A compound microscope consists of an objective lens of focal length \(2.0~\text{cm}\) and an eyepiece of focal length \(6.25~\text{cm}\) separated by a distance of \(15~\text{cm}.\) How far from the objective should an object be placed in order to obtain the final image at the least distance of distinct vision \((25~\text{cm})?\)
1. \(2.5~\text{cm}\)
2. \(0.5~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(5.0~\text{cm}\)

A person with a normal near point \((25~\text{cm})\) using a compound microscope with an objective of focal length \(8.0~\text{mm}\)  and an eyepiece of focal length \(2.5~\text{cm}\) can bring an object placed at \(9.0~\text{mm}\) from the objective in sharp focus. What is the separation between the two lenses?
1. \(7.20~\text{cm}\)
2. \(9.47~\text{cm}\)
3. \(2.50~\text{cm}\)
4. \(2.27~\text{cm}\)

A man with a normal near point \(25~\text{cm}\) reads a book with a small print using a magnifying glass: a thin convex lens of focal length \(5~\text{cm}.\) What is the ratio of maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?

The linear magnification and angular magnification in the microscope have similar magnitude when the image is at a distance of:
1. \(35~\text{cm}\)
2. \(\infty\)
3. \(25~\text{cm}\)
4. none of these