AlphaCrucis
- 10
- 1
- Homework Statement
- I'm trying to calculate how far away from some object is Unit Optical Depth at some given wavelength; but i'm confused as to what exactly Unit Optical Depth is? What am i Calculating
- Relevant Equations
- Below
\begin{equation}
\chi = n \sigma
\end{equation}
Where Chi is the Opacity, n is the number density of absorbers (constant), and $\sigma$ is the cross section(given).
We define the optical depth is just the number of photon mean-free paths in a given physical step, i.e. if we consider a physical step:
\begin{equation}
\Delta \tau = \chi \Delta z
\end{equation}
Therefore, in traveling from location z1 to z2 along a straight-line ray, the total optical depth is
\begin{equation}
\tau = \int_{z_1}^{z_2} \chi \,dz
\end{equation}I'm trying to calculate how far away from some object is Unit Optical Depth at some given wavelength; but I'm confused as to what exactly Unit Optical Depth is? What am i calculating? I am given n and the wavelength along with the cross section
\chi = n \sigma
\end{equation}
Where Chi is the Opacity, n is the number density of absorbers (constant), and $\sigma$ is the cross section(given).
We define the optical depth is just the number of photon mean-free paths in a given physical step, i.e. if we consider a physical step:
\begin{equation}
\Delta \tau = \chi \Delta z
\end{equation}
Therefore, in traveling from location z1 to z2 along a straight-line ray, the total optical depth is
\begin{equation}
\tau = \int_{z_1}^{z_2} \chi \,dz
\end{equation}I'm trying to calculate how far away from some object is Unit Optical Depth at some given wavelength; but I'm confused as to what exactly Unit Optical Depth is? What am i calculating? I am given n and the wavelength along with the cross section
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