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Question

Use Huygens' Principle to show how a plane wave front propagates from a denser to rarer medium. Hence, verify Snell's law of refraction.

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Solution

We assume a plane wave front AB propagating in denser medium incident on the interface PP at angle i as shown in
Fig.
Let T be the time taken by the wave front to travel a distance BC. If vi is the speed of the light in medium I.
So, BC=v1T

In order to find the shape of the refracted wave front, we draw a sphere of radius AE=v2T , where v2 is the speed of light in medium II (rarer medium).
The tangent plane CE represents the refracted wave front
In ΔABC=sin i=BCAC=v1tAC
and in ΔACE=sin r=AEAC=v2tAC
sin isin rBCAE=v1tv2t=v1v2 ...(1)
Let c be the speed of light in vacuum
So, μ1=Cv1 and μ2=Cv2
μ2μ1=v1v2 ...(2)
From equations (1) and (2), we have
sin isin r=μ2μ1
μ1 sin i=μ2 sin r
It is known as Snell's law.

1654768_1784583_ans_c5d5b9b062c343e0ab33e6f1cc64e9d5.png

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