Late one night on a highway, a car speeds by you and fades into the distance. Under these conditions the pupils of your eyes have diameters of about 6.5 mm. The taillights of this car are separated by a distance of 1.3 m and emit red light (wavelength = 641 nm in vacuum). How far away from you is this car when its taillights appear to merge into a single spot of light because of the effects of diffraction?
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Since you've marked my earlier effort wrong, I'm guessing that the index of refraction stuff about the eyeball should not have been considered.
When the car is distance d away, the angle presented by the two tailgate lights is
Θ = s / d = 1.3m / d (small angle approximation, Θ ≈ sinΘ)
The Rayleigh criterion tells us the smallest angular separation we can resolve is given by
Θ = 1.22λ/D = 1.22*641e-9m / 6.5e-3m = 1.20e-4 rads
Then 1.20e-4 rads = 1.3m / d
means that the distance d = 10805 m ≈ 11 km