Problem 19.55 14 of 14 Constants Once dark adapted, the pupil of your eye is app

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Problem 19.55 14 of 14 Constants Once dark adapted, the pupil of your eye is approximately 6 mm in diameter. The headlights of an oncoming car are 120 cm apart. Part A 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.) Express your answer to two significant figures and include the appropriate units | 16.0 km SubmitP Previous Answers Reguest Answar X Incorrect, Try Again: no points deducted

Explanation / Answer

wavelength=lambda=600 nm

index of refraction=n=1.33

let at a distance of L headlights are marginally resolved.

diameter of eye pupil=d=6 mm=0.006 m

headlights of car are apart by D=120 cm=1.2 m

using rayleigh criterion, d*sin(theta)=1.22*lambda

==>theta=1.22*10^(-4) rad

then L=d/theta=9836.1 m=9.836 km

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