Question

The headlights of a car are 1.6 m apart and produce light of wavelength 575 nm in vacuum. The pupil of the eye of the observer has a diameter of 4.0 mm and a refractive index of 1.4. What is the maximum distance from the observer that the two headlights can be distinguished?

Answer 1

To solve this problem it is necessary to apply the concepts related to angular resolution, for which it is necessary that the angle is

$\theta = 1.22\frac{\lambda}{nd}$

Where

d = Diameter of the eye

n = Index of refraction

D = Distance between head lights

$\lambda$= Wavelength

Replacing with our values we have that

$\theta = 1.22 \frac{(1.22)(575*10{-9})}{1.4(4*10^{-3})}$

$\theta = 1.252*10^{-4}rad$

Using the proportion of the arc length we have to

$L = \frac{D}{\theta}$

Where L is the maximum distance, therefore

$L = \frac{1.6}{1.252*10^{-4}}$

$L = 12.77km$

Therefore the maximum distance from the observer that the two headlights can be distinguished is 12.77km