Name: Brewster’s Law
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: Light is a transverse electromagnetic wave with electric field vectors vibrating in infinite directions perpendicular to the direction of propagation. Let's...

Question

Define wavefront and secondary wavelets. Establish the laws of reflection of light on the basis of Huygen's principle.

Accepted Answer

Wavefront: It is defined as the locus of all the particles of a medium vibrating in the same phase at a given instant.

Secondary wavelets: Every point on a wavefront is a source of new disturbance which produce secondary wavelets.

Laws of reflection on the basis of Huygen's principle:

Suppose, $M M'$ is a plane mirror on which a wave front is allowed to fall. $A B$ is the wavefront incident at an angle of incidence. Let there be three wavelets $P$ , $Q$ and $R$ of the wavefront $A B$ .

Now, according to Huygen's principle the time taken by the wavelet $P A$ to reach from $A$ to $N$ and the time taken by the wavelets $R B$ to reach $B$ to $K$ are equal.

Then, $t = \frac{A N}{v} = \frac{B K}{v}$ ....................... $(1)$

Here, $v$ is speed of light.

If it takes $t_{1}$ time for the wavelet $Q C$ to reach from $C$ to $L$ to $D$

Then, $t_{1} = \frac{C L}{v} + \frac{L D}{v}$ ....................... $(2)$

In right $△ A C L$ : $\sin i = \frac{C L}{A L} \Rightarrow C L = A L \sin i$

In right $△ L D K$ : $\sin r = \frac{L D}{L K} \Rightarrow L D = L K \sin r \Rightarrow L D = (A K - A L) \sin r$

In right $△ A N H$ : $\sin r = \frac{A N}{A K} \Rightarrow A N = A K \sin r$

Now from equation $(2)$

$t_{1} = \frac{A L \sin i}{v} + \frac{A K \sin r}{v} - \frac{A L \sin r}{v}$

$t_{1} = \frac{A L}{v} (\sin i - \sin r) + \frac{A N}{v} \Rightarrow t_{1} = \frac{A L}{v} (\sin i - \sin r) + t$

According to Huygen's principle, $t_{1} = t$

Then, $\frac{A L}{v} (\sin i - \sin r) = 0 \Rightarrow \sin i - \sin r = 0 \Rightarrow i = r$

Hence, angle of incidence is equal to angle of reflection.

Define wavefront and secondary wavelets. Establish the laws of reflection of light on the basis of Huygen's principle.

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