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 refractive index of 3 . A ray of light travelling in M 1 along the direction given by the vector A → = 4 3 i - 3 3 j - 5 k ^ , is incident on the plane of separation. The value of difference between the angle of incident in M 1 and the angle of refracti

Step-by-step solution

Given: A → = 4 3 i - 3 3 j - 5 k ^ 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 A z A = cos - 1 5 ( 4 3 ) 2 + ( 3 3 ) 2 + 5 2 = cos - 1 5 10 ⇒ i = 60 ° Applying Snell's law of refraction at the interface of two media μ 1 sin i = μ 2 sin r ⇒ 2 sin 60 ° = 3 × sin r ⇒ r = 45 ° Difference between i and r = 60 ° - 45