A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave propagation with the x-axis is: [2025]

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Q.
A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave propagation with the x-axis is: [2025]

1 $\cos^{- 1} (\frac{1}{\sqrt{3}})$

2 $\cos^{- 1} (\frac{2}{3})$

3 $\cos^{- 1} (\frac{1}{3})$

4 $\cos^{- 1} (\sqrt{\frac{2}{3}})$

Ans.
(1)

Direction of propagation $\vec{A} = \hat{i} + \hat{j} + \hat{k}$

The direction of propagation of light is perpendicular to the wave front and is symmetric about x, y and z-axis.

Direction cosine associated with x-axis,

$\cos α = (\frac{A_{x}}{\sqrt{A_{x}^{2} + A_{y}^{2} + A_{z}^{2}}})$

$\cos α = (\frac{1}{\sqrt{1 + 1 + 1}}) \Rightarrow α = \cos^{- 1} (\frac{1}{\sqrt{3}})$

Solution

Q.
A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave propagation with the x-axis is: [2025]

1 $\cos^{- 1} (\frac{1}{\sqrt{3}})$

2 $\cos^{- 1} (\frac{2}{3})$

3 $\cos^{- 1} (\frac{1}{3})$

4 $\cos^{- 1} (\sqrt{\frac{2}{3}})$

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Solution

Q. A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave propagation with the x-axis is: [2025]

1 cos–1(13)

2 cos–1(23)

3 cos–1(13)

4 cos–1(23)

Ans. (1) Direction of propagation A→=i^+j^+k^ The direction of propagation of light is perpendicular to the wave front and is symmetric about x, y and z-axis. Direction cosine associated with x-axis, cosα=(AxAx2+Ay2+Az2) cos α=(11+1+1) ⇒ α=cos–1(13)

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Q.
A light wave is propagating with plane wave fronts of the type x + y + z = constant. The angle made by the direction of wave propagation with the x-axis is: [2025]

1 $\cos^{- 1} (\frac{1}{\sqrt{3}})$

2 $\cos^{- 1} (\frac{2}{3})$

3 $\cos^{- 1} (\frac{1}{3})$

4 $\cos^{- 1} (\sqrt{\frac{2}{3}})$