Laws of Refraction (Snell's Law ) on the basis of Huygen’s Wave Theory

I

The velocity of light changes when passes from one medium to another. This bending of light wave when it enters into other medium is called Refraction.

As per the diagram shown below consider a plane wave front AB which is incident on the surface. Let v1 and v2 be the velocities of the incident ray and refracted ray of medium 1 and medium 2 respectively (v1>v2).The velocity of the waves depends upon the medium. From Huygens’s principle A and C forms the source of secondary spherical wavelets. Let t be the time taken from B to reach C.

So BC = v1t in medium 1

To determine the shape of the refracted wavefront, we draw a sphere of radius v2t from the point A in the second medium. It denotes the secondary spherical wavefront at time t.

AD = v2t in medium 2.

Now CD is the tangent drawn from point C to the sphere. Thus AD and CD are the refracted wavefronts.

Now consider ΔABC and ΔADC

Sin i / Sin r = (BC/AC) / (AD/AC)

= BC/AD

= v1t/v2t

= v1/v2

= µ which is a constant. µ is the reflective index of the medium.

Refractive Index is the ratio of velocity of light in vacuum to the velocity of light in other medium.

Hence Snell’s Law of refraction is proved using Huygens’s principle. Also the incident wavefront, the refracted wavefront and the normal lie in the same plane.

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