Chapter 46: Problem 26

Question: In June of 1985 a laser beam was fired from the air force optical station on Maui, Hawaii and reflected back from the shuttle Discovery as it sped by , $h~=~354~{\rm km}$ overhead. The diameter of the central maximum of the beam at the shuttle position was said to be $w~=~9.14~{\rm m}$ and the beam wavelength was $\lambda~=~500~{\rm nm}$. What is the effective diameter of the laser aperture at the Maui ground station.

Solution: The laser spreads due to diffraction, and we know that the angular separation between the center of the central maximum and the first minimum is roughly the same as the width of the central maximum. $a\sin\theta~=~1.22\lambda$, and so $a~=~1.22\lambda {h\over w}~=~2.36{\rm cm}$.