Resolving Power of a Microscope and Telescope

Limit of resolution (self-luminous objects):

d = \[\frac{1.22\lambda}{2\sin\theta}=\frac{0.61\lambda}{\sin\theta}\]

Limit of resolution (objects illuminated by light of wavelength λ):

d = \[\frac{\lambda}{2\sin\theta}\]

If a liquid of refractive index μμ is between object and objective:

d = \[\frac{\lambda}{2\mu\sin\theta}\]

where θθ is the angle subtended by an object at the objective.

Smallest angular separation dθdθ (Circular aperture):

\[d\theta=\frac{1.22\lambda}{D}\]

where D is the aperture (diameter) of objective of the telescope.

Smallest angular separation (Rectangular aperture):

\[d\theta=\frac{d}{D}\]

where d is slit separation and D is distance.