A monochromatic light wave is travelling in vacuum along the direction $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$. The wavefront of the light wave is represented by:

x + y = constant

The correct answer is Option (4) → x + y = constant

The direction of propagation of light wave is -

$\vec K=\frac{1}{\sqrt{2}}(\hat i+\hat j)$

The equation of a plane is -

$\vec r.\vec n$ = constant

where,

$\vec r = x\hat i+y\hat j+z\hat k$

$\vec n = \hat k=\frac{1}{\sqrt{2}}(\hat i+\hat j)$

$∴\frac{1}{\sqrt{2}}x+\frac{1}{\sqrt{2}}y$ = constant

⇒ x + y = constant