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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:

  1. 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)
  2. They are very expensive
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    $\begingroup$ About the 'they are large' issue: you can always cut the surplus away. It's still going to be a lens, just one that's collecting less light. The image will not be as bright, but it will actually be easier to focus. $\endgroup$ – relatively_random Mar 4 '20 at 8:26
  • $\begingroup$ "We are not able to use a laser light because of safety issues" — don't you think that if you succeed in putting the same power as one from the supposed laser into a similarly small point, you'll get exactly the same safety issues? The main safety issue of lasers is the ability to focus large power into a very small point. $\endgroup$ – Ruslan Mar 4 '20 at 8:36
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    $\begingroup$ @Ruslan Not exactly. The lens-focused light is dangerously intense only at the point of focus. Laser is dangerous along its entire flight path. If you remove the sheet and walk behind where it used to be, a laser can still damage your eyes. A focused light won't. $\endgroup$ – relatively_random Mar 4 '20 at 8:38
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    $\begingroup$ @relatively_random well, if you enclose the laser behind the focusing lens, it's no different from a well-focused high-power LED. $\endgroup$ – Ruslan Mar 4 '20 at 8:40
  • $\begingroup$ @relatively_random actually, if the lasers in question are laser diodes, then they are almost as safe as LEDs, since they are not collimated unless one tries to do it. In particular, diode-based laser pointers always have a lens on their exit aperture. $\endgroup$ – Ruslan Mar 4 '20 at 8:54
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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!

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  • $\begingroup$ Thanks for your response! that is helpful to our thought process. It's good to understand that our exact design issue makes it impossible to get exactly what we want. We're going to play around with using two fresnel lenses as soon as we can get our hands on some, we'll post an update! $\endgroup$ – Emily Johnson Mar 4 '20 at 21:19
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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.

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  • $\begingroup$ Thank you! That makes sense now why it's so much bigger. We might need to "fold the light path" as you put it, which I see can be difficult over a short distance $\endgroup$ – Emily Johnson Mar 4 '20 at 21:21
  • $\begingroup$ Another option being two lenses, one with short focal length and one with long. A telescope! $\endgroup$ – Gilbert Mar 5 '20 at 15:38

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