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 √2 and M_2 with Z<0 has a…
JEE Main 2022 — Physics Optics
2022integermedium
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.
Official previous-year question
Held on 29 Jul 2022 · Verified 6 Jul 2026.
Did you get this right?
Sign in to track your attempts and accuracy.
Solution
Given: A=43i−33j−5k^
As incident vector A makes i angle with normal Z-axis and refracted vector R makes r angle with normal Z- axis.
The angle made by the incident ray with the normal is given as
i=cos−1(AAz)=cos−1((43)2+(33)2+525)
=cos−1(105)⇒i=60∘
Applying Snell's law of refraction at the interface of two media
μ1sini=μ2sinr
⇒2sin60∘=3×sinr
⇒r=45∘
Difference between i and r=60∘−45∘=15∘
Your note
Sign in to keep a private note on this question. Nothing you write is ever public.