well, right before i take a STAB at that? Now that i at least have your attention, let me use that attention to “plop” the rest of the answer out.
you will notice that the “simple” equation to calculate the new effective focal length of the new compound lens to replace the original single lens? its all stated as mainly “reciprocals” which are a pain in the tookus to work with. you CAN “play” with different values of lenses to see what results come out of the playtime, but, its tedious. Also you have to plug in the BackFocalLength each and every time.
heres the same equation? stated the way you WANT to see it, and its much easier to plug in values and use them. I simply re-solved the equation again and again, until i didnt make any stupid algebra errors. The solution with all variables? It QUICKLY grows more and more complex, getting nuts… until right at the end? All the huge craziness starts to “cancel out” and it simplifies down…
new focal length = (F1 * F2) / (F1 + F2 - Airgap)
all units have to be identical (i suggest millimeters, for obvious reasons)
F1 = focal length of lens 1
F2 = focal length of lens 2
Airgap = distance of air between both lenses
you “plug in” to the BFL equation with each solution to see the new back focal length.
it should be obvious, that if the lenses are touching? the airgap is zero millimeters… and you are left with just the “products” divided by the “sums”. If you start using two DIFFERENT focal lengths? and start varying them each time you play? is when it really starts to get interesting…
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Now that we are all c-a-l-m ? And you are at least willing to entertain my idea? I can now state… that i am sorry i had to act a little rude, and a little arrogant, to get your attention. I heartily apologize. But, you are the FIRST person, on three different sites, and of all the hundreds of people? That at least seemed to know what he is doing with math! I NEEDED you… where have you BEEN the last 3 years, tall dark and handsome? eh?
in addition to “playing” with the CORRECTLY STATED “re-solved” equation i made? to see what 2 lenses will MAKE when used as a compound lens?
How about… you start putting THIS idea into your (very powerful) ray tracing software, and seeing what you can get out of it? Up until NOW, you have been stuck with the notion of finding “just the right collimation lens” to stick behind “the cool single lens”.
I think but do not know… that when you talk about putting the “small asphere collimation lens” next to the LED emitter? i think what you are doing, is putting it at its focal length? Stop doing that… start LOOKING at the problem the proper way. Namely, that you are going to find two lenses focal length values, that combine to produce “one compound lens”.
the BFL ? will tell you for each play, how far away from the LED it is “set”. The “airgap” tells you the distance to the front lens…
I am not “smarter” than anyone else here, in fact? you are smarter and better educated than “me” at this, sunshine. You have a VERY POWERFUL TOOL, your ray tracing software? I just want you to start USING your (i admit it) superior math skills? and your superior tools at your disposal? To crack this.
Heres what will happen, if you just “pick” two lenses out of a hat? you WILL GET some advantage, but, at first blush, it wone be enough of an advantage, to overcome the slight loss of using a second lens. But, once you get “somewhere”, you can go back and “replace” one of those 2 lenses? with two other lenses.
your new THREE lens solution? will be the same focal length as the ORIGINAL single lens ! and each lens will shape a little of the beam down along the way… THAT overcomes the slight losses of using more lenses…
you ray tracing model will not be perfect in real life? but… “hand tuning” with a yardstick and “helping hands” holding lenses… will guide you with practical real world results to guide you quicker. cigarette smoke blown in to allow you to SEE whats going on, and moving a piece of white paper back and forth to measure the diameters of the cones of light? will tell you where you are “losing” at each small step thru the lenses.
YOU know “who” the brains on this site are? Who dont poop their pants when faced with a little algebra? you guys just need to start LOOKING at the problem from THIS point of view… its the keys to the kingdom, and its not as hard as it looks, once you start playing and hand tuning the solution…
for the record? i went to a small state university, that wasn’t very “highly rated” when i got out into my own professional field when young. Smug men were always showing off their “much better school” degrees and making fun of me. You know what? I programmed them “under a table” and fried them…
You guys are all standing around ina group, looking up a TREE, wondering how to get up to the upper branches? I come along, and i am looking at the tree from the other side? I have a COMPLETELY different VIEW of the “problem”…
“hey guys! we can climb up right over here! come look!”
you guys can build better than me, there are MANY guys way better than me at the math. Your just not looking at the problem fromthe correct point of view. THIS is the correct view.