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Question
The wavefronts of a light wave travelling in vacuum are given by x + y + z = c. The angle made by the direction of propagation of light with the X-axis is _________ .
Options
0°
45°
90°
\[\cos^{- 1} \left( 1/\sqrt{3} \right)\]
Solution
\[\cos^{- 1} \left( 1/\sqrt{3} \right)\]
On writing the given equation in the plane equation form lx + my + nz = p,
where l2 + m2 + n2 = 1 and p>0, we get
\[\frac{1}{\sqrt{3}}x + \frac{1}{\sqrt{3}}y + \frac{1}{\sqrt{3}}z = \frac{c}{\sqrt{3}}\]
If \[\theta\] is the angle between the normal and +X axis, then
\[\cos\theta = \frac{1}{\sqrt{3}}\]
\[ \Rightarrow \theta = \cos^{- 1} \left( \frac{1}{\sqrt{3}} \right)\]
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