The least distance of distinct vision is $25 \ cm$. Find the magnifying power of a simple microscope of focal length $5 \ cm$ if the final image is formed at the least distance of distinct vision.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: For a simple microscope,the angular size of the object equals the angular size of the image.
Reason $R$: Magnification is achieved as the small object can be kept much closer to the eye than $25\, cm$ and hence it subtends a large angle.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of the original objective lens. To retain the same magnification while keeping the object distance unchanged, the tube length has to be

The focal lengths of the objective and eye-lens of a microscope are $1 \,cm$ and $5 \,cm$ respectively. If the magnifying power for the relaxed eye is $45$,then the length of the tube is $....... \,cm$.

The objective lens of a compound microscope produces a magnification of $10$. In order to get an overall magnification of $100$ when the image is formed at $25 \, cm$ from the eye,the focal length of the eye lens should be:

$A$ man uses a thin convex lens of focal length $5 \, cm$ as a magnifying glass. He reads a book by holding it close to his near point of $25 \, cm$. What are the closest and farthest distances at which he can keep the book from the lens to read clearly?