What is the mathmatical equation for calculating the intensity of
light (in lumins / square foot) at point "P" ( the point of
intersection) from two sources at distance "D" apart having angle
"Theta" to point "P"

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Request for Question Clarification by shivreddy-ga on 20 Dec 2002 10:34 PST

Hi,

Thank you for your question. I am interested in providing an answer
for you, but need to know a few details. You insist that the formula
produce the intensity in Lumins/sq.foot. Will it suffice if I give you
the intensity in the form of an amplitude of the waves involved.
Afterall, the intensity is proportional to the amplitude and in most
cases the formula utilised directly is the amplitude one. Also please
let me know if there are any special cases ( like the distance between
the sources maybe neglected when compared to the distance from the
sources...) you would like considered.

Thank you once again,
Shiv Reddy

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Request for Question Clarification by hedgie-ga on 25 Dec 2002 06:45 PST

Hello  rdorsey

  The answer  to your question would have  three steps

1) Propagation of light amplitude from two sources to  P
2) adding the amplitudes at P
3) squaring the amplitude to get intensity  

It would be in  Watts, but as explained here:
Since the lighting flux is measured in lumens, the unit of light
intensity  will be the lumen in a steradian, which is called candle
(cd).
http://www.dcmsistemes.com/medidasi.html
that can be easily converted

You would also have to ignore shiv, who, as it seems STILL thinks
that:
intensity is proportional to the amplitude

Perhpas he confuses the linear and quadratic dependence ??

Do you want the reference to 3 steps as an answer?

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Clarification of Question by rdorsey-ga on 26 Dec 2002 05:38 PST

Thanks for the responses,
Let me clairify the scenaro to which I am referring.
I am trying to determine the additive effect of two strobes mounted on
a ceiling at a point between the two strobes.
The basic formula for effective insity for a singlr strobe is as
follows:
E=I/(D sq)* a where:
E= Effective intensity in lumens/sq ft
I= Intensity of source in candela (cd)
D= on-axis distance between the source and point P
a= angle efficiency - a reduction in intensity as angle theta
increases from "on axis" to the source.
Examples of "a" for some angles are as follows:
0 degrees = 1
10-25 degrees = .9
30-45 degrees = .75
60 degrees = .4
75 degrees = .3
90 degrees = .25
My question is, how would this equation be modified to solve for the
intensity of light from two sources.
Robert Dorsey

Hello  rdorsey 

   Thanks for the explanation. In the light of that, the answer is
   quite different, more simple. It has just two steps.

You just add intensities.

Ergo :

  I(P) = I at P =  I1/(D1P * D1P)  + I2/D2P * D2P)

where intensity of source 1 is I1 and distance to P is D1P 
and so for 2.

Let me just add (as a bonus) the reason for the difference.


  From the first short question we assumed you are adding
coherent light (in that case you add amplitudes).
  From explanation we assume sources are not coherent, and

so you add Intensities directly (considering time variablity, 
as needed).

  We  assume here your are using conventional strobes (not lasers)
 over the  (macroscopic (feets) distances.

 The issue of coherence is complex, but (fortunately) not relevant
to your case.  So, do not bother with this reference:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/interfcon.html

hedgie

Thanks for your help. FYI The reason for my question is that in fire
alarm systems' engineering with respect to visual appliances strobes
are located within a room based upon the equation that I provided. The
minimum light intensity allowable for any point in the room is .0375
lumens /sq ft. If it can be demonstrated that the sum of two light
sources is greater than the minimum, fewer strobes can be used to
provide coverage. However, my efforts are probably just an exercise in
academics. When talking with a local fire alarm plan review engineer,
he asked me,"what if the person was facing away from the strobes?" Is
the light intensity less when it flashes on the back of ones
head...?!?
Thanks again.
rdorsey

note to shiv: intensity is proportional to amplitude squared

lol
Yes of course! Intensity is indeed proportional to amplitude squared!
I was just making a point that since intensity is anyway
related(directly proportional) to amplitude why look for a direct
solution in terms of intensity when a formula is already available for
the same with the amplitude.

shiv Reddy

Hi again
thanks for the rating.

I will just comment on the physics and common sense of 
 the situation, as ammended.


If the the strobes are providing the visual warning (e.g.
for the hearing impaired) than the adding of intensities is
irrelevant (and formula given not useful).  Person is looking
at one strobe which is in his/her field of view and that one strobe is
detected in dependence in intensity radiated INTO THAT ANGLE.

It would be a rare case that light would be so faint as to be
non-detectable by a person with normal vision. So, practical criterion
for number of strobes is to have a  light in everyone's field of
vision
(and not considering those behind him/her).

A different situation would be when we want to have a given
illumination of
a given surface. In that case the angle of that surface, let's say a
wall,
relative to the source needs to be considered.  Adding of light source
contributions could make sense in such a case.

Let's say, a person watching the wall  may notice
the flashes (if synchronised) depending on such cumulative
illumination)
http://www.natmus.dk/cons/tp/lightcd/lumen.htm

That probably is not what standard is trying to set, so I am glad the
quetion is just academic. Calculation would be slightly more
complicated
for a realistic case.

Hedgie