First slide

Diffraction of light-Wave Optics

Question

The wavefront of a light beam is given by the equation x + 2y + 3x = c (where c is arbitrary constant), then the angle made by the direction of light with the y-axis is

Moderate

A

$\cos^{- 1} \frac{1}{\sqrt{14}}$
B

$\sin^{- 1} \frac{2}{\sqrt{14}}$
C

$\cos^{- 1} \frac{2}{\sqrt{14}}$
D

$\sin^{- 1} \frac{3}{\sqrt{14}}$

Solution

$T h e d i r e c t i o n o f l i g h t b e a m i s p e r p e n d i c u l a r t o t h e p l a n e w a v e f r o n t . ∴ d i r e c t i o n o f l i g h t i s g i v e n b y n o r m a l v e c t o r \hat{n} = \frac{\hat{i} + 2 \hat{j} + 3 \hat{j}}{\sqrt{1^{2} + 2^{2} + 3^{2}}} = \frac{\hat{i} + 2 \hat{j} + 3 \hat{j}}{\sqrt{14}} H e n c e, A n g l e m a d e b y t h e \hat{n} w i t h y - a x i s i s g i v e n b y \cos β = \hat{n} . \hat{j} = (\frac{\hat{i} + 2 \hat{j} + 3 \hat{j}}{\sqrt{14}}) . (\hat{j}) = \frac{2}{\sqrt{14}}$

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