i am building a real “math model” for this hobby, i have had it up to here with meaningless terms like “throw”, and invoking non existing laws like “absolute throw” which somehow trumps established mathematical principles like “F number”.
aspherics “throw” better than “plano convex” because of…. an opinion. I say? Let him who hath understanding, reckon the number of the beast, for it is a human number… and that number is math.
i reserved the top 5 posts, anyone and everyone can do whatever they want in the rest to follow. when it becomes the inevitable train wreck of misinformation i have seen befpre on cpf? i will copy my work over, and continue fresh, till i am done. its my thread, i will do what i want.
everyone is free to say anything, positive, negative, or neutral. my thread, my rules. YOU can make YOUR thread? to demonstrate the superiority of “throw” and “absolute throw laws” which i claium dont exist, at l;east not mathematically and quantifiably.
first order of business? ground rules… i will be starting with well established LAWS, not opinions. nor hearsay. nor moon bat units. my five reserved posts are MINE, do anything you wish with the rest, i dont care.
i will build, only on laws, and on sound mathematics. algebra, trig, geometry should suffice. i might solve equations, but, it will be held for any peer review. if i do an “einstein” and divide by zero? i expect to be set on fire for it.
FIRST THINGS FIRST
we cant trust chinese focal length claims. we can measure the diameter, but, we cant trust their focal length claims.
1) with a THIN LENS, of standard t-h-i-n bi-convex construction? of either glass or plastic, your choice, does not matter… coated or uncoated, any diameter… biconvex? is the ones shaped like THIS ()
2) you take that thin biconvex lens? and point it squarely at the full moon, simply because thats the furthest “infinity object” available to everyone on the planet, with enough fine detail you KNOW when its in perfect focus.
3) you take a flat piece of white paper, and holding it square, you move the lens in and out, until you have drawn upa perfect in focuc image of the moon on the paper. you might wanna make a “jig” out of a yardstick, and wen you are done? measure the exact distance from the MIDDLE of the EDGE of the thin biconvex lens? back to the squared up piece of white paper.
4) in millimeters, this is the “focal length” for THAT lens.
5) if you are REAL careful? there is a formula for “subtracting off” when you focus up at shorter distances… which works, but, its harder. nothing can be as simple as focusing up the moon perfectly in detail on flat squared up white paper, and THAT being the result.
6) i dont care what the manufacturer might have told you, i dont care what might be on the side of the box, whatever…THAT measurement, IS the focal length. thats the “infinity focus”, which “is” the focal langth.
7) focal length changes in practical use… it still “is” that exact focal length, but only at “infinity distance”, which is a set distance for different focal length lenses with different diameters (governed of all things? by the almighty F NUMBER)
8) at this “infinity distance” everything after that, is still in perfect focus… it could be 40 feet, it could be 1200 yards… depends on the focal length and the diameter (which is… the F NUMBER)
9) at any shorter distance? some distance closer will get out of focus, and will only be IN focus further out for a certain distance)
10) some other terms you will see used? back focal length = distance from the back edge of the lens, not the side exact middle. also effective focal distance, infinity focalpoint, practical focal distance, etc etc… none of that matters.
to recap? you take a THIN biconvex lens, you draw up an image of the moon carefully, fully squared up and straight, and the measurement from the middle edge to the paper, if all is atraight and squared up? IS the “focal length” for THAT lens. you can easily get within 1% of the “correct” answer if you are careful and use a “jig” you make… this focallangth, and no other, is the focallength AND is also properly called the “infinity focus” for that lens.
now, if you can find a different lens, of any diameter, and of any f number? and it is a thin biconvex, and it gets the exact same measurement? then they both share the same focal length. period.
11) these are not my opinions, these are not my terms for these things, these are well established laws. any idiot can measure the diameter of the thin lens, and now you KNOW, not think, what the FL actually “is” and mathematically too.
if you want, go on and calculate the F number of THAT lens, you obviously have the diameter, and you obviously now have the correct FL… FocalLength-mm / Diameter-mm = F number (unitless, the units cancelled out)
so, we now have a thin biconvex lens… and we know the actual focal length, and we know the true diameter, which yields the F number.
time for the second FACT. its not an opinion, its not a hunch, its a law. (you might notice a trend here, this trend will hold) now, it does not matter WHO has WHICH thin biconvex lens at their house, thats the funny thing about math and the laws of physics.
LAW: any lens, of any shape, diameter, type of glass or plastic, coated with anything from cat poop vapor to something NASA puts on the space shuttle windows? ANY lens you find, that has THAT measured focal length? WILL focus up to the moon and yield the same FL result. The PROBLEM is, anything other than a true thin biconvex lens will take its measurement from “somewhere else on the lens” some kind of reference or “datum point” of some kind… as we now have to trust the manufacturer.
and i dont trust anyone except math, rules, and laws.
another law: take an emitter, ANY emitter… focus it up, at a known distance. just like the moon? has to necessarily be square and straight and flat line. you cant go up or downhill, to a straight wall and project a rhomboid…
the emitter should be dedomed, and you know the exact measurements of the emitter. you also now know the exact distance to that wall you focused up the emitter on, the farther the better. i suggest 50 or 100 yards, meters, whichever.
the law is, and its not a polite hunch or suggestion? the law is, an emitter of THAT EXACT SIZE will “focus up” onto the wall at known distance? to a certain size. you go UP to the wall, and you MEASURE IT. its called science, and you write it down. if its not square? you write both down. accurate records keeping,along with accurate measurements, are the hallmarks of proper science and mathematics.
everyone agreeing on the PROPER terminology, invoking only well established “actual” laws? is all that can be accepted. We are going to steadily BUILD what we need. we are not going to THINK we have answers? we are going to KNOW.
as right as you may well be? what you heard from this “really smarty guy” on this or any other website? i cant use it. i trust you, but, trust is for whoosies in the world of math and science. we want to PROVE what we do, every step of the way.
only well established laws and accepted equations are suitable. because i am going to eventually solve equations for things i want, and that will serve asa proof, as long as i dont violate any laws of algebra, geometry, or trig. and by the gods if i screw up or mis-state some optical concept? i expect to be jumped on. it.. called… peer.. review.
NOW, that out of the way once again? you will notice i said to take YOUR thin biconvex lens? of YOUR focal length? and focus up a DEdomed emitter, onto a wall, straight line, and measure the projected SIZE of the emitter made. neatness and accuracy counts, both in diustance/angle to the far away wall, and in actual measurement of the PROJECTED/FOCUSED emitter image.
notice i avoidedf the loaded word “throw”. It is a meaningless term, it has no quantitative value. we throw rocks, we FOCUS or PROJECT light from an emitter. If you can show me a “absolute throw” L-A-W ? i wioll certainly use it as a “given”, hearsay so and so said so and hes really smart? does not count. sorry.
also? the fact that you can build a better light than me? doesnt make your opinions count in any way. you dont get to make up a word, or a made up law, drop it authoritatively on newbs, and start the made up law circulating. the days of THAT puppy sh!t flying are over, at least for me.
congratulations, you are now a 100% certified scientist. This might well be your first accurate measurements, and your first sound application of discrete repeatable and sound mathematical and physics principles. crack a beer, you have earned it.
now, what can we derive useful from this? for starters, a certain size emitter light source, will focus up on a wall a certain distance away, to an absolute size. that size is entirely dependent upon only the focal length of the lens.
we have a known focal length lens, and we know exactly what size emitter it projects onto the wall. Believe it or not? using the proper equation properly… allow us to take a new to us and UNKNOWN focal length lens? and run our known size dedomed emitter thru it, onto the same wall at the same distance? and we simply measure accurately the size of that lenses projected emitter? and a few taps on the calculator will tell us exactly and precisely the focal length of the lens.
its a LAW. it will no longer depend on what someone wrote on the website they sold it from, it will nolonger depend opn the conmparative hunches, and this lens did that, and its almost the same sioze, so it seems to be about…
we will KNOW, not think… what the focal length of A-N-Y lens is, easily, from that time out.
i am done for tonight, feel free to scorch me, post funny pictures of me, whatever. i wont hit any rude buttons. do it in this thread all you want. i only need my five posts for now, i reserved them. do what you want, or ignore me. does not change the laws of math and physics. i will dig up the “white paper” i used… and we will see how this plays out.
i expect this to get tested, with YOUR thin lenses, and YOUR unknown aspherics. the only thing i dont have down cold? is whether this one thing is stated in “half angles” or “full angles” the white paper left that out? but that doesnt matter… i will be either half predicted size, correct, or double predicted size… which will easily let us “prove” which is correct.
i am sick as a dog, i am tired, and i am in serious pain… i need a hot shower and to stokje the fire up, the chills are coming again… but i “throw” rocks… i project and focus up light thru lenses. the difference? is huge.
you see, we are going to take a KNOWN lens of KNOWS focal langth? and project an emitter and measure it, and run this “all known” thru the equation… once we establish that the PREDICTED aize of that emitter that got projected matches? we will have PROVEN that equation works… and we can then freely APPLY IT to any lens of any kind, and back solve the same equation to DERIVE the true and correct focal length for the unknown lens.
you see, once we have proven something? only then can we use it. good night and god bless, i will work further on this at my convenience and not until. YOU are free to “prove” your set of laws, any way you want. i have said nothing up to now? that i dont stake my reputation on, to any degreed optics pro. these are not opinions, these are facts.
Throw is dead… long live focus and projecting.
again? the fact you can build a cooler light than me, or that you bought way cooler lights than i can afford? changes nothing i have stated, which is all provable a-c-c-e-p-t-e-d fact. I intend to take it, to the point that, you will be claiming the earth is flat.
With enough black coffee and cigarettes? all things are possible…
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