Question

An experiment based at New Mexico’s Apache Point observatory uses a laser beam to measure the distance to the Moon with millimeter precision. The laser power is 120 GW, although it’s pulsed on for only 90 ps. The beam emerges from the laser with a diameter of 7.0 mm. It’s then beamed into a telescope aimed at the Moon. When the beam leaves the telescope, it has the telescope’s full 3.5-mm diameter. By the time it reaches the Moon, the beam has expanded to a diameter of 6.5 km.

a. Find the intensity of the beam as it leaves the laser. Express your answer with the appropriate units.
b. Find the intensity of the beam as it leaves the telescope. Express your answer with the appropriate units.

Answer 1

The intensity of the laser beam as it leaves the laser is 7.79x10¹⁴ W/m², and after passing through the telescope, the intensity is reduced to 1.25x10¹⁰ W/m² due to the increase in beam diameter to 3.5 m.

Step-by-step explanation:

Intensity of a Laser Beam

The intensity of a laser beam as it leaves the laser is calculated using the formula I = P/A, where I is the intensity, P is the power, and A is the area of the beam's cross-section. The power given is 120 GW, and the area can be found using the equation A = πr², where r is the radius of the laser beam.

For the laser, the radius is 3.5 mm (0.007 m), so the area is A = π(0.007 m)² = 1.539x10⁻⁴ m². Therefore, the intensity as it leaves the laser is I = 120 GW / 1.539x10⁻⁴ m² = 7.79x10¹⁴ W/m².

As for the intensity of the beam as it leaves the telescope, we use the same formula, but this time the diameter of the beam is 3.5 m. The new area is thus A = π(1.75 m)²= 9.62 m² since the radius is half the diameter. Consequently, the intensity after the telescope would be I = 120 GW / 9.62 m² = 1.25x10¹⁰ W/m².

Answer 2

Sorry but i dont know

Step-by-step explanation: