Question

A plane wavefront is incident on a water surface at an angle of incidence $60^\circ$ then it gets refracted at $45^\circ$. The ratio of width of incident wavefront to that of refracted wavefront will be
$\left[\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}, \; \sin 60^\circ = \frac{\sqrt{3}}{2}, \; \cos 60^\circ = \frac{1}{2}\right]$

• A. $\dfrac{\sqrt{3}}{2}$
• B. $2\sqrt{3}$
• C. $\dfrac{1}{\sqrt{2}}$
• D. $\sqrt{2}$

Hint:

Wavefront width changes with refraction due to change in direction of propagation.

Answer 1

The Correct Option is C

Step 1: Relation between wavefront width and angle.
Width of wavefront is proportional to the cosine of the angle it makes with the interface.

Step 2: Write ratio expression.
\[ \frac{\text{Width of incident wavefront}}{\text{Width of refracted wavefront}} = \frac{\cos i}{\cos r} \]

Step 3: Substitute given values.
\[ \frac{\cos 60^\circ}{\cos 45^\circ} = \frac{\frac{1}{2}}{\frac{1}{\sqrt{2}}} = \frac{1}{\sqrt{2}} \]

Step 4: Conclusion.
The required ratio is $\dfrac{1}{\sqrt{2}}$.