The headlights of an oncoming car are 1.2 m apart.What is the maximum distance from the car at which you can resolve the lights as two sources if the diameter of the pupil of your eye is 5.0 mm and the wavelength of the light is 555 nm?
A)8.9 km
B)22 km
C)4.4 km
D)5.4 km
E)13 km

Question

Quizplus · Accepted Answer

The resolution of two sources as distinct depends on the Rayleigh criterion, which is given by the formula $\theta = 1.22 \frac{\lambda}{D}$, where $\theta$ is the angular resolution in radians, $\lambda$ is the wavelength of light, and $D$ is the diameter of the aperture (in this case, the pupil of the eye). To find the maximum distance ($L$) at which the car's headlights can be resolved, we use the formula $\theta = \frac{s}{L}$, where $s$ is the separation between the headlights. Combining the two gives $L = \frac{sD}{1.22\lambda}$.Given: $s = 1.2$ m, $D = 5.0$ mm = $0.005$ m, and $\lambda = 555$ nm = $555 \times 10^{-9}$ m.Substituting these values gives:$$L = \frac{1.2 \times 0.005}{1.22 \times 555 \times 10^{-9}} \approx 8900 \, \text{m} = 8.9 \, \text{km}.$$

The Headlights of an Oncoming Car Are 1