•• In three of the Apollo lunar experiments, astronauts left reflector panels on the moon so that laser beams from the earth could be reflected off the panels and back to earth. Lasers with λ = 532 nm send pulses of 0.3 J to the moon, and the round-trip time is measured within δt ≈ 0.4 ns. In this way the one-way distance to the reflector on the moon is determined regularly within δl = c δt/2 ≈ 6 cm. The beams from the lasers have a diameter of 5 km on the moon. (This is the result of spreading due to diffraction and to atmospheric turbulence.) The reflector panels contain 300 mirrors, each of diameter 4 cm. (a) Find the number of photons sent from the earth in a single pulse, (b) Find the fraction of these photons that strike any one of the small mirrors (c) Find the angular divergence δθ ≈ λ/d of the reflected beam from this mirror (where d is the mirror’s diameter), (d) What is the diameter of the reflected beam when it returns to earth? (e) The return light is measured by a photomultiplier at the focus of a telescope. What fraction of the return light is captured by the telescope, whose diameter is 1 m? (f) For a single pulse, find the total number of photons captured by the telescope from all 300 mirrors. (The actual number is somewhat smaller becausc of losses in the atmosphere and in the telescope.) This experiment monitors the moon’s orbit within a few centimeters (compared to the earth–moon distance of 4 × 108 m), allowing stringent tests of competing theories of gravity.
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