Question

For a given pair of transparent media, the critical angle for which colour is maximum?

• A. Red
• B. Blue
• C. Violet
• D. Green

Answer 1

The Correct Option is A

The critical angle (\(C\)) for total internal reflection is given by the relation: 

\[ \sin C = \frac{1}{\mu} \]

where \( \mu \) is the refractive index of the denser medium relative to the rarer medium.

Important: Refractive index (\(\mu\)) varies with wavelength (colour) due to dispersion. For visible light, the refractive index is highest for violet (shortest wavelength) and lowest for red (longest wavelength).

Step-by-Step Logic:

• Red light has the longest wavelength, thus the smallest refractive index (\(\mu\)).
• As refractive index decreases, the critical angle increases, because:

\[ \sin C = \frac{1}{\mu} \]

Therefore, among visible colours, red will have the smallest refractive index, and thus the maximum critical angle.

Answer 2

The critical angle \( \theta_c \) for a pair of transparent media is given by the equation: \[ \sin \theta_c = \frac{n_2}{n_1} \] where:
\( n_1 \) is the refractive index of the denser medium,
\( n_2 \) is the refractive index of the rarer medium.

The critical angle depends on the refractive index of the medium. The refractive index decreases as the wavelength of light increases. Since red light has the longest wavelength and thus the smallest refractive index among the visible spectrum, the critical angle is the largest for red light.

Therefore, the critical angle for red light is maximum.