Scientists use laser range finding to measure the distance to the moonwith great accuracy. A very brief (100 ps) laser pulse, with a wavelengthof 532 nm, is fired at the moon, where it reflects off an array of 100 4.0-cm-diameter mirrors placed there by Apollo 14 astronauts in 1971. The reflected laser light returns to earth, where it is collected by a telescope and detected. The average earth-moon distance is 384,000 km. The laser beam spreads out on its way to the moon because of diffraction, reaching the mirrors with an intensity of 300 W/m2. The reflected beam spreads out even more on its way back because of diffraction due to the circular aperture of the mirrors.a. What is the round-trip time for the laser pulse to travel to the moon and back?b. If we want to measure the distance to the moon to an accuracy of 1.0 cm, how accurately must the arrival time of the returning pulse be measured?c. Because of the spread of the beam due to diffraction, the light arriving at earth from one of the mirrors will be spread over a circular spot. Estimate the diameter of this spot.d. What is the intensity of the laser beam when it arrives back at the earth?
Scientists use laser range finding to measure the distance to the moon
with great accuracy. A very brief (100 ps) laser pulse, with a wavelength
of 532 nm, is fired at the moon, where it reflects off an array of 100 4.0-cm-diameter mirrors placed there by Apollo 14 astronauts in 1971. The reflected laser light returns to earth, where it is collected by a telescope and detected. The average earth-moon distance is 384,000 km. The laser beam spreads out on its way to the moon because of diffraction, reaching the mirrors with an intensity of 300 W/m2. The reflected beam spreads out even more on its way back because of diffraction due to the circular aperture of the mirrors.
a. What is the round-trip time for the laser pulse to travel to the moon and back?
b. If we want to measure the distance to the moon to an accuracy of 1.0 cm, how accurately must the arrival time of the returning pulse be measured?
c. Because of the spread of the beam due to diffraction, the light arriving at earth from one of the mirrors will be spread over a circular spot. Estimate the diameter of this spot.
d. What is the intensity of the laser beam when it arrives back at the earth?
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