## Resolving two point sources of light## A person is standing on a long straight road with a truck approaching in the distance. How far is the truck front the person when he/she can resolve the two headlights as separate sources of light?To figure this out, we need to use the Rayleigh Criterion, which tells
us the minimum angular separation š¯›³ between two sources such that they
can be resolved from some distance The Rayleigh Criterion comes from the equation for the the minima in a
circular aperture diffraction pattern, where š¯›³ is the angular distance
from the center of the central bright spot to the first dark ring and
Without getting into too many of the details, the intensity pattern for
a circular aperture far-field diffraction pattern (aka the Airy pattern)
is modeled using a first order Bessel function (where Using the geometry of our diagram and the small angle approximation, we
can rewrite the Rayleigh Criterion as an expression for our distance
Now comes the estimation part. The aperture diameter in our equation is the diameter of the pupil. In the lab light, we estimated the pupil is about 3mm in diameter, so probably 5mm is a good approximation of its size at night. We estimated that the distance between the two headlights of the truck is probably 2m, and that the light they would be emitting would be yellowish-white - so 500 nm, in the middle of the visible spectrum. With all these measurements considered, we found the distance |