The X−Y plane be taken as the boundary between two transparent media M1 and M2. M1 in Z≥0 has a refractive index of 2 and M2 with Z<0 has a refractive index of 3. A ray of light travelling in M1 along the direction given by the vector A=43i−33j−5k^, is incident on the plane of separation. The value of difference between the angle of incident in M1 and the angle of refraction in M2 will be _____ degree.
Held on 29 Jul 2022 · Verified 6 Jul 2026.
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When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is $\_\_\_\_$. $\left(\tan ^{-1}(1.52)=57.7^{\circ}\right.$, refractive indices of air and glass are 1.00 and 1.52, respectively.)
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Light ray incident along a vector $\vec{AO}$ $(\vec{AO} = 2\hat{i}-3\hat{j})$ emerges out along vector $\vec{OB}$ $(\vec{OB} = C\hat{i}-4\hat{j})$ as shown in the figure below. The value of $C$ is ________. 
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