You are driving at night on a long, straight highway in the desert as another ca

Question

You are driving at night on a long, straight highway in the desert as another car approaches. What is the maximum distance at which you can tell that the car is not a motorcycle by seeing its two headlights, which are 1.7 m apart?
(a) Assume that your visual acuity is limited only by diffraction. Use 509 nm for the vacuum wavelength, and assume that your pupils are dilated to a 6.3 mm diameter. (The refractive index for eye is 1.34.)
(b) Assume a more realistic, typical visual acuity with ?min = 5.0 10-4 rad.

Explanation / Answer

The power of an eye is    ? = 1.22 ? ' / D here ?' is the wavelegnth of light in a medium , D is diameter of the pupil
? ' = ? / n =509nm/1.34 = 379.85nm for small angle ? = y / L here y is the distance between the lights, L is distance from car to eye    y / L = 1.22 ? ' /D L = y D / 1.22 ? '    = 1.7m(6.3x10^-3)/1.22(379.85x10^-9) = 23110.9 m
b) given ? = 5x10^-4 rad    ? = y /L L = y/? =1.7 / 5x10^-4     = 3400m
   

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