Resolving power of microscope:
The diagram related to the calculation of resolution of microscope. A microscope is used to see the details of the object under observation. The ability of microscope depends not only in magnifying the object but also in resolving two points on the object separated by a small distance dmin.
Smaller the value of dmin better will be the resolving power of the microscope.
The radius of central maxima is, r0 = \(\frac{1.22λv}{a}\)
In the place of focal length f we have the image distance v. If the difference between the two points on the object to be resolved is dmin, then the magnification m is, m =\(\frac{r_0}{d_{min}}\)
On the object side, 2tan β ≈ 2sin β = \(\frac{a}{f}\)
dmin = \(\frac{1.22λ}{2sinβ}\) ∴ [a = ƒ2 sinβ]
To further reduce the value of dmin the optical path of the light is increased by immersing the objective of the microscope in to a bath containing oil of refractive index n.
dmin = \(\frac{1.22λ}{2nsinβ}\)
Such an objective is called oil immersed objective. The term n sin p is called numerical aperture NA.
dmin = \(\frac{1.22 λ}{2(NA)}\)
