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

State Huygens's principle of wave theory? Using this principle derive the law of reflection or refraction. Which quantity remains unchangedwhen a light wave suffers reflection of refraction?

Accepted Answer

Huygens proposed that every point that a luminous disturbance meets turns into a source of the spherical wave itself. The sum of the secondary waves, which are the result of the disturbance, determines what form the new wave will take.

Proof of the law of refraction on the basis of Huyen's theory:

Consider a plane wavefront $AB$ incident on a plane surface $XY$ , separating two media $1$ and a denser medium $2$ , Let $v_{1} & v_{2}$ be the velocities of light in the two media respectively $v_{1} > v_{2}$ .

The wave front first strikes at $A$ and then the successive points towards $C$ . According to Huygens' principle from each point of the wavefront $AC$ , the secondary wavelets will start travelling in the second medium with speed $v_{2}$ . Let the disturbance take time $t$ to travel from $B to C$ ,

So that we have $BC = v_{1} t$ ..................................................(1)

During the time, the disturbance from $B$ reaches the point $C$ , the secondary wavelets from point $A$ spreads over a hemisphere of radius $AD = v_{2} t$ in the second medium.

The tangent plane $CD$ drawn from point $C$ over this hemisphere of radius $v_{2} t$ will be the new refracted wave front.Let the angles of incidence and refraction be $i and r$ respectively,

From right angle triangle, ∆ABC, we get.

$\sin (∠ ABC) = \sin (i) = BC / AC$ .

From right angle triangle, $△ADC$ , we get,

$\sin (∠ DCA) = \sin (r) = AD / AC$

Therefore,

$\frac{\sin (i)}{\sin (r)} = \frac{BC}{AD} = \frac{v_{1} t}{v_{2} t} = \frac{v_{1}}{v_{2}} = {}_{1}μ_{2}$

This constant is called the refractive index of the second medium with respect first medium.

This proved Snell's Law of refraction.

The frequency of the wave is the quantity which remains unchanged when light suffers refraction or reflection

State Huygens's principle of wave theory? Using this principle derive the law of reflection or refraction. Which quantity remains unchangedwhen a light wave suffers reflection of refraction?

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