Question

The x-y plane is the boundary between two transparent media. Medium 1 with z $\geq$ 0 has a refractive index $\sqrt{2}$ and medium 2 with z < 0 has refractive index $\sqrt{3}$. A ray of light in medium 1, given by vector $\vec{A}= 6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the plane of separation. Find the unit vector in the direction of the refracted ray in medium 2.

Answer 1

Answer:

Explanation:

Refractive index of medium one = √2

Refractive index of medium two = √3

μ1 sinθ1 = μ2 sinθ2

cosθ1 = 10/√ (6√3)² + (8√3)² + 100

= 10/ √400

= 10/20

= 1/2

= cosθ1 = 1/2

θ1 = 60°

√2 sin60° = √3 sinθ2

√(2 x 3)/2 = √3 sinθ2

sinθ2 = 1/√2

θ2 = 45°

Thus, the unit vector in the direction of the refracted ray in medium two is 45°.