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.

Question

Yael Pratt

Physics

28 January, 04:49

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.

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Answers (1)

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Timothy Elliott · Answer 1

Answer: 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