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Fix sentence in light-matter interactions physics-intro
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shreyas3156 committed Mar 16, 2023
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Expand Up @@ -122,4 +122,4 @@ where :math:`\alpha` is called the **opacity**. Note that for our purposes, the

We can interpret this in the following way: prior to traveling a distance :math:`d`, a photon will have had a :math:`e^{-\alpha d}` probability of *not* interacting with matter (and thus a :math:`1-e^{-\alpha d}` probability of having gone through an interaction). As you would expect, the larger the distance, the more likely it is that a photon interacts prior to traveling that distance, since it would have "more opportunities" to interact. Additionally, a higher :math:`\alpha` means a photon has a higher likelihood of interacting. So, more dense materials, for example, have a higher :math:`\alpha` since there is more matter for the light to interact with. Because :math:`\alpha` must take into account all three types of light-matter interactions, many of which depend on the frequency of light, it can be very difficult to calculate -- this is one of TARDIS's main tasks.

Finally, the term :math:`\alpha d` has a special name: the **optical depth** :math:`\tau`. It is a dimensionless quantity that gives information about how likely it is for a photon to have gone through an interaction. Specifically, there is a :math:`1-e^{-1}\approx 63.2\%` of a photon interacting prior to traveling an optical depth of 1. The actual distance required to travel and optical depth of 1 depends on :math:`\alpha` and thus the material and the frequency of the light.
Finally, the term :math:`\alpha d` has a special name: the **optical depth** :math:`\tau`. It is a dimensionless quantity that gives information about how likely it is for a photon to have gone through an interaction. Specifically, there is a :math:`1-e^{-1}\approx 63.2\%` of a photon interacting prior to traveling an optical depth of 1. The actual distance required to travel an optical depth of 1 depends on :math:`\alpha` and thus the material and the frequency of the light.

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