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A parallel cylindrical beam of light enters a medium whose refractive index depends on intensity as mu(I) = mu0 + mu2 * I, where mu0 and mu2 are positive constants and I is the beam intensity that decreases with increasing radius from the axis. As the beam enters this medium, it will:

1. travel as a cylindrical beam
2. diverge
3. converge
4. diverge near the axis and converge near the periphery

Correct answer: converge

Solution

Since intensity I decreases with radius, mu(I) = mu0 + mu2*I is largest at the beam axis (r = 0) and smallest at the periphery. A medium with higher refractive index at the centre acts like a converging lens. Rays from the periphery experience a refractive index gradient pointing inward (toward the axis), so they bend toward the axis. Therefore the beam converges.

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