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

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Accepted Answer

Correct answer: B. (b) The light wave is propagating with plane wave fronts described by the equation x+y+z= constant. The wave propagates in a direction perpendicular to these wave fronts. This direction is symmetric with respect to the x ,y, and z axes. Since the wave is symmetric about these axes, the angle it makes with each axis is the same. Let these angles be , , and , which are the angles made by the light with the x ,y, and z axes, respectively. This implies: cos ⁡ = cos ⁡ = cos ⁡ According to the sum of the squares of the direction cosines: cos^2 ⁡ + cos^2 ⁡ + cos^2 ⁡ =1 Substituting the equality of direction cosines, we get: 3 cos^2 ⁡ =1 cos^2 ⁡ = 13 Thus, the angle is given by: = cos^-1 ⁡ ( 1 3 )

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

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