You shine a 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 4.0 −cm aperture, that its white light has an average wavelength of 550 nm, and that the beam spreads due to diffraction only. Express your answer using two significant figures.

12.9 km

Explanation:

θ = 1.22 * (λ/d), where

θ = angle of resolution

λ = wavelength

d = width of slit

Also, the radius of the beam on the moon is

r = lθ, were

l = distance from the earth to the moon, = 384*10^6 m

if we substitute the relation for θ, we should have

r = (1.22 * lλ) / d

Now, we substitute the values into the equation

r = (1.22 * 384*10^6 * 550*10^-9) / 0.04

r = 258 / 0.04

r = 6450 m

Diameter of the beam, d = 2r

d = 2 * 6450

d = 12900 m or 12.9 km