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Michalson

Light

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I''m looking for a simple (fast approximation) formula to calculate the "Luminance" of a light source at a particular distance (Assuming normal atmosphere, etc.) Thus: CandlePowerAtPoint = SomeFunction(CandlePowerAtSource, DistanceFromSource) Any units of measurement are fine (as long as CandlePower is a linear measurement)

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To elaborate on TerranFury's correct answer (so that you can understand why it is correct)...

Intensity is a measure of energy per unit area. The word luminescence is often used when meaning intensity of light but strictly speaking it means something else (a method of producing light by means other than incandescence)!

Anyway...

Consider a point source of energy at r=0. If I0 represents the intensity of energy released at this source then we can look at the intensities I1 and I2 at radii r1 and r2. Let's assume space has 3 dimensions so that the energy surface at a non-zero radius is a sphere. The energy must be evenly spread over the surface of the sphere, since it is neither lost nor created after emmission. The surface area of a sphere is equal to 4PIr2. Therefore, conservation of energy says that

I24PIr22 = I14PIr12

which implies that

I2 = I1*(r1/r2)2

This gives the ratio of intensity as the inverse square of the ratio of distances. Clearly if r1=0 then the intensity of energy at a distance r2 is
I2 = I0/r22,

as TerranFury indicated.

Hope this helps with your understanding of the problem.

Cheers,

Timkin

Edited by - Timkin on February 7, 2002 9:22:39 PM

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Guest Anonymous Poster
Everything is now clear in case of vacuum. It''s interesting, what kind of equations would we have got to deal with, assuming the "real" atmosphere? Would it be some kind of I(r) = I0 * a/r^3, where a depends on density, temperature, and so on...?

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quote:
Original post by Anonymous Poster
Everything is now clear in case of vacuum. It''s interesting, what kind of equations would we have got to deal with, assuming the "real" atmosphere? Would it be some kind of I(r) = I0 * a/r^3, where a depends on density, temperature, and so on...?


Yes, the inverse square law is based on energy surfaces in a vacuum. However, it is still a good approximation for other mediums. I recall deriving equations for energy dissipation in the atmosphere many years ago while doing astrophysics - it''s related to the absorption of energy as it travels outward from the core of a star - however I don''t recall them at the moment. For light propogating in an atmospheric environment I''d just use the inverse square law... it''s close enough that you''d probably never notice the difference.

Cheers,

Timkin

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