Explain the reflection of a plane wave using Huygens' principle.

(N/A) Consider a plane wave $AB$ incident at an angle $i$ on a reflecting surface $MN$.
The velocity of the wave in the medium is $v$ and $\tau$ is the time taken for the wavefront to move from point $B$ to $C$. Therefore,$BC = v \tau$.
As shown in the figure,the plane wave $AB$ is incident on the reflective surface $MN$ and its reflected wavefront is $CE$.
In the figure,$\triangle EAC$ and $\triangle BAC$ are congruent triangles.
Here,$AE = BC = v \tau$ (since the distance traveled by the wave in the same medium is the same).
$\angle AEC = \angle ABC = 90^{\circ}$.
And $AC = AC$ (common side).
Therefore,$\triangle EAC \cong \triangle BAC$ by the $RHS$ congruence criterion.
This implies $\angle BAC = \angle ECA$.
Since $\angle BAC = i$ and $\angle ECA = r$,we have $i = r$,which is the law of reflection.