A monochromatic light wave with wavelength λ₁ and frequency ν₁ 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 λ₂ and frequency ν₂ of the refracted wave are: (a) λ₂ = λ₁, ν₂ = 1/√(2)ν₁ (b) λ₂ = λ₁, ν₂ = √(2)ν₁ (c) λ₂ = √(2)λ₁, ν₂ = ν₁ (d) λ₂ = 1/√(2)λ₁, ν₂ = ν₁

Answer: (d). μ = (sin 45°)/(sin 30°) = √(2). Frequency does not change on refraction: ν₂ = ν₁. λ₂ = (λ₁)/(μ) = (λ₁)/(√(2)). So the answer is (d).

A monochromatic light wave with wavelength λ₁ and frequency ν₁ in air… | JEE Main 2023 (6 Apr, Shift 1)

Q34JEE Main 2023 · 6 APR · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

A monochromatic light wave with wavelength $\lambda_1$ and frequency $\nu_1$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^\circ$ and $30^\circ$ respectively, then the wavelength $\lambda_2$ and frequency $\nu_2$ of the refracted wave are:

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Answer: (d)

$\mu = \dfrac{\sin 45^\circ}{\sin 30^\circ} = \sqrt{2}$ .
Frequency does not change on refraction: $\nu_2 = \nu_1$ .
$\lambda_2 = \dfrac{\lambda_1}{\mu} = \dfrac{\lambda_1}{\sqrt{2}}$ .
So the answer is (d).

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Refraction, Glass Slab & Apparent Depth question from JEE Main 2023 (6 Apr, Shift 1)

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