Derivation of Lens Formula

 


 

1) Suppose AB is an object placing in front of a convex lens of focal 

length  f = CF




2) C ---->  optical centre.



3) A real image is forming at B' that  A'B'



4) We see that


<DFC  =  <A'FB'

&    <DCF  =  <A'B'F




Therefore    





 

 Therefore





Now    DC = AB



Therefore









5) Again   <ACB  =  <A'CB'

<ABC  =  <A'B'C



Therefore     





Therefore







 

Therefore from   9.13 & 9.31








Now 

CF = f  (focal length)

B'C = v  (image distance)

BC = -u   (object distance)








fv  =  -uv  +  uf

uv =  uf   -   fv













This is the lens formula


 





Magnification of lens:

The magnification of a lens is denoted as m

Where





h' = height of the image

h = height of the object

v = distance of the image from optical centre

u = object distance from optical centre



1) m is positive for virtual image

2) m is negative for real image