Name: Constructive and Destructive Interference of Light Waves
Uploaded: 2019-07-19
Duration: 11 min 15 s
Description: If 2 balls rolling on a surface with a certain speed approach each other, then we expect that they will collide, and their velocities get altered after the c...

Question

Prove law of refraction using Huygens' principle.

Accepted Answer

Huygens' principle, in optics, a statement that all points of a wave front of light in a vacuum or transparent medium may be regarded as new sources of wavelets that expand in every direction at a rate depending on their velocities.

A plane wave $AB$ is incident on the interface of the two media $PP'$ at an angle $i$ . The plane wave undergoes refraction and $CE$ represent the refracted wave front.

Let $PP$ be the interface of the medium $1$ and medium $2$ . The speed of the light in this medium is represented by $v_{1} and v_{2}$ If we draw a perpendicular from point ‘A’ to this ray of light, Point A, and point B will have a line joining them and this is called as wavefront and this wavefront is incident on the surface.

If ‘ $t$ ‘ represents the time taken by the wavefront from the point B to C then the distance,

$BC = v_{1} t$
So to determine the shape of the refracted wavefront, we draw a sphere of radius $V_{2} t$ from the point A in the second medium. Let $CE$ represent a tangent plane drawn from the point C on to the sphere. Then, $AE = v_{2} t$ and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we readily obtain

$\sin i = \frac{BC}{AC} = \frac{V_{1} t}{AC}$ , and

$\sin r = \frac{AE}{AC} = \frac{V_{2} t}{AC}$ .

Where’ $i$ ‘ and ‘ $r$ are the angles of incidence and refraction, respectively. Substituting the values of $v_{1} and v_{2}$ in terms of we get the Snell’s Law,

$n_{1} \sin i = n_{2} \sin r$

Prove law of refraction using Huygens' principle.

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