Discuss about simple microscope and obtain the equation for magnificaiton for near point focusing and normal focusing.
Simple microscope:

Explanation

A simple microscope is a single magnifying (converging) lens of small focal length. The idea is to get an erect, magnified and virtual image of the object. For this the object is placed between F and P on one sid of the lens and viewed from other side of the lens. There are two magnificaitons to be discussed for two kinds of focusing.
(i) Near point focusing - The image is formed at near point. i.e. 25 cm normal eye. This distance is also called as least distance D of distinct vision. In this position, the eye feels comfortable but there is little strain on the eye.
(ii) Normal focusing - The image is formed at infinty. In this position the eye is most relaxed to view the image.
Magnification in near point focusing
Object distance u is than f. The image distance is the near point D. The magnification m is given by the relation.
`m = (v)/(u)`
With the help of lens equation, `(1)/(v) - (1)/(u) = (1)/(f)` the magnification can further be written as,
`m = 1 - (v)/(f)`
Substituting for v with sign convention, v = - D
`m = 1 + (D)/(f)`
This is the magnification for near point focusing.

Magnification in normal focusing (angular magnification)
We will now find the magnification for the image formed at infinty. If we take the ratio of height of image to height of object `(m = (h.)/(v))` to find the magnification, we will not get a particial relation as the image will also be of infintie size when the image if formed at infinity. Hence, we can practically use the angular magnification. The angular magnification is defined as the ratio of angle `theta_(1)` , subtended by the image with aided eye to the angle `theta_(0)` subtended by the obect with unaided eye.

`m = (theta_(i))/(theta_0))`
For unaided eye, `tan theta_(0) approx theta_(0) = (h)/(D)`
For aided eye, `tan theta_(1) approx_(1) = (h)/(f)`
The angular magnification is, `m = (theta_(i))/(theta_(0)) = (h//f)/(h//D)`
`m = (D)/(f)`
This is the magnification for normal focusing. The magnification for normal focusing is one less than that for near point focusing.