Deriving the Thick Lens Equation: How to Obtain the Equations for a Thick Lens?

[Arman777]

Homework Statement

Derive the equations for the thick lens and obtain,

$\frac {1} {f}=\frac {n_L-n'} {nR_2}-\frac {n_L-n} {nR_1}-\frac {(n_L-n)(n_L-n')} {nn_L}\frac {t} {R_1R_2}$

Homework Equations

$n$ is the medium where light ray enters,
$n_L$ is the medium of the lens and $n'$ is the outer medium where light ray goes out.

The Attempt at a Solution

I used three equations to derive the upper equation

$\frac {n} {s_1}+\frac {n_L} {(s_1)'}=\frac {n_L-n} {R_1}$ (1)
$\frac {n_L} {s_2}+\frac {n'} {(s_2)'}=\frac {n'-n_L} {R_2}$ (2)
$s_2=t-(s_1)'$ (3)

so I inserted the (3) in (2) and then I added new (2) with (1) and I get

$\frac {n} {s_1}+\frac {n'} {(s_2)'}+n_L[\frac {1} {(s_1)'}-\frac {1} {(s_1)'-t}]=\frac {n_L-n} {R_1}+\frac {n'-n_L} {R_2}$

but now I am stucked maybe is there another equation that I might need to consider or what should I do ?

 

[kuruman]

How resistant are you to just looking up the derivation?

Spoiler

http://scienceworld.wolfram.com/physics/ThickLensFormula.html

 

[Arman777]

How resistant are you to just looking up the derivation?

Spoiler

http://scienceworld.wolfram.com/physics/ThickLensFormula.html

I have already found that site. But on the site, it assumes $n'=n=1$ but I don't have that option so it doesn't simplify my solution.

But thanks

 

[rude man]

Looks like just a lot of grunt work with Snell's law and geometry. Or Fermat's principle and geometry.

 

[Arman777]

Yes i derived them using matrix method