Question

What is wavefront? Explain laws of refraction of light on the bases of Huygens wave theory.

Answer 1

The locus of point on which all particle oscillate in same phase is called as wavefront.

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 $c/n_i$, where $n_i$ is the refractive index. Similarly, the speed of light in the lower medium is $c/n_t$. The points D, E and F on the incident wavefront arrive at points D, J and I of the plane interface 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 $v_{i}t$, a wavelet of radius $v_{t}t$ is constructed with center at D. The radius DM can also be expressed as

$DM=v_{t}t$

$DM=v_t(\frac{DG}{v_i})$

Similarly, a wavelet of radius $\left(ni/nt\right)JH$ 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 ${\theta }_i$ and ${\theta }_t$, formed by the representative incident ray AD and refracted ray DL, is Snell's law, which may be expressed as

$n_{i}sin{\theta }_i=n_{t}sin{\theta }_t$