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Light travels from medium M to medium N through a convex spherical surface. A ray from M hits the surface at point A with angle of incidence alpha1 = 30 deg and refracts into N at point B (after passing through C, the center of curvature) with angle of refraction alpha2 = 60 deg. If AC = l1 and BC = l2, find l2/l1.

1. 0
2. 1
3. 2
4. 3

Correct answer: 1

Solution

The center of curvature C lies at distance R from every point on the spherical surface. Point A is on the spherical surface, so AC = R. Since the refracted ray passes through C and B is another point of consideration, if B is also on the spherical surface, then BC = R as well. But if C is the center, all points on the surface are equidistant from C. Therefore l2/l1 = BC/AC = R/R = 1. Snell's law at A: n_M * sin(30) = n_N * sin(60), giving n_M/n_N = sin(60)/sin(30) = sqrt(3), which is consistent with the geometry. The key insight is that both A and any other point B on the spherical surface satisfy the condition distance to C = R.

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