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=sini=BCAC=v1tAC
and in ΔACE=sinr=AEAC=v2tAC ∴sinisinrBCAE=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 sinisinr=μ2μ1 μ1sini=μ2sinr It is known as Snell's law.