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Lens maker formula with full derivation


Priyanshu Joshi 3rd Dec, 2018
Answer (1)
Faizan Salim 3rd Dec, 2018

Hiiiii

Here is a deriation for lens makers formula:

Assumptions

1. Let us consider the thin lens  with 2 refracting surfaces having the radii of curvatures R1 and R2 respectively.
2. Let the refractive indices of the surrounding medium and the lens material be n1 and n2 respectively.

Derivation

 Using the formula for refraction at a single spherical surface we can say that,

For the first surface,
   
        n2/v1  -  n1/u  = n2-n1/ R1  ....... (1)


For the second surface,
  
       n1/v  - n2/v1  =  n1-n2/ R2 ...... (2)


Now adding equation (1) and (2),

     n1/v  - n1/u  = ( n2-n1 ) [ 1/ R1 - 1/R2 ]

     1/v -  1/u  = ( n2/n1  - 1) [ 1/R1 - 1/R2 ]


When u = ∞ and v = f,  then

     1/f  =  ( n2/n1  - 1 ) [ 1/R1 - 1/R2]

But also,

   1/v - 1/v = 1/f      ( lens formula)


Therefore we can say that, the lens makers formula is 
   
         1/f = (μ - 1 ) [ 1/R1 - 1/R2]           (Where μ is the refractive index of the material.)


I hope this will be helpful and you understand it easily.
If you have any doubt about the same please mention in the comment section below.

Thanks!!

5 Comments
Comments (5)
3rd Dec, 2018
Hii,buddy.
It's look like horrible
I can't understand it
Reply
3rd Dec, 2018
Where are you facing the problem? what are you not able to understand?
Reply
3rd Dec, 2018
I would suggest you to copy this down on paper and then try to practice it once or twice so that you can get what is done.Even then if you will not be able to get then you can revert back to us.
Reply
3rd Dec, 2018
Thx
Now I get relief
Finally get understand
So so thx for your work
Reply
3rd Dec, 2018
Plz
Can you give me for some information about IIT JEE
Reply

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