If an astronomical telescope has objective and eye-pieces of focal length $200 \mathrm{cm}$ and $4 \mathrm{cm}$ respectively, then the magnifying power of the telescope for the normal vision is:

Draw the ray diagram for formation of image in a simple microscope.

Draw a labelled diagram of simple microscope and establish an expression for the magnifying power of simple microscope, when the image formed at 

$\left(\mathrm{i}\right)$ Infinity

Given below are two statements : one is labeled as Assertion $A$ and the other is labeled 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 $25 \mathrm{cm}$ 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 has an eye piece of  focal length 10 cm and an objective of focal length of 4 cm. Calculate the magnification, if an object is kept at a distance of 5 cm from the objective then final image is formed at the least distance of distinct vision

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

In a compound microscope, the magnifications produced by the objective lens and the eye lens are $25$ and $6$ respectively. The magnification of the compound microscope be