B An exact Paraxial equation derivation, 100% Cartesian

AI Thread Summary
The discussion centers on the derivation of a paraxial equation using a Cartesian approach, with the original poster expressing a desire to share their findings from years of hobbyist study in trigonometric ray tracing. There is a request for improved formatting using LaTeX for clarity, though the poster is hesitant due to time constraints and a lack of familiarity with the software. The conversation also touches on the distinction between exact ray tracing and paraxial optics, with some confusion about the purpose of the derivation. Additionally, the poster seeks advice on suitable academic journals for publishing their work and recommendations for PDF editing software that can handle trigonometric equations effectively. Overall, the thread highlights a blend of sharing knowledge and seeking guidance on academic presentation.
difalcojr
Messages
380
Reaction score
263
TL;DR Summary
The equation for the focal point is valid for all refractions through a spherical convex surface.
There are no angle or other length approximations used in the derivation. See what you think of this.
trig1 OP.jpeg


trig2 OP.jpeg

trig3 OP.jpeg
 
Last edited:
Mathematics news on Phys.org
You obviously spent significant time and effort in preparing your post. Can you spend some more of that on learning LaTeX and posting everything, including your exposition, in nice, readable text format?
 
  • Like
Likes PhDeezNutz and berkeman
Years. Been a hobby, trigonometric ray tracing, for a long time.

I probably can reproduce the above in LaTex if I have to. But I don't know it at all and have limited time to give to learn it, if just to reproduce the above in that format. Am still working at a job is one reason. I thought that a neat, handwritten copy would probably suffice. Hope that doesn't prevent an analysis of it in this form, but, if needed, I can comply. @berkeman advised me on that recently too.
 
As with your thread on the same topic in the Optics forum, I don't really understand what you think you are doing. You aren't doing paraxial optics, despite your thread titles. You appear to be doing exact ray tracing for a spherical surface, which is fine, then doing a paraxial approximation at the end, which is fine, but for a reason I don't understand. You usually use the paraxial approximation to compute image locations, not where arbitrary rays from the axis cross. Knowing image locations is a great tool for roughing out an optical system. Then you either use aberration theory to understand and correct for how bad the system is, or just jump straight to getting a computer to throw hundreds of rays through it using exact ray tracing and optimisation algorithms to improve it. This doesn't really seem to help that, so I don't understand what you are trying to achieve.
 
Yes, you have summarized it exactly, thanks.

I had some things from years of a hobby study that I just wanted to show and tell to others, that's all.
I don't have problems to solve, just a few items of study to show to others I thought might be of interest.

I'd never seen an exact derivation, so I thought mathematicians might like to see that.

Had a simple, trig ray trace program and wanted to show off what it could do. For all the paraxial points, and all the other areas of a spherical surface too. Wasn't sure if an existing program could do all of that.

Found a perfect lens model and rules for monochromatic, monocentric lenses. Other members proved it valid too. That didn't get much interest.

I have no problem to solve here, just had some results to show. That's all.
 
If I write any more equations in any post, I will comply and write them in LaTex. There. It's on the record. Luckily, though, I don't think I have any more equations to write down, as I told @berkeman too. So, that's all I have for this thread or any others, I hope.

Yes, I just wanted to show an exact, Cartesian-referenced derivation of that old, well-known paraxial equation. Because every textbook author had only used approximations in the derivation. That's it.

Third thing I still have to show was what the simple trig, ray trace program can do. But I will start a 2nd OP in the Optics section called "Simple trig trace program" or something like that. And show a few more diagrams and possibilities. I plotted a lot of stuff over the years. Hope this is OK.
 
renormalize said:
You obviously spent significant time and effort in preparing your post. Can you spend some more of that on learning LaTeX and posting everything, including your exposition, in nice, readable text format?
You probably don't remember this post, but, since the question of what journal is the ideal for a published subject matter came up in another thread, recently, and thank you again for your comments there, would you or any other academic members in this forum, suggest a correct journal to submit something of this type as stated in the OP, if one journal is considered better or more appropriate than another? I was unaware of this grading. Same subject matter: basic optics theory. Geometrical optics. A fuller exposition as you mention could be written. High school math again only, though.

Also, is one PDF editor software better than another for writing trigonometry equations in an academic paper? I am getting a lot of offers in my email? As long as it doesn't look like LaTex. :)

IJRAP had a terrible time converting my original Word file into PDF. Botched it up a lot, finally got it right after publishing it incorrectly for about a week! Had to get and keep after them! Did not clear the final PDF copy with me before they published it, and it was a mess! Not communicative, felt like AI on the emails, almost. Still, they put up a good copy, finally, online, and I am happy and thankful to them a lot for that.

Any suggestions are helpful and appreciated, thank you.
 
Back
Top