Let the x-y plane be the boundary between two transparent media. Medium 1 in z > 0 has a refractive index of $\sqrt{2}$ and medium 2 with z < 0 has a refractive index of $\sqrt{3}$ . A ray of light in medium 1 given by the vector $A = 6 \sqrt{3} \hat{i} + 8 \sqrt{3} \hat{j} - 10 \hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is

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75⁰

60⁰

30⁰

45⁰

answer is A.

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Detailed Solution

$\begin{array}{l} \bar{AB} = \bar{EB} + \bar{AE}; \bar{AE} = 6 \sqrt{3 i} + 8 \sqrt{3} j - 10 \hat{k} \\ \bar{EB} = - 10 \hat{k}; \cos i = \frac{100}{200} => i = 60^{\circ} \\ μ_{1} \sin i = μ_{2} \sin r; r = 45^{0} \end{array}$

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