JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Geometrical Optics

A monochromatic light wave with wavelength

λ_{1}

and frequency

v_{1}

in air enters another medium. If the angle of incidence and angle of refraction at the interface are

4 5^{\circ}

and

3 0^{\circ}

respectively, then the wavelength

λ_{2}

and frequency

v_{2}

of the refracted wave are :

Answer: (B)

Solution

Applying Snell's law at the interface:

μ_{1} sin 4 5^{\circ} = μ_{2} sin 3 0^{\circ}

\frac{μ _{1}}{μ _{2}} = \frac{sin 3 0 ^{\circ}}{sin 4 5 ^{\circ}} = \frac{1/2}{1/ 2} = \frac{1}{2}

Since

μ = c / v = c / (λ ν)

and frequency remains constant during refraction:

\frac{μ _{1}}{μ _{2}} = \frac{λ _{2}}{λ _{1}} = \frac{1}{2}

Therefore:

λ_{2} = \frac{λ _{1}}{2}

and

v_{2} = v_{1}

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Single correct option