Scientists use laser range-finding to measure the distance to the moon with grea

Question

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. Staying within this diameter is accomplished by using a special large-diameter laser.

Explanation / Answer

The formula for a round aperture is sin = 1.22 D

Where is the angle between the central bright part of the pattern and the dark edge of the pattern.

The distance between these points is 500 m, and we can get the angle by tan = y/ L = 500 m /3.84 × 108 m = 1.302 × 106

If we solve for D, we get D = 1.22/ = 1.22 *( 504 × 109 m )/ 1.302 × 106 = 0.472258 m = 47.22 cm

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