Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The

Question

Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 130 cm apart.

If the lens of your eye is limited only by diffraction, at what distance are the two headlights marginally resolved? Assume the light's wavelength in air is 600 nm and the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.)

Explanation / Answer

here given is

wavelength = 600*10^(-9) m

by the Rayleigh criterion

the angular spreading of a source of light

d(theta) = 1.22*lambda/D

here D is diameter and lambda is wavelegth

d(theta) = 1.22*600*10^(-9)/(7*10^(-3)) = 10.45*10^(-5) rad

and d(theta) = d/L

L = 130*10^(-2)/(10.45*10^(-5)) = 12440.19 m

L = 12.44*10^3 m = 12.44 km [ANSWER]

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