If focal length is directly proportional to wavelength, why is Resolving power independent of focal length?
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Answer:
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
Now, the resolving power of microscope is the reciprocal of the minimum distance.
Therefore, we have
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.
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