transverse electromagnetic waves.

Derive the law of reflection using Huygen ' s Wave Theory.

According to Huygen ' s principle, each point of the wavefront is the source of a secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave and if we draw a common tangent to all these spheres, we obtain the new position of the wavefront at a later time. Let XY be a plane reflecting surface and AMB the incident plane wavefront. All the particles on AB will be in vibrating in phase. Let i be the angle of incidence and r the angle of reflection. In the time t , the disturbance at A reaches C , the secondary waves from the point B must travel a distance BD equal to AC . With the point B as centre and radius equal to AC a sphere is constructed. From the point C , we draw tangents CD and CD ' . Then, BD = BD ' . In ∆ BAC and ∆ BDC , BC is common, BD = AC , and ∠ BAC = ∠ BDC = 90 ° ∴ ∆ B A C ≅ ∆ B D C and ∠ ABC = ∠ BCD But ∠ ABC = i and ∠ BCD = r , i.e., i = r or the angle of incidence is equal to angle of reflection. Since AB , AD and XY are in the same plane. Therefore, the incident ray, reflected ray and normal at the point of incidence are all in the same plane. This is first law of reflection.