Chapter 36: Q93P (page 1115)

In June 1985, a laser beam was sent out from the Air Force Optical Station on Maui, Hawaii, and reflected back from the shuttle Discovery as it sped by 354 km overhead. The diameter of the central maximum of the beam at the shuttle position was said to be 9.1 m, and the beam wavelength was 500 nm. What is the effective diameter of the laser aperture at the Maui ground station? (Hint: A laser beam spreads only because of diffraction; assume a circular exit aperture.)

Expert verified

The effective diameter of the laser aperture at the Maui ground station is 0.047 m.

Step by step solution

The given data can be listed below,

When there are a lot of waves interacting, how interference makes waves spread out after being contained by an aperture is defined by diffraction.

The ratio of central maxima the distance of shuttle from station is given by,

$\frac{D}{L} = \frac{2.44 λ}{d}$

Here, dthe diameter of laser and $λ$ is the wavelength of light.

Substitute all the values in the above, the diameter of the laser is calculated as,

$d = \frac{2.44 λ L}{D} = \frac{2.44 (500 \times 10^{- 9} m) (354 \times 10^{3} m)}{9.1 m} = 0.047 m$

Thus, the effective diameter of the laser aperture at the Maui ground station is 0.047 m.

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