Question
Explain the reflection of a plane wave using Huygen's principle.
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Answer
→Consider a plane wave AB incident at an angle $i$ on a reflecting surface MN .
→If $v$ is the speed of wave in the given medium, $\tau$ represents the time taken by the wavefront to advance from point B to C , then the distance $BC =v \tau$.
→In order to construct the reflected wavefront we draw a sphere of radius $v \tau$ from the point A as shown in fig.
→Let $C E$ represent the tangent plane drawn from the point C to this sphere.
→Obviously,
$AE = BC =v \tau$
→From fig., incident and reflected wave fronts make angle $i$ and $r$ with reflecting surface, MN respectively.
→From fig.,
AC is the common side between $\triangle AEC$ and $\triangle ABC$.
Also, $\angle AEC =\angle ABC =\frac{\pi}{2}$.
$\text { and } AE = BC =v \tau$
→So $\triangle AEC$ and $\triangle ABC$ are congruent.
→And therfore, $\angle i=\angle r$,
which is law of reflection.
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