Question

Expression of minimum separation of compund microscope

Answer 1

The resolving power of a compound microscope can be defined as the ability of the microscope to form separate images of two objects placed very close to each other.

The minimum separation between two objects that are to be resolved by a microscope is given as

begin mathsize 12px style straight d subscript min equals fraction numerator 1.22 straight lambda over denominator 2 nsinθ end fraction end style
Now, the resolving power of microscope is the reciprocal of the minimum distance.

Therefore, we have

begin mathsize 12px style straight R. straight P equals 1 over straight d subscript min equals fraction numerator 2 nsinθ over denominator 1.22 straight lambda end fraction therefore straight R. straight P proportional to nsinθ over straight lambda end style

Therefore, from the above expression we can see that

(a) When refractive index of medium increases.
As the R.P is directly proportional to the refractive index (n), it increases when n increases.

(b) When wavelength of light used increases.
As the R.P is inversely proportional to the wavelength (λ), it decreases when λ increases.

(c) When diameter of objective lens increases.
When diameter of objective is increased, θ increases. Hence, sinθ also increases.
As the R.P is directly proportional to the sinθ, it increases when diameter of objective increases.

(d) When focal length of objective lens increases.
As the R.P is independent of focal length of the lens, it remains unchanged when focal length increases.