JEE Main 2025 · 2 April · morning · Single correct · +4 / −1
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 :
- (a) cos ⁻¹(2 / 3)
- (b) cos ⁻¹(1/√3)
- (c) cos ⁻¹(1/3)
- (d) cos ⁻¹(√(2/3))
Answer and solution
Answer (b) cos ⁻¹(1/√3)
Solution
Physics sir · 3 steps
The wave travels along the normal to its wavefront, so read the normal straight off x+y+z.
- Direction of travel. A plane wave always moves perpendicular to its wavefronts. For a plane ax+by+cz= constant, the normal is along aî+bĵ+ck̂.
- Read the normal. Here a=b=c=1, so the wave travels along n⃗=î+ĵ+k̂, which has magnitude √(1²+1²+1²)=√3.
cos α = (n⃗·î)/|n⃗| = 1/√3
- So. The angle with the x-axis is cos⁻¹(1/√3), which is option (b).
The idea to keep. For a wavefront ax+by+cz= constant, the propagation direction is (a, b, c). Its direction cosines, like a/√(a²+b²+c²), give the angles with the axes.
Answer from the NTA final answer key. Solution by PrepWiser.