Telescope and microscope
It is used for observing far off objects in the sky. In normal adjustment (final image at ∞), angular magnification/magnifying power, M= f0/-fe . When final image is screen at least distance of distinct vision (d), then M = f0/-fe (1- fe/d).
Reflecting type telescope
In a reflection type telescope, objective lens is replaced by a large concave reflector of radius of curvature R M = f0/|fe| = (R/2)/ |fe|.
It is used for observing far off objects on the ground. The essential requirement of such a telescope is that final image must be erect with respect to the object. To achieve it, an inverting convex lens is used in-between the objective and eye piece of astronomical telescope. This, however, increases the length of telescope tube. In Galilean telescope, no additional lens is used. Instead, the eye lens is a concave lens, instead of being convex. This, of course, reduces the field of view of Galilean telescope.
Power of a microscope
Resolving power of a microscope is given by R.P. = 1/d=2 μsin θ/λ Where d is minimum distance between two point objects which can just be resolved, λ is wavelength of light used, μ is refractive index of medium between object and objective lens. The distance (d) is a measure of limit of resolution of the microscope. Clearly, smaller is the limit of resolution; greater is the resolving power of the microscope.
Power of a telescope
Resolving power of a telescope is given by R.P. = 1/dθ =D/1.22λ Where dθ is angular separation of two stars which are just resolved in the telescope, D is diameter of objective lens and λ is wavelength of light used. Note that dθ is a measure of limit of resolution of the telescope. Smaller the limit of resolution, greater is the resolving power of telescope.
Simple microscope or magnifying glass
It is used for observing magnified image of tinny objects .It consists of a single convex lens of small focal length. The angular magnification or magnifying power, M= (1+d/f), where d is least distance of distinct vision and f is focal length of the lens.