# Define the term wavefront. Using Huygen's wave theory, verify the law of reflection.

A surface of constant phase is termed as a wavefront.

Let us consider a plane wave AB be incident on a reflecting surface and MN at an angle of incidence (i). Let $\tau$ be the time taken by the wavefront to advance from B to C. Let v be the speed of the wave. Then,

$BC\; = v\tau$

Now, to draw the reflected wavefront. Let's draw a sphere of the radius centred at A. Now, In accordance with Huygen's principle, the tangent plane to this sphere passing through point c will give the refracted wavefront.

Remember that,

$\angle BAC = i \; \; and\; \; \angle ACE = r$

Let us consider the triangles EAC and BAC,

$\because \angle AEC = \angle CBA$

$AE=BC=V\tau$

$AC = AC$

So, by RHS, $\Delta EAC\; \cong \Delta BCA$

Thus, $i = r$

Hence, the angle of reflection and angle of incidence are equal, by Huygen's wave theory.

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