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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If $n_{2} > n_{1} then r < i and w_{2} > w_{1}$

If $n_{2} > n_{1} then r < i and w_{2} < w_{1}$

If $n_{2} < n_{1} then r > i and w_{2} < w_{1}$

If $n_{2} < n_{1} then r > i and w_{2} > w_{1}$

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:

From the diagrams we can verify that
$\begin{array}{l} \frac{w_{2}}{w_{1}} = \frac{ACcos r}{ACcos i} = \frac{\cos r}{\cos i} \\ n_{2} > n_{1} \Rightarrow r < i \Rightarrow \cos r > \cos i \Rightarrow w_{2} > w_{1} \\ n_{2} < n_{1} \Rightarrow r > i \Rightarrow \cos r < \cos i \Rightarrow w_{2} < w_{1} \end{array}$