# Spherical aberration in Biconvex lens

• A
VVS2000
I was recently looking for proven relations between focal length, radius of curvature, refractive index etc of a convex lens as I was working on an experiment, I did Find a relation, between Height from principal axis and focal length, and it was a huge relation!I did the experiment to verify it, and it holds good. But I still don't know how to even derive such a huge relation. the image is attached.

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Gold Member
What is your goal here? To get some intuition? To get an idea of where it comes from in the math? To get actual predictions or improve an optical design? It's a broad question.

VVS2000
What is your goal here? To get some intuition? To get an idea of where it comes from in the math? To get actual predictions or improve an optical design? It's a broad question.
to get an idea of where it comes in from the math. Like whether it's a geometric derived result or some kind of solution obtained out of brute force numerical method

Mentor
Paging @Andy Resnick • jim mcnamara
Homework Helper
to get an idea of where it comes in from the math. Like whether it's a geometric derived result or some kind of solution obtained out of brute force numerical method
Numerical meethods are very unlikely to come up with explicit expressions like in the sheet you posted (source?)

Gold Member
The short version is that you get this expression when you use Snell's law and solving for the focal point of an incident ray where ##\theta## is the angle between the incident ray and the normal axis to the biconvex lens at the point at distance h off the optical axis. Naturally, you have to use Snell's again where the ray exits the lens on the second convex surface.

In practice, virtually no one uses this formula. You can get the Taylor coefficients by using some neat ray tracing tricks, so we tend to use ray tracing software to do aberration analysis. It's far more computationally efficient and general. My point is: don't feel like you need to know the above expression.

• • VVS2000, vanhees71, BvU and 1 other person
VVS2000
Numerical meethods are very unlikely to come up with explicit expressions like in the sheet you posted (source?)
thomas k gaylord, georgia tech optical engineering notes

• BvU
VVS2000
The short version is that you get this expression when you use Snell's law and solving for the focal point of an incident ray where ##\theta## is the angle between the incident ray and the normal axis to the biconvex lens at the point at distance h off the optical axis. Naturally, you have to use Snell's again where the ray exits the lens on the second convex surface.

In practice, virtually no one uses this formula. You can get the Taylor coefficients by using some neat ray tracing tricks, so we tend to use ray tracing software to do aberration analysis. It's far more computationally efficient and general. My point is: don't feel like you need to know the above expression.
That's the thing, How would one apply snell's law and get such a result, if you have any hint to get me started on the right direction I can make an attempt to solve it. I just want to know the math behind it all, like how one would approach such a complex situation

• BvU