Power of a lens:

Power of a lens is denoted as P and it is defined as


f = focal length of the lens




 

Power of combinations of two lens:

 

1) Suppose 2 lenses with optical centre C1   &   C2 are placed coaxially and in contact with each other.





2) Suppose O  is an object.


3) Rays coming from O passes through the two optical centre C1   &   C2



4) Another ray coming from the object O refracted. And form an image at I1



5) So

OC1 = u  (object distance)

C1I1 = v1  (first image distance)

As shown in the diagram.




6) if   f1   is the focal length of first lens






7) Now the first image is behave like an object for the second lens of focal length f2



8) the second lens forms the final image at I position where


u = C1I1 = v1  (now distance)


C2I = v  (image distance)



Again 

Now







Now on adding 9.34   &   9.56






 

9) Now suppose F is the focal length of a single lens for which image I  is developed due to the object O



So,






Therefore we get







10) Now suppose we combine n lenses with their focal length f1, f2, f3, …………… fn



Then their combination makes a lens of net focal length F  then









11) If P1, P2,  P3, ……………….. Pn are the power of n lenses then power of the net lens is




P = P1  +  P2  +  P3  + ……………….. +  Pn