Lens: The resolving power of a lens is its ability to resolve two points that are close to each other.
Eye: In case of the eye, two points can be seen distinctly if they subtend at the eye an angle equal to about one minute of arc. (This is on the assumption that the pupil of the eye is about 2 mm in diameter). The reciprocal of this angle is the resolving power.
Microscope, The limit of resolution of microscope is deter mined by the least distance between two point objects which can be distinguished. This distance d is given by
d = \(\frac{\lambda}{2\mu\ sin\ \theta}\)
where λ is the wavelength of light used to illuminate the object, θ is the half angle of the cone of light from the point object and µ the refractive index of the medium between the object and the objective Fig. For oil immersion objective microscopes, the resolving power is high. The expression µ sin θ is called numerical aperture, (for eye, µ sin θ = 0.004).
∴ Resolving power of microscope = \(\frac{1}{d} = \frac{2\mu\ sin\ \theta}{\lambda}\)
Telescope: The resolving power of a telescope is defined as the reciprocal of the smallest angular separation between two distant objects whose images are separated in the telescope. This is given by
dθ = \(\frac{1.22\lambda}{a}\)
where λ is the wavelength of light, a is the diameter of the telescope objective and dθ = angle subtended by the point object at the objective.
∴ Resolving power of telescope
= \(\frac{1}{d\theta} = \frac{a}{1.22\lambda}\)
To get a high resolving power, a telescope with large aperture objective has to be used or wavelength of light used should be small.
