Optical depth is a measure of transparency, and is defined as the fraction of radiation that is scattered between a point and the observer. One way of visualizing optical depth is to think of a fog. An object that is immediately in front of you has an optical depth of zero. As it moves away, the optical depth increases until it reaches one and is no longer visible. As the object continues to move away the optical depth can continue to increase and then reflects the number of scatterings that a photon has before reaching you.
Another example occurs in astronomy where the photosphere of a star is defined as the surface where its optical depth is one. This means that each photon emitted at the photosphere suffers an average of one scattering before it reaches you.
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optical depth equations
