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Question

Using Huygen's principle for refraction of a plane wave, arrive at Snell's law of refraction.

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Solution

Let XY represent the surface separating the medium I and medium II.
Let v1 and v2 be the speed of light in medium I and medium II respectively.
Consider a plane wave front AB incident in medium I at angle i.
Let the secondary wavelet from A will travel a distance v2t as radius draw an arc in the medium II in the same time t. Therefore with A as centre and v2t as radius draw an arc in the medium II. The tangent from C touches the arc at D.
Let r be the angle of refraction
From leABC,sini=BCAC=v1tAC
leACD,sinr=ADAC=v2tAC
sinisinr=v1tAC×ACv2t=v1v2
If c represents the speed of light in vacuum then,
n1=cv1 and n2=cv2
n2n1=cv2×cv1c=v1v2
sinisinr=n2n1
n1sini=n2sinr
This is the Snell's law of refraction

874561_946900_ans_d78e443216c94d988533f8eb2940857f.png

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