Spherical aberration in Biconvex and Plano Convex lenses

[VVS2000]

I wanted to know about spherical aberration in a biconvex and plano convex lens as I was planning an experiment with them.
I was reading about them and came upon the following passage.
I don't know whether the given equation is an empirical one or a derived equation.
Can anyone help me if you have any sources regarding aberration in plano convex and bi convex lenses or how to start with deriving such an equation?

 

[vanhees71]

Everything concerning refraction can be derived from Maxwell's equations applying the right boundary conditions on the surfaces of the adjecent dielectrica (for everyday applications usually some glass lens with a given index of refraction, which is dependent on the wavelength of the light, in air, which can be treated as vacuum). You end up with the Fresnel equations.

https://en.wikipedia.org/wiki/Fresnel_equations

This gives you the complete information, including the polarization of the light.

For the purpose of geometrical optics it's sufficient to know Snell's Law, which also follows from the wave-optics derivation a la Fresnel. It's the relation for the wave vectors in and out of the medium.

https://en.wikipedia.org/wiki/Snell's_law

 

[sophiecentaur]

For the purpose of geometrical optics it's sufficient to know Snell's Law, which also follows from the wave-optics derivation a la Fresnel. It's the relation for the wave vectors in and out of the medium.

Ray optics is probably an easier first time around approach. It would produce an equivalent to the formula in the OP's attachment for the different lens type, I think.