Magnification

A measure of the extent to which an optical system enlarges or reduces an image is called magnification.

Magnification is of two types;
1. Linear Magnification
2. Angular Magnification

Linear Magnification : It is defined as the ratio of the size (height) of the image to the size (height) of the object.

                       m = Size of image / Size of object
                           = I/O

If m > 1, then system is enlarging.
If m < 1, the system is reducing.

Linear magnification can also be defined in terms of distances of image and objects from the optical centre.

The formula for magnification is:
                                                m = f / f+u

Angular Magnification (M) : It is defined as the ratio of angles formed by the final image and the object ( when viewed directly) in most favored position available at the eye.

This is also called magnifying power of an optical system. 

OR

The ratio of the angle subtended by the image at the eye as seen through an optical instrument to the angle subtended by the object at the objective of the instrument is called angular magnification of the instrument.

Practice Problem :

1. The image of an object placed 15 cm from a lens is formed erect and double the size of the object. What will be the focal length and nature of lens ?
Solution: 
               Given,    
                              u = –15 cm
                             m = 2
                         –v/u = 2
                              v = –2(u)
                              v = –2 X (+15)
                                 = –30 cm
from lens formula;
                                      1/v –1/u = 1/f
                                              1/f = (1/–30) – (1/ (–15))
                                                   = (–1/30) + (1/15)
                                              1/f = 1/30 
                                                 f = 30 cm
 Since Magnification and f are positive hence given lens is a convex lens.