# Define the term w

(First Choice)

A wavefront is a surface of constant phase.

Let a plane wave AB be incident on a reflecting surface MN at an angle of incidence . Let be the speed of the wave. Let be the time it takes by the wavefront to advance from B to C.

Then,

We want to draw the reflected wavefront. Draw a sphere of radius centred at A. Now, the tangent plane to this sphere passing through point C gives the refracted wavefront in accordance with Huygens’ principle.

Note that and

Consider triangles EAC and BAC,

By RHS,

Thus,

Hence, the angle of incidence and the angle of reflection are equal.

OR

The refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in the medium.

Let the surface PP’ separate medium 1 and medium 2. Note that medium 1 is optically denser than medium 2. Let the speed of light be and in medium 1 and medium 2 respectively. Note that .

A plane wave AB propagates and hits the interface at an angle . Let be the time taken be the wavefront to travel the distance BC.

We wish draw the refracted wavefront. With A as centre, we draw a sphere of radius . Take the surface tangent to the sphere passing through point C as the refracted wavefront. Let the surface be tangent to the sphere at E.

In ABC,

Also, in AEC,

Dividing the two equations, we get

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