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I'm building a light source for photography and I'm trying to calculate the focal length for a lens that will give me a 40 degree (full width) cone beam from a LED emitter.

See attached image.

[PLAIN]http://dl.dropbox.com/u/2301/LEDOpticDrawing.jpg [Broken]

The emitter itself measures about 0.5 x 0.5 mm and sits inside a 5.5 mm x 5.5 mm package. The plan is to mount plano convex lenses on top of an array of these emitters. I'm out of my element here and clearly in need of help :-). This is what I've tried...

First I tried to calculate using angle of view:

Edim is the emitter size: 0.5 mm

f is focal length

Beam angle = 2 * arctan(Edim/(2 * f) * rad

Solving for f, this gives a focal length of 0.7 mm. The result looks unreasonable. If I try to calculate what such a lens would look like using the formula 1/f = (n – 1)/R, I get a 9 mm thick 5.5 mm dia lens.

Next I tried to get to focal length via numerical aperture:

D is lens diameter: 5.5 mm

f is focal length

n is refractive index: 1.585 (polycarbonate)

Beam angle = arcsine( (2 * (D/f)) / n) * rad

Solving for f, this gives a focal length of 10.8 mm. Can this be correct? Frankly, it seems larger than I expected.

Does the NA formula assume that the emitter is positioned at the focus point? How can I take the distance from the emitter to the lens into the formula? I will need to mount the lens very close to the emitter, ideally 1.4 mm from the actual emitter surface.

M

See attached image.

[PLAIN]http://dl.dropbox.com/u/2301/LEDOpticDrawing.jpg [Broken]

The emitter itself measures about 0.5 x 0.5 mm and sits inside a 5.5 mm x 5.5 mm package. The plan is to mount plano convex lenses on top of an array of these emitters. I'm out of my element here and clearly in need of help :-). This is what I've tried...

First I tried to calculate using angle of view:

Edim is the emitter size: 0.5 mm

f is focal length

Beam angle = 2 * arctan(Edim/(2 * f) * rad

Solving for f, this gives a focal length of 0.7 mm. The result looks unreasonable. If I try to calculate what such a lens would look like using the formula 1/f = (n – 1)/R, I get a 9 mm thick 5.5 mm dia lens.

Next I tried to get to focal length via numerical aperture:

D is lens diameter: 5.5 mm

f is focal length

n is refractive index: 1.585 (polycarbonate)

Beam angle = arcsine( (2 * (D/f)) / n) * rad

Solving for f, this gives a focal length of 10.8 mm. Can this be correct? Frankly, it seems larger than I expected.

Does the NA formula assume that the emitter is positioned at the focus point? How can I take the distance from the emitter to the lens into the formula? I will need to mount the lens very close to the emitter, ideally 1.4 mm from the actual emitter surface.

M

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