JEE Main 2011 — Optics

Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z \geq 0$ 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 $\vec{A}=6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is

Direction: The question has a paragraph followed by two statements, Statement $-1$ and statement $-2$. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane - convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement-1 : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi$. Statement-2 : The centre of the interference pattern is dark.

A car is fitted with a convex side-view mirror of focal length $20 \mathrm{~cm}$. A second car $2.8 \mathrm{~m}$ behind the first car is overtaking the first car at relative speed of $15 \mathrm{~m} / \mathrm{s}$. The speed of the image of the second car as seen in the mirror of the first one is :