Question

You see a light approaching you from a distance on the highway. Is it a motorcycle (one light) or a car (two lights)? You may assume the air is perfectly clear and still, and the headlights emit exclusively blue light (λ = 475 nm).

Assume your pupil (the aperture of your eye) is 5 mm in diameter. If a car with two blue headlights that are separated by 1.5 meters is approaching you, at what maximum distance could you still distinguish the two lights clearly? (Assume that diffraction at the aperture of your eye is the only factor in determining resolution; you may ignore the index of refraction inside your eye.)

Rod cells in the fovea (the central part of your retina) are packed closely together. There would be no point in having rod cells packed more tightly than needed to resolve two points limited by diffraction. If the eyeball is roughly spherical with a diameter of 25 mm, calculate the approximate separation needed between adjacent rod cells? (You may ignore any effects due to the index of refraction inside your eye. You may use the same wavelength as in part (a) above.)

Answer 1

We can use Rayleigh criteria to angular separation

= 1.22 / D w

where D is diameter of the pupil

so,

= 1.22 * 475e-9 / 5e-3

= 1.159e-4 rad

so,

we know

The distance 'd' between two objects a distance 'x' away and separated by an angle is d = x

so,

x = 1.5 / 1.159e-4

x = 1,294e4 meter

or

x = 12.94 km

________________

For eyeball

= d / x

1.159e-4 = d / 25e-3

d = 2.89e-6 m

or

d = 2.89 um