A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle of 4.6×10−5 rad.

1. What diameter spot will it make on the Moon?

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To determine the diameter spot the laser beam will make on the Moon, we can use the formula for the spot size of a laser beam given the divergence angle and the distance to the target.

The formula is:
Spot diameter = 2 * Distance * tan(Divergence angle)

Given:
Divergence angle (θ) = 4.6×10^(-5) rad
Distance to the Moon (d) = 380,000 km = 380,000,000 meters

Substituting these values into the formula, we have:
Spot diameter = 2 * 380,000,000 * tan(4.6×10^(-5))

Now we can calculate the spot diameter.

To determine the diameter spot the laser beam will make on the Moon, we need to use the concept of angular diameter and trigonometry. The angular diameter (θ) can be calculated using the formula:

θ = d / D

where
θ is the angular diameter,
d is the actual diameter of the object (spot),
and D is the distance between the object and the observer (Earth to the Moon).

In this case, the distance between the Earth and the Moon (D) is given as 380,000 km, which is equivalent to 380,000,000 meters. The angle of divergence (θ) is provided as 4.6×10^(-5) rad.

To find the diameter of the spot on the Moon (d), we rearrange the formula as follows:

d = θ × D

Now substitute the given values:

d = (4.6×10^(-5)) × (380,000,000)

Calculating this expression will provide the answer to the diameter of the spot the laser beam will make on the Moon.

spot diameter =

distance * (divergence angle in radians)

The diameter will be in km if you use the distance in km.