How does a microscope eyepiece work?

. A compound microscope has a magnifying power of `$100$` when the image is formed at infinity. The objective has focal length $0.5 \mathrm{cm}$ and the tube length is $6.5 cm$  What is  the focal length of the eye-piece

A compound microscope consists of two convex lenses having a focal length of $1.5 \mathrm{cm}$ and $5 \mathrm{cm}$. When an object is kept at a distance of $1.6 \mathrm{cm}$ from the objective, the final image is virtual and lies at a distance of $25 \mathrm{cm}$ from the eyepiece. Calculate magnifying power of the compound microscope in this setup.

What is meant by the resolving power of a telescope? State any one method of increasing the resolving power of an astronomical telescope.

An astronomical telescope has an objective of focal length $200 \mathrm{cm}$ and an eye-piece of focal length $10 \mathrm{cm}$. An observer adjusts the distance of the eyepiece from the objective to obtain the image of the sun on a screen $40 \mathrm{cm}$ behind the eye-piece. The diameter of the sun’s image is $6.0 \mathrm{cm}$. Find the diameter of the sun. The average earth-sun distance is $1.5\times {10}^{11}\mathrm{m}$.