# 6" Long Reflector on E21

I am only talking about parabolic reflectors of differents sizes. Luminous intensity (throw) only depends on the frontal surface area (a flat circle with a hole in the middle) and the luminance of the light source (and some losses because of reflectivity, transmission etc.). The divergence doesn't affect it in a meaningful way. Try the calculators I linked to above.

We have had this discussion multiple times over the years here in the forum and in other forums. Here's a German explanation (use google translate).

Also, you don't need to consider any special equations for specific LEDs (unless they have a dome and a very untypical emission angle like 80° etc.). All LEDs without a dome are lambertian emitters and thus all work the same in conjuntion with reflectors.

The maximum luminance values of many LEDs can be found here. You can use those to calculate what is possible with a given reflector (or optic).

All of the intensity measurements that this community has done support what the driver says. The beam intensity is equal to the emitter luminance multiplied by the frontal area of the reflector or lens.

There have been many discussions of this. Maybe the first thread introducing this concept to the community is the one by Dr Jones.

JoshK, are you saying that you can get more beam intensity from a smaller diameter reflector than a significant larger one just by making the reflector longer? If so take some measurements and see.

Try out the formula above. Read the threads. Build some lights and measure them. It will all work out. What you are stating is a common misconception, like I said.

Why do you mention a toothpick sized reflector? It obviously needs to be wider than the die of the LED as you also mention.

## Example:

Lets say you have two identical LEDs with a luminance of 200cd/mm2. Each has a die with an area of 1mm2.

Lets also say that you have two parabolic reflectors. Both have an LED hole with a diameter of 10mm. Both have a center depth of 20mm. Both have an aluminium coating with 90% reflectance of visible light. Both have an ar-coated glass lens with 96% transmittance (typical chinese flashlight quality) on top.

Reflector A has an outer diameter of 20mm.

Reflector B has an outer diameter of 50mm.

Now you want to find out how far you can see at night with these two lights (the ANSI range of a flashlight). To calculate this distance you need the luminous intensity [candela]. To calculate luminous intensity you need to calculate the frontal surface area of both reflectors.

### Reflector A:

refl_a_area = area_circle - area_led_hole

= (20mm / 2)2 * pi - (10mm / 2)2 x pi

= 314.2mm2 - 78.5mm2

= 235.7mm2

refl_a_lum_intensity = luminance * refl_a_area * transmission_losses * reflectivity

= 200cd/mm2 * 235.7mm2 * 0.96 * 0.9

= 40,729cd

Note here that cd is the same as lux@1m.

refl_a_ansi_range = sqrt ( refl_a_lum_intensity / 0.25 Lux )

= sqrt (40,729lux / 0.25lux)

= 403.6m

### Reflector B:

refl_a_area = area_circle - area_led_hole

= (50mm / 2)2 * pi - (10mm / 2)2 * pi

= 1963.5mm2 - 78.5mm2

= 1885mm2

refl_b_lum_intensity = luminance * refl_a_area * transmission_losses * reflectivity

= 200cd/mm2 * 1885mm2 * 0.96 * 0.9

= 325,728cd

refl_b_ansi_range = sqrt ( refl_b_lum_intensity / 0.25 Lux )

= sqrt (325,728lux / 0.25lux)

= 1141.5m

As you can see, the depth of the reflector has no effect on the results.

I think I see where our points of view differ. Let me explain it using your calculator instead of my modelling software.

Here’s a simple 4” reflector. We will use this as the base. It will be visible in the background of the other pictures.

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Now when I say “a wider function” or “wider mathematically”, I mean this:

All other things equal, it becomes shorter, and reduces the “degrees of light captured”. This is why the diameter (and front surface area) of the reflector is unreliable as a measure of throw.
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Now when you say wider, you mean this:

I hope that all makes the sense I intended it to.
I learned this stuff in my college class Non-linear Equations. So I think about it starting from the equation. I know that’s not the most intuitive.

You are correct it’s not just the outer diameter that matters, it’s the frontal area. To find this you subtract the area of the small inner circle from the area of the large circle. But because of the way area grows with diameter the inner circle area is always relatively small. So making the reflector shallow, within reason, doesn’t have a huge effect on the frontal area.

This is not correct. Most flashlights use reflectors with similar collection angles. So would you expect, for example, that the BLF GT reflector would make a larger less intense spot than a C8 reflector, with the same LED? This is obviously not the case.

Ok, I have been working on this and discovered an error on my part.
When I was making changes I was accidentally allowing the focus point to shift. But because it didn’t shift much, it went unnoticed. The error was even there in the reflector I printed.

So I came back to correct my mistake and hopefully explain this clearly.
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For parabolic reflectors, you only have 1 thing you can change about the geometry. That’s the vertex location. (The vertex is a theoretical point behind the LED). The effect of moving the vertex away from the LED is more total offset of the reflector surface.

For thrower flashlights, you want enough offset to properly fit the reflector around the LED, and that’s it. Then the only choice that’s left is where to chop off the infinite geometry. You could call this the “diameter”, like The_Driver does… But this causes confusion, because as you see in the pic above, diameter isn’t forced to increase when you fiddle with the vertex. Diameter can be kept the same just by chopping off that infinite geometry sooner. Again, see pic.

You need to mathematically show how you derive the luminous intensity (= throw). That's what I did (even accounting for typical losses!). The size of the inner opening in a reflector has a very small impact on the overall frontal surface area (because the area of a circle increases with the radius squared). The radius (and thus outer diameter) is the deciding factor.

You have switched to using the term "performance" instead of "throw". How can you quantify that?

Do you own a lux meter? You could try doing some measurements with it.

I think the real issue here might be your understanding of what throw is?

We are talking about throw, so I don’t see an issue with the word performance, but I edited the word as you wish.

I didn’t say your math was bad. It looks good to me because you used “area” and subtracted the flat area around the emitter. It’s the fact you say front diameter is all you need to know that causes confusion. IRL it works well, but it causes confusion in discussions.

Saying throw is based on “area_circle - area_led_hole” sounds good to me. Saying it’s based on the front diameter only, confuses people. It confused me.

I really cant see how a lux reading at 1 meter gives any meaningful information on throw unless the divergence of the beam is taken into account also

for example i can setup a reflector that has a wonderful tight hot spot at 1 meter with very high lux reading but by 5 meters it will have flooded like crazy

Alternatively i could setup a well collimated beam with the same lux at 1 meter but it will still be concentrated at 5 meters

Obviously the later is going to go further

Maybe im just being thick here and missing something?

Well in this discussion we are only talking about parabolic throw reflectors, so in all cases the hotspot is mostly collimated. So they all act like lasers of varying area and lumens.

Though it’s also true that smaller reflectors suffer more from the LED not being an exact point source.

Ah ok so the lux at 1 meter to throw distance assumes a near collomated beam… that makes sense

it’s just i’ve never seen a torch beam that is even close to truly collomated or what id call properly collomated even the W30 diverges a fair bit but im used to working with lasers so perhaps i expect to much

I’d like to say thank you for the debate. Especially to The_Driver. If we hadn’t went on about this I wouldn’t have discovered the error in my 3D printed reflector geometry. And I also learned a better way to think about parabolic reflectors.

So I fixed the geometry error and supersized it!
It looks good with some sanding and painting. The took on an orange-peal look though. I will fix that some other day with a bit more sanding. I also had a problem with the 6” wide reflector bumping the limit switch on the printer. So the end of it is kind of messed up.

I had to make due with an E21A because that’s all I have on hand. I also chipped the phosphor last night.

Check it out

That is a rather impressive beam you have there

Indeed.

Dang it , I can’t see any pics in this thread

If the pics don’t work, wait a few minutes and refresh. Dropbox images can be flaky like that.

I know. It’s like having a BLF GT for the cost of a 10 hour print and some spray paint.

Nice beam!

Can you maybe try printing a wide, but very flat reflector? :)