Question

The wave fronts of light wave traveling in vacuum are given by $x+y+z=c$ . The angle made by the light ray with the x-axis is:

• A. 0${}^{\circ }$
• B. 45${}^{\circ }$
• C. 90${}^{\circ }$
• D. $co{s}^{-1}\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $co{s}^{-1}\frac{1}{\sqrt{3}}$

Normal to the wave front is
(1,1,1)
So, angle between normal and x-axis is angle between light ray and x-axis
So, $(i+j+k).\left(i\right)=\sqrt{3}\left(1\right)cos\theta$
$cos\theta =\frac{1}{\sqrt{3}}$
$\theta =co{s}^{-1}\left(1/\sqrt{3}\right)$