Question

Proof of law of reflection using huygens principle

Answer 1

Answer:

Explanation:

Here we must take into account a different speed of light in the upper and lower media. If the speed of light in vacuum is c, we express the speed in the upper medium by the ratio c/ni, where ni is the refractive index. Similarly, the speed of light in the lower medium is c/nt. The points D, E and F on the incident wavefront arrive at points D, J and I of the plane interface XY at different times. In the absence of the refracting surface, the wavefront GI is formed at the instant ray DF reaches I. During the progress of ray CF from F to I in time t, however, the ray AD has entered the lower medium, where the speed is different. Thus if the distance DG is vit, a wavelet of radius vtt is constructed with center at D. The radius DM can also be expressed as

formula

Similarly, a wavelet of radius (ni/nt)JH is drawn centered at J. The new wavefront KI includes point I on the interface and is tangent to the two wavelets at points M and N. The geometric relationship between the angles thetai and thetat, formed by the representative incident ray AD and refracted ray DL, is Snell's law, which may be expressed as

                                                        formula