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Q.

Which of the following statement(s) is(are) correct with respect to Huygen’s wave theory for refraction of wave at plane surface separating two media
𝑛1 = refractive index of incident medium, 𝑛2 = refractive index of refracted medium,
𝑖 = angle of incidence, 𝑟 = angle of refraction,
𝑤1 = width of incident wave front, 𝑤2 = width of refracted wave front

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a

If n2>n1 then r<i and w2<w1

b

If n2<n1 then r>i and w2<w1

c

If n2>n1 then r<i and w2>w1

d

If n2<n1 then r>i and w2>w1

answer is A, C.

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Detailed Solution

Refraction at plane surface according to Huygen ‘s principle is represented by the following diagrams:

Question Image
Question Image

From the diagrams we can verify that
w2w1=ACcos⁡rACcos⁡i=cos⁡rcos⁡in2>n1⇒r<i⇒cos⁡r>cos⁡i⇒w2>w1n2<n1⇒r>i⇒cos⁡r<cos⁡i⇒w2<w1

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Which of the following statement(s) is(are) correct with respect to Huygen’s wave theory for refraction of wave at plane surface separating two media𝑛1 = refractive index of incident medium, 𝑛2 = refractive index of refracted medium,𝑖 = angle of incidence, 𝑟 = angle of refraction,𝑤1 = width of incident wave front, 𝑤2 = width of refracted wave front