The Dutch physicist Christian Huygens imagined each point of a propagating disturbance as capable of originating new pulses that contributed to the disturbance an instant later. To show how his model of light propagation implied the laws of geometrical optics, he formulated a principle which says that each point on the leading surface of a wave disturbance may be regarded as a secondary source of spherical waves, which themselves progress with the speed of light in the medium and whose envelope at later times constitutes the new wavefront. Notice that the new wavefront is tangent to each wavelet at a single point. According to Huygens, the remainder of each wavelet is to be disregarded in the application of the principle. In so disregarding the effectiveness of the overlapping wavelets, Huygens avoided the possibility of diffraction of the light into the region of geometric shadow. Huygens also ignored the wavefront formed by the back half of the wavelets, since these wavefronts implied a light disturbance traveling in the opposite direction. Despite weaknesses in this model, remedied later by Fresnel and others, Huygens was able to apply his principle to prove the laws of both refection and refraction. Similarly, we can use a Huygens construction to illustrate the law of refraction.
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 interfaceXY 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
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 i and t, formed by the representative incident ray AD and refracted ray DL, is Snell's law, which may be expressed as
(6.1)