Question

You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.657 m apart. At what distance, in kilometers, are you marginally able to discern that there are two headlights rather than a single light source? Take the wavelength of the light to be 549 nm and your pupil diameter as 4.63 mm.

Answer 1

4.54168 km

Step-by-step explanation:

Angular resolution is given by

`\theta=1.22(\lambda)/(D)`

where,

`\lambda` = Wavelength = 549 nm

D = Diameter of pupil = 4.63 mm

`\theta=1.22(549* 10^(-9))/(4.63* 10^(-3))\\\Rightarrow \theta=0.00014466`

`sin\theta=(d)/(L)` but for small angle
`sin\theta=\theta`

where

d = Distance between the lights = 0.657 m

`\theta=(d)/(L)\\\Rightarrow 0.00014466=(0.657)/(L)\\\Rightarrow L=(0.657)/(0.00014466)\\\Rightarrow L=4541.68\ m`

The distance at which you will be able to marginally discern that there are two headlights rather than a single light source is 4.54168 km