Derivation of Lens-Maker's formula: As shown in figure the centre of the lens is denoted as C and the principal axis is X'X. The R1 and R2 are the radii of the curvature of the surfaces of lens and...
A basic derivation can be found here: http://books.google.com/books?id=rpbdozIZt3sC&pg=PA128&lpg=PA128&dq=kramers+heisenberg+dispersion+formula&sour...
The following proof is trigonometric, and basically uses the cosine rule. First we compute the cosine squared in terms of the sides, and then the sine squared which we use in the formula...