Question

How does the Huygens principle explain reflection?

Answer 1

Huygens principle:

Huygens hypothesized in $1678$ that at each location a light vibration becomes the source of a circular wave, and the sum of these secondary waves allows us to predict the shape of the wave at any given time. Huygens's wave theory does not explain why this is so, but he assumed that secondary waves only travel in the forward direction.

Huygens principle derivation:

The Huygens principle allows us to demonstrate the following laws governing light reflection:

The wavefront that makes contact with a reflecting surface $XY$ with an angle of incidence $i$ is designated as $AA\text{'}$. Using Huygens's concept, any point on $AA\text{'}$ will produce secondary wavelets.

Knows, $Time=\frac{Dis\tan ce}{Velocity}$

The time from $A\text{'}$ to $D$ is equal to the time from $B\text{'}$ to $C$.

$\frac{A\text{'}D}{v}=\frac{B\text{'}C}{v}$

$A\text{'}D=B\text{'}C$

$A\text{'}C\sin \left(i\right)=A\text{'}C\sin \left(r\right)$

So, $I=R.$

Hence, both the angle of incidence and the angle of reflection are equal. The first law of reflection also states this. Also, the second law of reflection is because the incident wavefront $AB$, the normal wavefront, and the reflected wavefront are all on the same plane.