You are given four sources of light each one providing a light of a single colour – red, blue, green and yellow. Suppose the angle of refraction for a beam of yellow light corresponding to a particular angle of incidence at the interface of two media is 90°. Which of the following statements is correct if the source of yellow light is replaced with that of other lights without changing the angle of incidence?
The light is clearly bent away from the normal. Hence, we are moving from optically denser medium to optically lighter medium. Let the light move from medium 1 to medium 2. Let the refractive index of 1 with respect to 2 be n.
By Snell’s law,
where θi is the angle of incidence and θr is the angle of refraction. The θi at which θr = 90° is known as the critical angle. Substitute θi = θc and θr = 90°,
If the angle of incidence larger than critical angle, there is no refraction but only reflection. This is known as total internal reflection.
Option (a):
‘n’ is larger for yellow than for red. Hence, the critical angle for red is larger. Thus, there is no way that red light will go through total internal reflection at the critical angle for yellow.
Option (b):
We have established that the first medium is optically denser that the first medium. Hence, light always bends away from the normal.
Option (c):
‘n’ for blue is more than that for yellow. Hence, the critical angle for blue is less than that for yellow. Hence, blue will go total internal reflection if it is incident at an angle equal to the critical angle for yellow. Hence, (c) is correct.
Option (d):
‘n’ for green is more than that for yellow. Hence, the critical angle for green is less than that for yellow. Hence, blue will go total internal reflection if it is incident at an angle equal to the critical angle for yellow. Hence, (d) is incorrect.