The Effects of Reflector Design and Lamp Orientation

[Rox]

someone wrote:


The light going from a point source lamp arc directly to half of a 220 mm fl condensor fresnel forms a triangle with a 220 mm base and a 7.5" height. By Pythagorean Theorum, the hypotenuse is 291 mm. Taking the arcsine of (7.5" / 291 mm), we get a half angle of 40.9 degrees. So the total arc of light falling on the 15" fresnel is 81.8 degrees. This is 81.8/360 = 22.7 % of the light coming out of the lamp. With a 90% reflective aluminum spherical reflector behind the lamp, the fresnel will also get another (22.7% * 0.9) = 20.45% of the lamp's light


I say:
well it is not correct. Here 360 is like all the light that bulb gives, but thats erroneus. Lets say we have 400W. then we have like 32000 lumens, if we apply 40% of 32000 lumens, we have 12800 lumens. That is too much light .

the problem is that the 360 degrees are in plane. You need to use stereoradian to measure the aperture of light cone (solid degrees?, it is "angulo solido" in spanish). I believe you will never get 25% of total lumens in the best of the cases, just using a spherical reflector.

now, does somebody know what is the focal of a spherical reflector? (what is the definition of focal for this refplector?)

[Guy Grotke]

>You need to use stereoradian

I wrote that estimate, and I agree with you. I made a simple two-dimensional estimate to compare the arc of light that hits the fresnel with a spherical reflector versus an elliptical reflector. To calculate the true number of lumens you would need to use a three dimensional calculation and you would also need to account for the rectangular shape of the fresnel.

But I was not trying to do that. I was just pointing out that the model of a spherical reflector system used in an advertisement was deceptively bad.

Spherical reflectors have a center of curvature. (All points of the reflector are equidistant from that point.) If you try to use it as a very bad parabolic reflector, then some of the light will focus at a point half the distance to the center of curvature. That is called the focal point. It is only useful if you are making a telescope. For a projector, we always put the lamp arc at the center of curvature.

[ace3000_1]

For a projector, we always put the lamp arc at the center of curvature.

R1, its inside radious.

Trev

[Rox]

then you mean that if we have paralell rays goint to the spherical reflector, they somehow focus in r/2? cold you xplain this "somehow"? whats the criteria to accep the focusing is at X?

in parabolic shape it is matematically true.
X^2=shape 0.25=focus point.
6X^2=shape 0.041=focus point.

PX^2=shape F=1/4P generic focal point.

could you tell me the maths behind spherical reflector´s focal?

[ace3000_1]

they somehow focus in r/2?

R2 is taken from the outside of the reflector not the inside curvature. I dont think that that manny will reply to what your asking as its been discused manny of times before.

The focal point is measured with paralelle rays, this is its stated focal, however for it to be run with the light converging back to its source you need to run the lamps arc at its R1 spec, this is the inside radious of the curvature, or basically 2x the stated focal.

http://www.awi-industries.com/relectors.html

Trev

[Rox]

actually i would only use spherical reflectors that way (r1 centerd light) but would like to understand this focal teory, i guees nobody will tell me .

paralell rays will never get focused at a point, we are talking about spherical, not parabolic.

ace, didn´t you receive my 2nd email?

[ace3000_1]

paralell rays will never get focused at a point, we are talking about spherical, not parabolic.

Who said anything about that? you can focus paralelle rays to a point both with lenses and reflectors, just run it in reverse.

ace, didn´t you receive my 2nd email?

Ya i did i had a funeral.

Trev

[Rox]

sorry about that.


now, i mean spherical reflector althought your last link shows a picture where is focusing paralell rays to a point, it is not true, if it was true, you would have parabolic reflector, (thats the therory behind them).

i know what people do is aproximate spherical reflector to a parabolic when using to close to it. but if you want to focus paralell rays, just go for a parabolic one, forget those spherical.

did you receive any price from those manufacturers? lets say a eliptical for instance...

[ace3000_1]

sorry about that.

Np Rox, thats the way life goes, we come we go

i mean spherical reflector althought your last link shows a picture where is focusing paralell rays to a point, it is not true, if it was true, you would have parabolic reflector, (thats the therory behind them).

No it is true, thats how they measure the focal, why in that way, who knows, i guess for acuracy and aplication dependencies. I agree if you want paralelle rays you use a parabolic reflector not a spherical.

did you receive any price from those manufacturers? lets say a eliptical for instance...

I got sphericals right here, 18 wheeler is running a group buy on the ellipsidals , can be found here:

ellipsoidal reflectors group-buy?

I have got both and a parabolic, hands down im never going back to a spherical after trying the elliptical out. The sphericals are good for large lcds thats about it.

Trev

[Rox]

just one question more, in that spherical picture, why does he stop drawing lines there? he could have drawn a few more. have a look to the image, you´ll see it is half the spherical reflector used.

how much did you pay for your eliptical?