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If you could shine a very powerful flashlight beam toward the Moon, estimate the diameter of the beam when it reaches the Moon. Assume that the beam leaves the flashlight through a 7.0-cm aperture, that its white light has an average wavelength of 550 nm, and that the beam spreads due to diffraction only. The distance from the Earth to the Moon is 384×103 km.

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Answer:

7361.82857143 m

Explanation:

l = Distance to the moon = [tex]384\times 10^6\ m[/tex]

[tex]\lambda[/tex] = Wavelength = 550 nm

a = Aperature = 7 cm

The radius is given by

[tex]r=l\theta\\\Rightarrow r=l\dfrac{1.22\lambda}{a}\\\Rightarrow r=384\times 10^6\dfrac{1.22\times 550\times 10^{-9}}{7\times 10^{-2}}\\\Rightarrow r=3680.91428571\ m[/tex]

Diameter is given by

[tex]d=2r\\\Rightarrow d=2\times 3680.91428571\\\Rightarrow d=7361.82857143/ m[/tex]

The diameter would be 7361.82857143 m

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