Solution of the transfer equation for

Solution of the transfer equation for uniformly ex-oited aouraes 

We now assume that the volume emission and absorption coefficients are independent of x, i.e. the atomic densities and N and the lineshape factor g(w) are constant. The equation of transfer, equation (10.5), may then be solved by multiplication by the integrating factor exp(iC x), giving 

If the excited gas is taken to be in the form of a slab bounded by the planes x=0 and x=L, the intensity of radiation at the angular frequency w that would be observed at the face x=L is given by 

In this case t (z) would more correctly be termed the optical depth. The distance z at which t Cz) = 1 represents the effective depth within the sample from which, most of the light of frequency (o/2tt is emitted. For a commercial sodium discharge lamp this depth will vary from a fraction of a mm at the centre of one of the resonance lines to more than a cm in the wings of the line, owing to the rapid variation of with 0) as determined by the line profile, g(w). 

Optically thin sources, t, (L) 1. To investigate the intensity of radiation emitted by a uniformly excited column of gas of length L, we set the incident intensity, 

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