How calculate thrower magnification?

[eatkabab]

For a projection of the surface of the LED.
How do you calculate the viewing angle/projection angle/magnification?


With a 1.4mm (2mm^2) diode surface, I measured that a 15mm focal length lens gave me a roughly 12deg projection angle.

Using the same 1.4mm diode, a 10mm FL produced about a 24deg viewing angle.
(actual projection being about 4X as large as the 15mm FL)

What must the FL be to give me a roughly 12deg projection angle on a 1mm (1mm^2) diode?


The following formula is the best thing I could find, but it yields slightly different numbers than what I'm actually seeing.
Viewing angle (alpha) = 2arctan(d/2f) where d=projection diagonal and f=FL

Using a diode width of 1.41mm and FL of 15, the eqtn gives me an angle of 5.38deg. Why does my actual physical test vary?
It seems that if I use the formula 4arctan(d/2f) it is almost completely accurate to my real measurements...

 

[Walterk]

Here is a thread about calculating on Led's combined with Aspheric lenses.

Here is a thread about the apparant die-size, it might explain someting about the size of the die of the diode, and the dome on top of it.
It also has some information about TIR on the end.

For how to calculate the angle of the spotsize:
It's best to try in real life as you want a specific beampattern.
Instead of calculating I find it easier to use drafting software.

Two notes:
1 - The sketch is using the die, but that is wrong, you should use the 'apparant-die-size' as it is perceived by your eye, projected on the dome.
2 - The optical center of the lens is not at the first plane, but somewhere in the middle of the glass mass, towards the curved side.

So the sketch mainly shows how you can derive an indication for the beamangle.

Note: I see I posted this answer in the wrong thread earlier.
Edit: Updated link for 'apparant-die-size-thread'

 

[eatkabab]

Here is a thread about calculating on Led's combined with Aspheric lenses.


Note: I see I posted this answer in the wrong thread earlier.

This article you wrote are excellent! Thank you very much. (the link to apparent die size is the same though...)
and I don't think you posted in the wrong thread, I believe I just incorrectly started a new thread. There should be a way for the thread creator to delete the thread within an hour or something.

 

[Walterk]

I corrected the double link anyhow now.