A compound microscope has a magnifying power of $30$. The focal length of its eye-piece is $5 \mathrm{cm}$. Assuming the final image to be formed at the least distance of distinct vision ($25 \mathrm{cm}$), calculate the magnification produced by the objective of the microscope.

The magnification by the objective of a compound microscope is $8$. If the magnifying power of the microscope be $32$, then calculate the magnification by the eye-piece.

The length of a microscope is $14 \mathrm{cm}$ and for relaxed eye, the magnifying power is $25$. The focal length of the eye-piece is $5.0 \mathrm{cm}$. Calculate the distance of the object from the objective and the focal length of the objective.

A compound microscope has an objective of focal length $1.0 \mathrm{cm}$ and an eye-piece of focal length $3.0 \mathrm{cm}$. It forms a sharp image of an object placed at $1.2 \mathrm{cm}$ from its objective at the least distance of distinct vision ($25 \mathrm{cm}$). What is the length of the microscope? Magnifying power?

The distance between the objective of a compound microscope and the real image formed by it is $18 \mathrm{cm}$. If $f_0=0.4 \mathrm{cm}$, $f_e=2.0 \mathrm{cm}$, then calculate the magnifying power of the microscope for final image formed at the least distance of distinct vision.

A compound microscope has an objective of focal length $2.0 \mathrm{cm}$ and an eye-piece of focal length $6.25 \mathrm{cm}$ separated by a distance of $5 \mathrm{cm}$. Find the location of an object with respect to the objective so that the final image is formed at least distance of distinct vision. What is the magnifying power of the microscope?

On seeing with unaided eye, the visual angle of moon at the eye is $0.6°$. The focal lengths of the objective and the eye-piece of a telescope are respectively $200 \mathrm{cm}$ and $5 \mathrm{cm}$. What will be the visual angle on seeing moon through the telescope?

An astronomical telescope set for normal adjustment has a magnifying power $10$. If the focal length of the objective is $1.20 \mathrm{m}$, what is the focal length of the eyepiece?

The focal lengths of the objective and the eye-piece of an astronomical telescope are $2.5 \mathrm{m}$ and $5 \mathrm{cm}$ respectively. What is the magnifying power of the telescope when the image is formed at infinity?