I'm not exactly clear on what determines the focal length of a lens. I assume it's curvature or something like that?
In an event I have two small aspherical lenses. One is made of plastic and one out of glass. Both have a diameter of approximately 20 mm. The focal lengths are not the same however. The plastic lens has a shorter focal length and therefore projects an image of a larger emitter. The glass lens with the longer focal length projects the smaller image which of course will take longer to diverge.
The longer focal length lens should receive less light from the emitter than the shorter focal length lens. As far as throw is concerned however isn't the advantage generally going to be with the larger focal length.
My reasoning is just that increasing the diameter of a reflector or increasing the focal length of an aspheric (which generally comes with an increase in diameter at some point I think) has a direct (linear) relationship to throw whereas an increase in light output has a squared relationship to throw.
So, I would think the loss of brightness from being further away from the emitter would always be more than offset (only considering throw) by the direct increase in throw from increasing the focal length.
Is this factually correct or not?
Thanks.
One large factor in play but not considered is the viewing angle of the LED itself.
Optimizing the lens choice for a particular LED is a balance between the size, BFL (back focal length) and LED viewing angle.
It is considered (by me) and that's another reason for using the XR-E with its narrower beam angle when paired with an aspheric lens.
Focal length is determined by curvature and refractive index: the more it's curved, the shorter the focal length; and the higher the refractive index, the shorter the focal length.
Focal length itself does not have any influence on throw. Comparing a short fl and a long fl lens, the short one catches more flux (light) and projects a larger image of the die; but that image has that spot has the same intensity as with the long fl lens. The additional flux caught goes into the bigger spot size, not into a more intense spot. Neither is it less intense.
Shorter fl -> bigger spot with more flux (lumens), but same throw.
Throw is proportional to lens diameter. Twice the diameter means 4 times the apparent lens area, which in turn yields 4 times the spot intensity, which results in twice the throw.
The LED dome (viewing angle) itself does not have any influence on throw. XR-E's LED dome works as an additional lens, sort of pre-collimating the light (giving it a smaller viewing angle). In combination with the main lens that results in a shorter effective focal length, i.e.: bigger spot with more flux (lumens), but same throw.
So the best thing would be a big diameter, very short fl lens, but there's a limit to it: Short fl lenses have to be strongly curved, and you can't do that over a big diameter. As a rule of thumb, with a single aspheric, diameter can be reasonably made ~1.5 times the back focal length (measured from the flat back side), not much more.
I used the word "itself" above; by that I want to express that there is some indirect influence when dealing with non-ideal optics, i.e. lens errors/aberration.
Thanks for clarifying the focal length thing for me. I knew that in reality larger diameters (and surface brightness) were what throw was all about but with aspherics I wasn't certain if it was strictly diameter or if it was focal length with ended up controlling diameter.
Then I ended up with two aspherics of the same diameter but different focal lengths and wasn't sure exactly how focal length changed things other than I could see the emitter image getting smaller with the longer lengths.
Nice to know that the intensity is the same with same diameter aspherics and it's only the image size that is changing.
Out of curiosity, has anyone compared the KD 28mm optic and the DX 28mm optic? I would suspect that they are the same thing, but I don't know.