 0.38 \)
\( \text{(D)}: \sin 30^\circ = 0.50 \)
\( \text{(C)}: \sin 45^\circ \approx 0.71 \)
\( \text{(B)}: \sin 60^\circ \approx 0.87 \)
Ascending order of speed: (A), (D), (C), (B).
Shortcut: Since sin r increases with r between 0° and 90°, simply arrange the angles in ascending order: 22.5°, 30°, 45°, 60°.