JEE Main20236 Apr 2023Morning ShiftPhysicsRay OpticsActual
A monochromatic light wave with wavelength λ 1 and frequency ν 1 in air enters another medium. If the angle of incidence and angle of refraction at the interface are 45 ° and 30 ° respectively, then the wavelength λ 2 and frequency ν 2 of the refracted wave are:
Options
- Aλ 2 = 2 λ 1 , ν 2 = ν 1
- Bλ 2 = λ 1 , ν 2 = 1 2 ν 1
- Cλ 2 = λ 1 , ν 2 = 2 ν 1
- Dλ 2 = 1 2 λ 1 , ν 2 = ν 1
Correct answer
D. λ 2 = 1 2 λ 1 , ν 2 = ν 1
Step-by-step solution
By using Snell's law, n 1 sin θ 1 = n 2 sin θ 2 , the refractive index is μ = sin 45 ° sin 30 ° = 1 2 1 2 = 2 Also using the relation n = c v where n is the refractive index, c is the velocity of light in air and v is the velocity in the medium ⇒ c air  v   = 2 = λ 1  λ 2 The velocities are given by v = ν λ 2 c = ν λ 1 ⇒ λ 1 = 2 λ 2 and ν 1 = ν 2 . The frequency of light does not change when the medium changes.