JEE Main 2025 Apr 2 Shift 1, Physics Q1: Electromagnetic Waves

The direction of wave propagation is the normal to the wave front. For the family of planes $x+y+z=c$, the normal vector is $(1,1,1)$.

By symmetry, this direction makes equal angles with all three coordinate axes:

$$\cos \alpha =\cos \beta =\cos \gamma$$

The direction cosines obey the identity:

$${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$$

$$3{\cos }^2\alpha =1\Rightarrow \cos \alpha =\frac{1}{\sqrt{3}}$$

$\therefore$ $\alpha ={\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$. Option (1) is correct.