Wave Optics

JEE Main level, single correct, medium

5 of 191

Question 5 of 191

A light wave is propagating with plane wave fronts of the type x+y+z=x+y+z= constant. The angle made by the direction of wave propagation with the xx-axis is:

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Answer: (A) cos⁡−1(13)\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)

The direction of propagation of light is perpendicular to the wave front and is symmetric about x,y\mathrm{x}, \mathrm{y} and z axis.
∴\therefore Angle made by the light with x,y&z\mathrm{x}, \mathrm{y} \& \mathrm{z} axis is same.
∴cos⁡α=cos⁡β=cos⁡γ(α,β&γ\therefore \quad \cos \alpha=\cos \beta=\cos \gamma(\alpha, \beta \& \gamma are angle made by light with x,y&z\mathrm{x}, \mathrm{y} \& \mathrm{z} axis respectively)
Also cos⁡2α+cos⁡2β+cos⁡2γ=1\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1 [Sum of direction cosines]
∴α=cos⁡−113\therefore \alpha=\cos ^{-1} \frac{1}{\sqrt{3}}

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