Atmospheric Opacity and laser Attenuation query

[Jleidenfrost]

I would appreciate assistance with a thought experiment I've been having trouble with.

What I asked myself was, If I had two Lasers of equal Intensity/power, say 200 milliwatts, one appearing green and the other red, with wavelenghts of say 555 nanometres and the other 660 nm, which laser beam would retain the greatest amount of power when measured at 1 kilometre?

I had originally concluded that the red laser would have retained more of it's power because green light is subject to greater Rayleigh scattering than red light.
As is graphed here: http://en.wikipedia.org/wiki/Rayleigh_scattering

However Upon seeing a similar diagram to the one on the page below on Atmospheric opacity I have come to doubt what now seems to have been a very rash conclusion.
http://en.wikipedia.org/wiki/Optical_window

So I tried to determine once and for all which would retain more of it's intensity/power and bumped into the Beer-Lambert Law, which seems to be what I am looking for but I have no idea where to find or even guess what would bereasonable values to plug into the equation entitled the ''Beer–Lambert law in the atmosphere''.
http://en.wikipedia.org/wiki/Beer–Lambert_law


Any assistance would be greeted.

 

[vin300]

It depends on the molecules it's passing through.If the wavelength has enough energy to cause transition, it is absorbed. That is the reason why ozone blocks ultraviolet and not visible light.Other gases present in the atmosphere need lesser energy, so the opacity somewhat risesfrom violet light to become maximum at the infrared range.Similarly, there may be radio opacity.
It depends on how much and what altitude of the atmosphere(because composition of gases varies according to mass) is traversed and the zenth angle which is the angle between the normal to the surface of the Earth and the direction of laser(The m is approximately equal to sec(angle) as written there)so for greater angles to the normal you have lasser intensity

 

[Jleidenfrost]

Well that helps me understand the graph a bit more but in my thought experiment both the light source and measuring are done at sea level.

 

[vin300]

Remember that due to scattering the radiance over a closed surface remains constant(just like gauss' law, though not to be confused with intensity because radiance doesn't need considering normal component).
In this interpretation, the intensity of red light is retained(comparison valid to parallel lines)
even though the atmosphere is slightly more opaque to lesser wavelengths in the visible range

 

[Jleidenfrost]

So will the detector show greater Intensity from the red laser or Green?

 

[vin300]

So will the detector show greater Intensity from the red laser or Green?

It practically depends on too many factors to predict intuitively.The scattering depens on the angle of contact with every particle and the polarizability of every molecule, the composition being varying.It is definitely inversely proportional to fourth power of wavelength, but that is not enough.The absorption and beer lamber law is another thing affecting the intensity.
Application of beer lambert law requires the medium does not scatter radiation.

 

[Jleidenfrost]

May I ask if you have experience with optics in a professional standing? I do not mind if the answer cannot be guessed, I am not afraid of deductive reasoning via mathematics.

I do not agree with you in regard to your belief that the ambient atmosphere has unsuitably high scattering properties at the wavelengths in question. and It is apparently only in higher scattering mediums that the Beer Lambert law breaks down. I also believe that the effects of individual molecules polarizing and scattering the light etc, that you refer to, would more than likely cancel each other out and would produce negligible changes in the measured intensity of each specific light source.

I ask you this, in a world where you are right wouldn't the light intensity and properties coming from a reflection from say a static green leaf change widely due to to the highly variable ''scatterability'' of the atmosphere, our eyes are quite good at detecting changes in light intensity, would we not notice such fluctuations?

and consider this, in your world If I actually had the lasers and I wanted to take an average, in a short time span, wouldn't the intensity coming from our green laser change widely between each previous measurements result? I doubt it! a further example is that of the absolute magnitude of the Cepheid Variables, it does not change on average even with the photons coming from those stars having to pass through the whole atmosphere, yes a lot of scintillation occurs but this is on average remember.