Using the huygens principal describe reflection of a parallel beam of light from a plane mirror and prove the laws of reflection
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Law of Reflection from Huygens' Principle
drawing
The figure illustrates Huygens' construction for a narrow, parallel beam of light to prove the law of reflection. Huygens' principle must be modified to accommodate the case in which a wavefront, such as AC, encounters a plane interface, such as XY, at an angle. Here the angle of incidence of the rays AD, BE, and CF relative to the perpendicular PD is thetai. Since points along the plane wavefront do not arrive at the interface simultaneously, allowance is made for these differences in constructing the wavelets that determine the reflected wavefront. If the interface XY were not present, the Huygens construction would produce the wavefront GI at the instance ray CF reached the interface at I. The intrusion of the reflecting surface, however, means that during the same time interval required for ray CF to progress from F to I, ray BE has progressed from E to J and then a distance equivalent to JH after reflection. Thus a wavelet of radius JH centered at J is drawn above the reflecting surface. Similarly, a wavelet of radius DG is drawn centered at D to represent the propagation after reflection of the lower part of the beam. The new wavefront, which must now be tangent to these wavelets at points M and N, and include the point I, is shown as KI in the figure. A representative reflected ray is DL, shown perpendicular to the reflected wavefront. The normal PD drawn for this ray is used to define angles of incidence and reflection for the beam. The construction clearly shows the equivalence between the angles of incidence and reflection.
