Q 12-10-157JEE MainJEE Main 2025 (2 Apr, Shift 1)Easy
A light wave is propagating with plane wavefronts of the type $x + y + z = \text{constant}$. The angle made by the direction of wave propagation with the $x$-axis is:
Answer: (A) $\cos^{-1}\left(\dfrac{1}{\sqrt3}\right)$
A ray (direction of propagation) is always normal to the wavefront. The normal to the plane $x + y + z = \text{constant}$ is along $\hat i + \hat j + \hat k$.
Its direction cosines are equal: $\cos\alpha = \cos\beta = \cos\gamma$, and $\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1$, so
$$3\cos^2\alpha = 1 \Rightarrow \alpha = \cos^{-1}\left(\frac{1}{\sqrt3}\right)$$
Solution by Sreeraj P, M.Sc Physics