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Let the x-z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of √2 and medium 2 with z < 0 has a refractive index of √3. A ray of light in medium 1 given by the vector A = 6√3 i + 8√3 j − 10 k is incident on the plane of separation. The angle of refraction in medium 2 is:

1. 45°
2. 60°
3. 75°
4. 30°

Correct answer: 45°

Solution

With the boundary at z=0, |A| = 20 and A_z = -10 give cos(theta1) = 1/2, so theta1 = 60 deg and sin(theta1) = sqrt3/2. Snell's law sqrt2 * sqrt3/2 = sqrt3 * sin(theta2) gives sin(theta2) = 1/sqrt2, so theta2 = 45 deg.

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