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4. (a) A laser that emits a diffraction-limited beam (λ0 = 632.84 nm), produces a light spot on the surface of the Moon a distance of 376000 km away. How big is the circular aperture of the laser, if the light spot has a radius of 58 km? Neglect any effects of the Earth's atmosphere.
(b) Consider a ruby crystal with two energy levels separated by an energy difference corresponding to a free-space wavelength λ0 = 694.3 nm, with a Lorentzian lineshape of width ∆ν = 330 GHz. The spontaneous lifetime it tsp = 3 ms and the refractive index of ruby is n = 1.76. What value should the population difference N2 − N1 assume to achieve a gain coeffcient γ(ν0) = 0.5 cm−1 at the central frequency? [8]
(c) How long should the crystal be to provide an overall gain of 10 at the central frequency when γ(ν0) = 0.5 cm−¹?

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