Question

1. Traveling down a long, straight 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.

2. After passing the oncoming car, the driver looks at the dashboard to check the speedometer. The driver notices that he can clearly read the numbers 0.8 m away if he pushes his head against the headrest, but they get blurry if he leans forward. What pre- scription eyeglasses (in Diopters) would this driver need to comfortably read a book 25 cm from his face? (Assume the glasses would sit 2 cm in front of his eyes.)

Please explain in detail.

Answer 1

1.

Length, L = 1.22λ angle separation, wavelength, 580 nm pupil di ameter, d 4 mm 1.22λ 1.22x580 nm 10*m 1mm 4 mim 1 nm 10 m = 1.77×10-4 Separation distance, D = 5 ft D5ft θ 1.77×10 0.3048 m 1ft 8610.2m=8.6102 km