A monochromatic light wave is travelling in vacuum along the direction \( \displaystyle\frac{1}{\sqrt{2}}(\hat{\imath} + \hat{\jmath}) \). The wavefront of the light wave is represented by:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( x + y = \) constant
A wavefront is a surface of constant phase, and it is perpendicular to the direction of propagation. For a plane wave travelling along the unit vector \( \hat{n} \), the wavefronts are the planes \( \hat{n}\cdot\vec{r} = \) constant.
\( \displaystyle \hat{n}\cdot\vec{r} = \frac{1}{\sqrt{2}}(\hat{\imath} + \hat{\jmath})\cdot(x\hat{\imath} + y\hat{\jmath} + z\hat{k}) = \frac{x + y}{\sqrt{2}} \)
Setting this equal to a constant gives \( x + y = \) constant.
Option (4) \( x + y = \) constant — Correct. The normal to these planes is along \( \hat{\imath} + \hat{\jmath} \), the direction of propagation.
NCERT (2026-27):
Huygens Principle – “… Such a locus of points, which oscillate in phase is called a wavefront; thus a wavefront is defined as a surface of constant phase. The speed with which the wavefront moves outwards from the source is called the speed of the wave. The energy of the wave travels in a direction perpendicular to the wavefront.”