Question

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 \(\vec{A}=4\sqrt{3i}-3\sqrt{3j}-5\hat{k},\) 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.

Answer 1

Correct answer is 15

\(\vec{A}=4\sqrt{3i}-3\sqrt{3j}-5\hat{k}\)

As incident vector A makes i angle with normal z-axis & refracted vector R makes r angle with normal z – axis with help of direction cosine

Difference between i& r = 60 – 45 = 15