A tiny laser beam is directed from the Earth to the Moon. If the beam is to have a diameter of 2.50 m at the Moon, how small must divergence angle be for the beam? The distance of Moon from the Earth is 3.8 ｘ10⁸ m. (Ans: 6.6ｘ10⁻⁹ rad)



Data Given:


Length of arc = S = 2.50 m

Length of the beam from earth to moon = r = 3.8 ｘ10⁸ m


To Find:


Divergence angle  = θ = ?


Solution:


The plane angle Î¸  can be calculated as

S = r Î¸

or

θ = `\frac {S}{r}`

By putting values

θ = `\frac {2.50 m}{3.8 ｘ10⁸ m}`

θ = 0.657 ï½˜10⁻⁸ rad

or

θ = 6.57 ï½˜10⁻⁹ rad -----------------Ans.

Hence the divergence angle (in radian) for the moon is 6.57 ï½˜10⁻⁹ rad 



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