Question

Two light bulbs are 1.00 mapart. From what distance can these light bulbs be marginally resolved by a small telescope with a 3.90 cm-diameter objective lens?

Assume that the lens is diffraction limited and λ=600nm.

Answer 1

The angular resolution limit for two point sources of equal intensity is given by

                                                   (in radians)

where is the diameter of the lens and is the wavelength of light.

Let, from x distance these bulbs can be marginally resolved.

Therefore, we can write

                                       (where d is separation between the bulbs)

Now using both the equations, and putting all the values, we can write

                                    

                       or,      

                       or,