The headlights of a truck are 1.22 m apart and light of wavelength 5000 Å is used for the headlights. The pupil of the eye of the obeserver has a diameter of 1 mm. what should be the maximum distance of the truck from observer, so that the headlights are just separated for him?

Options

A. 2 km
B. 1.5 km
C. 3 km
D. 3.5 km

Answer

A

Explanation

Let D=diameter of the eye lens, d=distance between the two sources and distance of the truck=x
R.P. of the eye, `(1)/(theta)=(D)/(1.22lamda)`
but `tantheta=theta=(d)/(x)therefore(1)/(theta)=(x)/(d)`
`therefore(x)/(d)=(D)/(1.22lamda)thereforex=(Dd)/(1.22lamda)`
`thereforex=(1xx10^(-3)xx1.22lamda)`
`thereforex=(1xx10^(-3)xx1.22)/(1.22xx5000xx10^(-10))`
`=(10^(-3)xx10^(7))/(5)
`=2x10^(3)m=2km`