# From what point is the focal length of a thick lens measured?

1. Oct 24, 2013

### Stargazer19385

I'm designing an eyepiece for fun and want to be accurate. I just realized my physics book equations are approximated for thin lenses only.

Suppose I have a convex convex lens or a plano convex lens, lateral parallel rays coming from one side or the other, and a focal point on the opposite side, and the lens is thick enough that the vertical center of the lens is at least 40% closer to the focus laterally than edges are. If the focal length is, say 10mm, and the lens maybe 5mm thick and 12mm in diameter, from what point on the lens is it measured? The lateral center at the vertical center? The vertical center at the surface? At the edges? At the back surface? Please be specific so I'll know how to calculate it with two thick lenses in a row touching each other.

I think this is why the eye relief of an eyepiece is not necessarily equal to the focal length.

I thought about defining some ideal thick lenses in a spreadsheet via their conic section equations and derivatives, and then ray tracing them to their focus, and finding relationships in order to find the best focal length measuring method, but I think that would take a lot of work to do, especially with two lenses.

Last edited: Oct 24, 2013
2. Oct 24, 2013

### Stargazer19385

I googled "thick lens", and from Wikipedia, it looks like the distance I want is called the effective focal length, EFL. However, from the definitions that follow, it seems that they assume we are talking about a system of thin lenses rather than single highly curved thick one.

In this case, one thick lenses is probably equivalent to an infinite number of thin lenses whose total thickness is the same, which would mean they are talking about the axial distance. Still, what if it is a positive lens that is convex concave, with the convex surface stronger?

3. Oct 24, 2013

### Staff: Mentor

I think the concept you're looking for is "principal planes":

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/priplan.html

However, it's been many years since I taught an optics course in which I had to calculate the locations of the principal planes for a lens with given thickness and radii of curvature.

4. Oct 24, 2013

### UltrafastPED

5. Oct 24, 2013

### Stargazer19385

Thank you, both of you!

My goal was to have a single hyperbolic eyepiece lens for high contrast, and have a full 90 degree apparent FOV, which basically comes from the angle between each lens tip and the pupil. I later realized just how thick an f 1/2 lens would have to be, and how it would intrude into the eye relief if the convex side faced the eye. Later, I realized that even if I put the flat part on the eye side, the internal rays from the convex face would hit the plano face at a high incidence angle, and have total internal reflection. So I accepted that I will need at least two lenses to share the angles. Previously I thought that spherical aberration was the only reason single lenses are not used, and Plossl's have 2 and Naglers have 3, and I thought I only needed to make a hyperbolic.

I'm going to use the info in those two links and some graphs of some Fresnel equations of reflectance on Wikipedia, and see how many lenses actually are needed to get the eye relief and apparent field of view I want. Maybe there is a reason single lenses only get 15 degrees, Plossl's get 50, and Nagler's 82, though it would sure be nice to have the contrast of a minimum of lenses and still have the wide view.

6. Oct 24, 2013

### Stargazer19385

I started reading the first link. The picture in there gave me an idea. It showed a thick lens whose edges were ground flat, the that the curves have the same curvature and distance apart, but the diameter is reduced and there is what appears to be unused glass between them. That is when I realized, if the focal length has not changed even after the edges are ground off, then that means the edge locations don't matter. What matters is the only point that never changes, and that is the axial point on the center of the face of the lens. Each face is its own lens, and the axial point at the surface of that face is the point from which focal length is measured, and the distance between these points is a separation. I'll continue to read the links, but I predict that is what it will tell me.

7. Oct 24, 2013

### Stargazer19385

I read through both links. Both say the principle plane is not the vertex. I don't know why. The second link had a ton of useful equations and graphs, each of which I will need later, but it assumes that I know what each letter and subscript stand for. Maybe I can Google each one. The first link also has some useful equations, explained a little more.

As for the vertex not being used, and a principle plane being needed, I think that has to do with the fact that thin lens equations use the approximation sine theta = theta, which only holds for small angles. Most likely if I look at the derivation in my physics book, but skip the approximation, I can find an explanation for the theoretical plane distance.

8. Oct 24, 2013

### UltrafastPED

The labels are for the _cardinal points_ of the thick lens:
http://en.wikipedia.org/wiki/Cardinal_point_(optics [Broken])

Last edited by a moderator: May 6, 2017