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 0.633 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 547 nm and your pupil diameter to be 4.61 mm.

Answer 1

They can be seen from a distance of 4.372 kilometers.

Step-by-step explanation:

Using the Reyligh creterion for diffraction through a circular aperture we have

`(x)/(D)=(1.22\lambda )/(d)`

where symbol's have their usual meaning

thus applying values we get

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

`\therefore D=(0.633* 4.61* 10^(-3))/(1.22* 547* 10^(-9))\\\\D=4372.77m\\=4.372km`