A laser (wavelength ?o = 633 nm) is generating a Gaussian beam with 0.1 mm beam

Question

A laser (wavelength ?o = 633 nm) is generating a Gaussian beam with 0.1 mm beam waist (2wo). (1) Find the beams divergence angle and depth of focus (2) What will be its diameter when it reaches Moon? Earth-Moon distance = 3.5105 km. Search Lunar Ranging Project if you got interested. We DID land on moon. (3) Find the radius of curvature of the phasefront at z = 0, zo, and 2zo ? (4) What will be the intensity (in W/cm2) at the beam center (r = 0, z = 0) and a point along the axis (r = 0, z = zo)?

Explanation / Answer

Answer:- The distance to the Moon is calculated approximately using this equation: Distance = (Speed of light × Time taken for light to reflect) / 2. In actuality, the round-trip time of about 2½ seconds is affected by the relative motion of the Earth and the Moon, the rotation of the Earth, lunar libration, weather, polar motion, propagation delay through Earth's atmosphere, the motion of the observing station due to crustal motion and tides, velocity of light in various parts of air and relativistic effects.[5] Nonetheless, the Earth-Moon distance has been measured with increasing accuracy for more than 35 years. The distance continually changes for a number of reasons, but averages about 384,467 kilometers (238,897 miles). At the Moon's surface, the beam is only about 6.5 kilometers (four miles) wide[6] and scientists liken the task of aiming the beam to using a rifle to hit a moving dime 3 kilometers (approximately two miles) away. The reflected light is too weak to be seen with the human eye: out of 1017 photons aimed at the reflector, only one will be received back on Earth every few seconds, even under good conditions. They can be identified as originating from the laser because the laser is highly monochromatic. This is one of the most precise distance measurements ever made, and is equivalent in accuracy to determining the distance between Los Angeles and New York to one hundredth of an inch.[4][7] As of 2002 work is progressing on increasing the accuracy of the Earth-Moon measurements to near millimeter accuracy, though the performance of the reflectors continues to degrade with age.

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