Resolving power of a microscope:
The resolving power of a microscope is its ability to form separate images of two point objects lying close together. It is determined by the least distance between two point objects which can be distinguished.
This distance is given by,
The angle is the half-angle of the cone of light from the point object i.e., it is the angle which a marginal ray makes with the axis of the microscope.
The term is called the numerical aperture of the objective.
The resolving power of the microscope is defined as the reciprocal of the distance between two objects which can be just resolved when seen through the microscope.
The resolving power depends upon:
1. The wavelength of the light
2. The refractive index of the medium between the object and the objective of the microscope
3. The angle subtended by the radius of the objective on one of the objects.
Resolving power of a telescope:
The resolving power of a telescope is the reciprocal of the smallest angular separation between the distant objects whose images are separated in the telescope.
It is given by,
where, is the angle subtended by the point object at the objective
is the wavelength of light used
is the diameter of the telescope objective
A telescope with a larger aperture objective gives a high resolving power.
Note: Kindly ask the other questions as a separate query.