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!!