- #1

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

Last edited: