1) A 20.0-W laser emits a beam of light 4.0 mm in diameter. The laser is aimed a

Question

1) A 20.0-W laser emits a beam of light 4.0 mm in diameter. The laser is aimed at the Moon. By the time it reaches the Moon, the beam has spread out to a diameter of 85 km. What was the intensity of the light just as it first exited the laser?

- So I got the first question (the answer is 1.6E+06 W/m^2 ), however I'm having problems getting the next/second correlating question (below).

2) What is the value of the intensity where it hits the moon? (Assume there is no absorption in the atmosphere on the way)

Please help if you can! I've tried multiple ways and they were all wrong so I'm super stuck

Explanation / Answer

Solution:

Power = P = 20 Watts

Diametr = 85 km

Radius = R = 85/2 = 42.5 km = 42.5 x 10^3 m

Intensity = power/ area = 2 Po / pi w^2(z)

where w(z) is the Gaussian beam radius;

Since laser light travels in a straight line, its intensity does Not obey inverse square law.

for 99% of beam transmission, I = 2Po / pi w^2(z) where w(z) = r/1.52 = 42500/1.52 = 27960.5 m

=> I = 2(20) / pi (27960)^2 = 1.63 x 10^-8 W/m^2

Observe that the Intensity Decreases as the distance from the source Increases .

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