Explain how to get a new wavefront in time $\pi $ using Huygen's principle for plane wavefront.

The geometric figure of the plane wavefront propagates to the right at time $t=0$ is shown in figure and after $t=\tau$ time wavefront $\mathrm{G}_{1} \mathrm{G}_{2}$ is shown in forward direction.

Here if the wave velocity is $v$ then the distance covered by the wave in time $\tau$ is $v \tau$.

According to Huygen's principle all particle like $A_{1}, B_{1}, C_{1}, D_{1}, \ldots$ of $F_{1} F_{2}$ acts as independent secondary source and emits by itself secondary spherical waves having radius $v \tau$.

After time interval $\tau$, the surface tangential to all such secondary wavelets gives the position and shape of new wavefront shown as $\mathrm{G}_{1} \mathrm{G}_{2}$.

Thus, a new wave is now form from the wavefront at time $\tau$ and the wave propagates forward and forward in the medium.

Lines $A_{1} A_{2}, B_{1} B_{2}, C_{1} C_{2}, D_{1} D_{2}, \ldots$, etc. are perpendicular to both wavefront $F_{1} F_{2}$ and $G_{1} G_{2}$ which is known as light ray.

Line perpendicular to the wavefront and indicating the direction of propagation of the wave is called ray.

The most important point of the Huygen's wave theory is that it can be applied to all types of spherical or plane waves.