A telescope is used to resolve two distant stars. Bu what factor will the resolution of the telescope change if the diameter of the lens is doubled?

resolution of the telescope is halved

Explanation:

Solution:-

- The lens' circular aperture is analogous to a two-dimensional version of the single-slit experiment. Light passing through the lens interferes with itself creating a ring-shape diffraction pattern, known as the Airy pattern, if the wavefront of the transmitted light is taken to be spherical or plane over the exit aperture.

- The narrower the aperture of a lens the more likely the PSF is dominated by diffraction. In that case, the angular resolution of an optical system can be estimated (from the diameter of the aperture and the wavelength of the light) by the Rayleigh criterion:

                               Δl = 1.22*(f*λ) / D

Where,

             Δl : Spatial resolution

             f : Focal length of the lens

             λ : Wavelength of light

             D : diameter of the lens

- We know that diameter of the lens is doubled; using the given relationship we see that Δl : Spatial resolution is inversely proportional to diameter D of the lens. So, the resolution of the telescope is halved.