[madscientist]

Hi all,

I'm having a hard time figuring out how to calculate the Rayleigh ratio. Heres what I've come up with so far,

One way to calculate the Rayleigh ratio is:

Rayleigh ratio = R(theta)= 2I / (Io(1+ cos^2 theta))

I = Relative intensity of scattered light

theta = angle to the incident beam of light

I have these two variables already, what I'm having difficulty with is
finding a value for Io (the intensity of the incident light). the only
info I'm given about the incident light used is the wavelength. I cant
seem to find how wavelength is related to light intensity. I know that
intensity will change going from one end of the visible spectrum to the
other, (heading into the realms of scary blackbody radiation curves), is
there an equation which directly relates Io to wavelength? Any help at all would be appreciated.

Cheers,

Mad

[ARGOS++]

Dear MadScientist,

It seems that there exist quite a Lot of confusion in your Question and “your” Formula.
(At the end I give you also a hint for the relationship between wavelength and energy!)

With the more correct Formula from the “Goldbook” (IUPAC) and a fixed geometry of the experiment the Rayleigh ratio is given for small paricles by:

R_θ =  I_θ * r² / (I₀  * f * V)

Only in case you use unpolarized light you can set f to:

f  =  (1 + (cos(θ))²) / 2

As in most cases in a spectrometer you keep V = const. and r = const. you may shorten:

R_θ =  K * I_θ / (I₀  * (1 + (cos(θ))²))

This is coming pretty close to your Formula. But for this Formula you don’t need the wavelength or its corresponding Energy, as only a ratio is described.
For the relationship between Scattering and Wavelength you need another Formula, too!
Theta (θ) is not the angel of the incident light it is the observer angel to the basis of the continued incident light.
In a well designed spectrometer you can set the Intensity of the incident light (I₀)  equal 1.00 and now you are able to calculate the fraction part of your light you can observe under the angel θ by geometry = const. and for small particles and a concentration near zero.
So for some other cases also some different Formulas exist!

Under the Question: “Why Einstein meets Beer-Lambert Law?” you will find the answer for your Relationship between Wavelength and Energy. All this is located on the page:

Spectroscopy FAQ / Beer-Lambert Bouguer Law FAQ

There you can also find a poster about (Not only for your Printer!).

I hope this may be of any help to you.

Good Luck!
                    ARGOS⁺⁺