Question

Resolving power of optical instruments: Mention of expressions for limit of resolution of (a) microscope and (b) telescope - Methods of increasing resolving power of microscope and telescope.  

Answer 1

(1) The angular resolution of the telescope is determined by the objective lens of the telescope. 

(2) A parallel beam of light is incident on a convex lens. Because of diffraction effects, the beam gets focused to a spot of radius of the central bright region is approximately given by 

where f is the focal length of the lens and 2a is the diameter of the circular aperture or the diameter of the lens, whichever is smaller. Typically if λ ≈ 0.5 µm, f ≈ 20 cm and a ≈ 5 cm, we have 

r₀ ≈ 1.2 µm 

Although the size of the spot is very small, it plays an important role in determining the limit of resolution of optical instruments like a telescope or a microscope. For the two stars to be just resolved 

where Δθ is called limit of resolution.