To get an idea of the focal length look at the shape; if it has that extreme curve as the sipik sk68 lens, the lens has about the shortest possible focal length for that size. But, the bigger the lens, the longer the focal length is for a comparable shape (is this clear?). Some of the bigger aspheric lenses you find in cheap flashlights are less curved. This gives an impressive small hotspot when zoomed in, but the hotspot is not very bright because the lens is farther away from the led when focussed, and so catches a smaller proportion of the light compared to a more curved one with shorter focal length. (hope this makes some sense to some :-) )
so say you have two aspherics the same exact diameter, say 48mm. set them on a table, and say one is 12mm at the highest point and the other is 25mm. the 25mm will have a shorter focal length and more intense hotspot while focused.
think i got it…?
Almost, but unfortunately, although the one with shorter focal length will catch more of the led's light, it projects it into a larger hotspot, so the brightness does not neccesarily go up much. But you do get more light out of your flashlight.
Is there a formula relating radius if curvature to focal length?
Edit- for a concave mirror R~2F so to get a focal length of 10mm you’d need a radius of ~ 20mm. How close is this for tir optics?