Question

The two headlights of an approaching automobile are 1.4 m apart. At what (a) angular separation (in rad) and (b) maximum distance will the eye resolve them? Assume that the pupil diameter is 5.0 mm, and use a wavelength of 548 nm for the light. Also assume that diffraction effects alone limit the resolution so that Rayleigh's criterion can be applied, in meters. (ANSWER B) IN METERS NOT KM PLEASE)

Answer 1

Separation between the two headlights of an approachingautomobile x = 1.4 m

the pupil diameter of the observer d = 5 mm=5 * 10^-3 m

wavelength  ? = 548 nm = 548 * 10 ^ -9m

(a) angular separation will the eye resolve the twoheadlights is = 1.22 ? / d

=1.337 * 10^-4 rad

b) maximum distance will this occur y = ?
we know x = 1.22 y? / d
from this   y = xd / (1.22 ? )
                  = 10471.2 m