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659.


Problem 46.17 (RHK)


The two headlights of an approaching automobile are 1.42 m apart. We have to find (a) angular separation and (b) the maximum distance at which the eye can resolve them. We may assume a pupil diameter of 5.00 mm and a wavelength of 562 nm. Also, we will assume that diffraction effects alone limit the resolution.


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(a)

We will use Rayleigh’s criterion that two objects must have an angular separation at least to be resolvable by a lens of aperture d using light of wavelength .

Data of the problem are

Therefore,

(b)

The maximum distance at which the headlights separated by a distance of 1.42 m will be barely resolvable will therefore be