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Using a lens to couple a laser beam into a fiber optic cable

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We want to couple the energy of a metal vapor laser beam of wavelength (lambda = 628 nm) into a fiber optic cable. The beam of the laser has a cross-sectional area of 10mm^2 and all the beam has to be coupled into a diameter of 50 um (fiber core). A lens is used to couple the laser beam into the fiber.
a) What should be the ratio f/D to just couple the beam into such a small fiber?
b) Assuming the lens to be circular and knowing the laser beam to be filling the lens completely, calculate f of the lens.

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In this solution we solve two problems in optics involving a laser beam, a lens, and a fiber optic cable.

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