The wave front first strikes at and then the successive points towards . According to Huygens' principle from each point of the wavefront , the secondary wavelets will start travelling in the second medium with speed . Let the disturbance take time to travel from ,
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So that we have ..................................................(1)
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During the time, the disturbance from reaches the point , the secondary wavelets from point spreads over a hemisphere of radius in the second medium.
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The tangent plane drawn from point over this hemisphere of radius will be the new refracted wave front.Let the angles of incidence and refraction be respectively,
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From right angle triangle, ∆ABC, we get.
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.
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From right angle triangle, , we get,
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Therefore,
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This constant is called the refractive index of the second medium with respect first medium.
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This proved the Snell's Law of refraction.
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Form a wavefront in the second medium with a tangent surface or the radius of and compare the distance travelled by the light in two media.
Deduce Snell's law of refraction for a plane wave using Huygens' principle.
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On a hot summer night, the refractive index of air is the smallest near the ground and increases with a height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam,
A light beam travelling along the -axis with planar wavefront is incident on a medium of thickness, . In the region, where light is falling the refractive index can be taken to be varying such that . The light beam on the other side of the medium will emerge
Define wavefront of a travelling wave. Using Huygens principle, obtain the law of refraction at a plane interface when light passes from a denser to rarer medium.
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?