A monochromatic light wave with wavelength _1 and frequency v_1 i… - Vidyadip

MCQ

A monochromatic light wave with wavelength $\lambda_1$ and frequency $v_1$ 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 $v_2$ of the refracted wave are :

A
$\lambda_2=\lambda_1, v_2=\sqrt{2} v_1$
✓
$\lambda_2=\frac{1}{\sqrt{2}} \lambda_1, v_2=v_1$
C
$\lambda_2=\sqrt{2} \lambda_1, v_2=v_1$
D
$\lambda_2=\lambda_1, v_2=\frac{1}{\sqrt{2}} v_1$

✓

Answer

Correct option: B.

$\lambda_2=\frac{1}{\sqrt{2}} \lambda_1, v_2=v_1$

b
Snell's law $\mu_1 \sin 45^{\circ}=\mu_2 \sin 30^{\circ}$

$\frac{\mu_1}{\mu_2}=\frac{1}{\sqrt{2}}$

$\Rightarrow \frac{\mu_1}{\mu_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{\sqrt{2}}$

$\Rightarrow \lambda_2=\frac{\lambda_1}{\sqrt{2}}$

Frequency doesn't change on change in medium.

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