 #1
PhDeezNutz
 502
 265
 Homework Statement:
 Why when we look at the sun directly is it red/orange? and why does the sky appear blue?
 Relevant Equations:

For Rayleigh Scattering we have the scattering cross section
##\frac{\ d \sigma}{d \Omega} = \left( \frac{k_0^2 \alpha}{4 \pi}\right)^2 \left( 1  \left\hat{r} \cdot \hat{e}_0 \right^2 \right)##
Where ##\hat{r} = \hat{k}## (the scattered wave propagates radially). ##\hat{e}_0## is the unit vector of the incident electric field. For the sake of simplicity I'm going to assume normal incidence (see picture below)
The ##k_0^4## dependence in the numerator implies a ##\frac{1}{\lambda^4}## dependence of ##\frac{d \sigma}{d \Omega}##.
We know ##\lambda_{blue} < \lambda_{red}## so citing the formula above (in the relevant equations) it's apparent that blue light is scattered more than red light. But presumably this would hold for ##\theta = 0## as well but when we look at the sun head on we don't see blue, we see red/orange.
Am i interpreting this formula wrong?
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