Formula For Light Beam Angle?

[bristle]

There is a formula for calculating the beam angle of lights -

α = 2arcCos ( 1 - Lm ÷ ( 2πCd ))

where Lm = maximum light lumens
Cd = maximum light candela

This formula applies ONLY for light beam angle where the beam intensity (candela) has fallen off to 50% of the maximum candela intensity.

But, there is another light beam angle known as the "field angle" which is a bit wider than the main light beam angle. This field angle occurs when the beam intensity has fallen off to 10% of the maximum candela intensity.

As far as I'm aware, there doesn't appear to be a formula to calculate the field beam angle? At least I haven't as yet found such a formula by searching the web!?

So, is there a formula for calculating the field angle of light beam? If so, what is it please?

 

[bristle]

I thought this would be a tough question to answer.

Apparently there is a formula for calculating the "field angle" (where intensity has fallen to 10% of maximum), but I have yet to find it.

There is another question also. Why does the formula α = 2arcCos ( 1 - Lm ÷ ( 2πCd )) apply to only 50% of light intensity and not apply to all of the beam where the intensity drops off to 0!?

I sort of understand how the initial formula was derived. The formula is just a rearrangement of the equation Lm = 2πCd (1 - Cos ( α ÷ 2)). But I just can't see how the 50% figure is determined during the derivation of the equation/formula!!??

So there are two questions now -

1) How is the figure of 50% intensity determined/defined for the corresponding beam angle formula α = 2arcCos ( 1 - Lm ÷ ( 2πCd )) ?

2) What is the formula for calculating the field angle where the beam intensity is down to 10% ?

I have asked a similar questions elsewhere but have had no (tangible) results.

 

[LEDphile]

There aren't any general formulas for calculating beam or field angle from device candela and lumens, simply because different beam profiles can give different beam and field angles for the same peak candela and lumen values. Beam profile is determined by the design of the optical system, and isn't something you can determine without measurement (or simulation if you have the optical design files).