Question

A person standing in the middle of a long straight road sees a truck with its headlights on approaching in the distance. The trucks headlights are 3 m apart. Assuming the headlights are point sources emitting yellow light of wavelength 600 nm and the diameter of the human pupil is 5 mm, approximately how far is the truck from the person when he can first resolve the two headlights as separate sources

Answer 1

Answer:

$Given:\\d=5mm=0.005\\lambda=600nm=600*10^-^9$

$y=3m\\L=?$

applying Rayleigh criterion

$sin\alpha =y/L=1.22(lambda/d)=1.22(600*10^-^9nm/0.005)=1.464*10^-^4\\\alpha =1.464*10^-^4rad$

$sin\alpha =y/L\\=1.22(lambda/d)\\L=yd/1.22*lambda\\=3m*0.005/1.22*600*10^-^9\\=20 km$