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 1.3 m apart?
(a) Assume that your visual acuity is limited only by diffraction. Use 547 nm for the vacuum wavelength, and assume that your pupils are dilated to a 6.6 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 resolving power of an eye is    = 1.22 / D here is the wavelegnth of light in a medium , D is diameter of the pupil
            = ' / n             =547 nm / 1.34             = 408.20 nm 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      = 1.3m (6.6x10-3 m) / 1.22(408.20 x 10-9 m)     =  17228.7 m ............................................................................................. b) given = 5x10-4 rad    = y /L L = y/     =1.3 m /  5x10-4 rad        = 2600 m
The resolving power of an eye is    = 1.22 / D here is the wavelegnth of light in a medium , D is diameter of the pupil
            = ' / n             =547 nm / 1.34             = 408.20 nm 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      = 1.3m (6.6x10-3 m) / 1.22(408.20 x 10-9 m)     =  17228.7 m ............................................................................................. b) given = 5x10-4 rad    = y /L L = y/     =1.3 m /  5x10-4 rad        = 2600 m

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