JEE Main 2022 · 29 Jul · Shift 1 · Physics Q59

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PhysicsInteger+4 / -1Question 59 of 90

The X-Y plane be taken as the boundary between two transparent media M $_1$ and M $_2$ . M $_1$ in Z ⩾ 0 has a refractive index of $\sqrt2$ and M $_2$ with Z < 0 has a refractive index of $\sqrt3$ . A ray of light travelling in M $_1$ along the direction given by the vector $\vec P=4\sqrt3\hat i-3\sqrt3\hat j-5\hat k$ , is incident on the plane of separation. The value of difference between the angle of incident in M $_1$ and the angle of refraction in M $_2$ will be _______ degree.

Your answer

Answer and worked solution

Official answer: 15

Incidence. $|\vec P|=10$ and the normal component is 5, so $\cos i=\frac12$ , $i=60°$ .

Snell. $\sqrt2\sin60°=\sqrt3\sin r$ gives $\sin r=\frac1{\sqrt2}$ , $r=45°$ . Difference 15°.

Answer: 15

Topics:Refraction at plane surfaces Dot product

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JEE Main 2022 · 29 Jul · Shift 1, Physics question 59