Is it possible to use fresnel lens(es) to focus an LED light on a headlamp I was hoping that someone would be willing to offer any insight or guidance they have on a project that I am working on. We are trying to use a lens mounted on a headlamp to focus a plain white light to as small of a point as possible at about 2ft away. We are not able to use a laser light because of safety issues. We tried using a single convex lens but we were not able to focus the light enough. 
Our current thought is to use a fresnel lens. These is our issue: The lens needs to be very close to the light (no more than half an inch). We've been playing around with a cheap reading magnifier to focus the light, but we have to move the light a foot away to focus the light. 
Our question is that would we be able to stack multiple fresnel lenses together to achieve the focus length we need (we've determined that's roughly 300mm focal length) at a close distance to the light. Single fresnel lenses with around a 300mm focal length seem to have two problems: 


*

*They are very large (we would need a lens that is not much more than a few inches length and width to fit on a headlamp)

*They are very expensive

 A: A simplistic way to think about how a single lens (focal length $f$) works is as follows.
It will:
 1. Focus collimated light, of a single color, to a single point located at distance $f$.
 2. Focus light of a single color, diverging from a point source located at distance $2f$, to a point at distance $2f$ on the other side of the lens.
The reason lasers are nice to use for focusing is that they are easy to collimate and (typically more-or-less) monochromatic. So you can easily achieve a nice, diffraction-limited spot with a single lens.
If, on the other hand, you have a broadband, extended, diverging source, then focusing becomes more difficult. The primary way to achieve a small focus is to spatially filter the light by, e.g., collimating it over some distance with apertures (and throwing out all the light that’s going in the wrong directions). But from what I can tell, this isn’t going to work for you.
So, be advised that you likely can’t achieve exactly what you’re hoping for. However, two Fresnel lenses will definitely be better than one. Two, with a variable distance, would give you more degrees of freedom to find the optimal focus at the desired distance. Let us know how it turns out!
A: Simply put:  If the lens is 0.5 inch from the LED and the point where you're concentrating the light is 24 inches away, the focused image of the LED will be 24/0.25 = 96 times larger than the LED.  You can't escape that with a simple lens.
To make the focused image smaller, you need to increase distance of the lens to the LED.  Double the distance, and the spot size will be reduced by 1/2.
The only possible escape is to use a complicated lens system that folds the light path.  I'd suggest starting with a simple system: get a ~ 250 mm lens and put it slightly more than 250 mm from the LED.  If you need more light, use a brighter LED.
