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please explain how you found your answer Traveling down a long, straight Kansas

ID: 1348714 • Letter: P

Question

please explain how you found your answer

Traveling down a long, straight Kansas road late at night, a driver notices a light approaching in the distance. After a bit the driver notices that the single light has split into two distinct headlights. Estimate the maximum distance the approaching car can be assuming that the driver's pupils are 4 mm in diameter, the approaching car's headlights are 5 ft apart, the headlights emit primarily 580 nm wavelength light, and that the driver's eyesight is diffraction limited.

Explanation / Answer

use angular separation theta = 1.22* lambda /D

as

theta = dX/r

where delta x = spatial separation = 4 mm = 0.004 m

r = distance of object = ?

Then D = 1.220 lambda r / delta x

r = delta x * D/(1.22 * 580 e -9)

r = 0.004 * 1.54 /(1.22 * 580 e-9)

r = 8705.48 m or 8.7 km