Which of the following processes play a part in the formation of a rainbow? (i) Refraction (ii) Total internal reflection (iii) Dispersion (iv) Interference

When white sunlight enters a spherical raindrop, three distinct optical processes occur successively.

1. Refraction
  • The ray first passes from air into water. Because water has a higher refractive index than air, the ray bends towards the normal.
  • Snell’s law $$n_1\sin\theta_1 = n_2\sin\theta_2$$ governs this bending.
  • Refraction is therefore an essential step in rainbow formation.

2. Dispersion
  • The refractive index of water depends on wavelength: $$n_{violet} \gt n_{red}$$.
  • Consequently, different colours deviate by different angles at the first refraction. This spreads white light into its constituent spectrum, producing separate colour bands.

3. Total internal reflection (TIR)
  • After the first refraction, the ray strikes the inner surface of the drop at an angle larger than the critical angle for the water-air interface.
  • Hence it undergoes total internal reflection and stays within the drop, redirecting toward the front side.

4. Second refraction (exit of the drop)
  • The ray finally exits the drop, undergoing a second refraction from water back to air, which further separates the colours.

5. Interference is NOT involved
  • Interference requires a fixed phase relationship between two or more coherent waves (e.g., soap films, Newton’s rings).
  • Rainbow colours arise solely from geometric optics—different deviation angles for different wavelengths—not from constructive or destructive interference.

Thus, the optical phenomena that contribute to the formation of a rainbow are refraction, dispersion, and total internal reflection. Interference does not play any role.

Hence the correct set is (i), (ii) and (iii).

Option A which is: (i), (ii) and (iii)