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Snell's law with the ray directions given as vectors

This type of question, asked 2 times: 29 Jul 2022, 8 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    29 Jul 2022

    29
    The X-Y plane be taken as the boundary between two transparent media M1M_{1} and M2.M1M_{2}.M_{1} in Z≥0Z \geq 0 has a refractive index of 2\sqrt{2} and M2M_{2} with Z<0Z < 0 has a refractive index of 3\sqrt{3}. A ray of light travelling in M1M_{1} along the direction given by the vector A→=43i^−33j^−5k^\overrightarrow{A}= 4\sqrt{3}\widehat{i}- 3\sqrt{3}\widehat{j}- 5\widehat{k}, is incident on the plane of separation. The value of difference between the angle of incident in M1M_{1} and the angle of refraction in M2M_{2} will be_____ degree.

  2. Question 2

    8 Apr 2026 S2

    17
    Light ray incident along a vector AO→(AO→=2i^−3j^)\overrightarrow{AO}(\overrightarrow{AO}= 2\widehat{i}- 3\widehat{j}) emerges out along vector OB→(OB→=Ci^−4j^)\overrightarrow{OB}(\overrightarrow{OB}= C\widehat{i}- 4\widehat{j}) as shown in the figure below. The value of C is ____\_\_\_\_ .

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