Question

Which colour of light has a higher critical angle, red light or green light?

Answer 1

Hint: Critical angle has significance when a light ray is travelling from denser medium to rarer medium. It determines whether a light will escape to the second medium or get reflected internally. Critical angle depends on a number of factors like refractive index and wavelength.

Complete answer:
When a ray of light travels from denser medium to a rarer medium such that the angle of refraction is a right angle, in this case the angle of incidence is called the critical angle.
It is the maximum value of angle of incidence at which refraction takes place. If the angle increases more than the critical angle, then total internal reflection takes on the boundary between the medium.
The critical angle ($$C$$) is related to refractive index as-
$$\sin C={\displaystyle \frac{1}{\mu }}$$
$$\mu$$ is the refractive index when light travels from a rarer to a denser medium.
Now, refractive index is inversely proportional to the wavelength of light used, it is also inversely proportional to the critical angle. Therefore, wavelength is directly proportional to the critical angle.
This means as wavelength increases, critical angle also increases and vice versa.
Red has a greater wavelength than green. So by above relation, the critical angle of red light will be greater than the critical angle of green light.

Therefore, Red light has a higher critical angle.

Note: Refractive index is defined as the ratio of speed of light in the air to the speed of light in a given medium. As velocity increases, refractive index decreases, so denser mediums have greater refractive indices. Also, the refractive index also depends on the temperature.