Resolving Power Example

question: The two headlights on a truck are about 2 meters apart. How far away could a perfect human eye observe the headlights as two distinct objects? Assume that the eye has a diameter of 3 mm.

answer:
\[ \rm \mathbf{ \theta_{min}= \frac{1.22 \lambda}{d},} \]
l = 500 nm, d = 0.003 m

q_min = 2.0 $\cdot$ 10^-4 radians

The angular separation of two objects 2.0 m apart at a distance D away is 2.0/D, so

q_min = 2.0 $\cdot$ 10^-4 radians = 2.0/D

D = 10⁴ meters or 10 km. Unfortunately the retina has too few sensors and the lens has too many aberrations to achieve this resolution.