The focal length of the lens determines the size of the projected spot.
The longer it is, the smaller the spot is, and assuming constant F ratio, higher intensity.
Same lumens + smaller area = higher intensity.
If you don’t keep constant f-ratio, and the diameter stays the same, having a longer focal distance will STILL increase the lux.
I calculated it here: The "optimal" lens for use in thrower flashlights [mistake fixed]
Maybe you want to link that post you’re talking about?
The entire point of me comparing them is to point out that a smaller diameter lens+wavien collar will still get higher lux than a large recoil reflector.
Where did you get the 50% from? I was looking for tests that showed how many lumens you get when using a collar as compared to stock lumens.
If you can link a source that would be great.
This is based on the false assumption that all that matters is the front area of the optic.
I think you can see clearly that it is false by simply comparing an aspheric flashlight to a reflector flashlight with the same front area.
The throw will depend on the intensity, which is determined by a lot of factors such as LED spatial distribution, distance from the LED to the optic’s surface, angle between the LED and the optical surface (for a single ray) and also the reflection/refraction of the optic.