Explain how to obtain a new wavefront at time $\tau$ using Huygens' principle for a plane wavefront.

(N/A) The geometric representation of a plane wavefront propagating to the right at time $t=0$ is shown in the figure,and after time $t=\tau$,the new wavefront $G_{1} G_{2}$ is shown in the forward direction.
Here,if the wave velocity is $v$,then the distance covered by the wave in time $\tau$ is $v \tau$.
According to Huygens' principle,all particles like $A_{1}, B_{1}, C_{1}, D_{1}, \ldots$ on the wavefront $F_{1} F_{2}$ act as independent secondary sources and emit secondary spherical waves having a radius of $v \tau$.
After the time interval $\tau$,the surface tangential to all such secondary wavelets gives the position and shape of the new wavefront,shown as $G_{1} G_{2}$.
Thus,a new wavefront is formed at time $\tau$,and the wave propagates forward in the medium.
Lines $A_{1} A_{2}, B_{1} B_{2}, C_{1} C_{2}, D_{1} D_{2}, \ldots$ are perpendicular to both wavefronts $F_{1} F_{2}$ and $G_{1} G_{2}$,which are known as light rays.
$A$ line perpendicular to the wavefront that indicates the direction of propagation of the wave is called a ray.
The most important point of Huygens' wave theory is that it can be applied to all types of spherical or plane waves.