Today, Gritsan mentioned how to calculate distance defletion inside detector — chop it into slabs.

This idea is exactly as the way Lorentz got the formula connecting reflection index and scattering amplitude, which further helped Krammers and Kronig got optical theorem.
Optical Theorem connects two things, total cross section, and forward scattering amplitude. Rediculous at the first sight, it is incredible as you give a second thought. Let us have a close view at what happened between Lorentz and K&K. The earlier person got a macroscopic quantity, reflection index, as an expression of a microscopic quantity, scattering amplitude. The story is pretty similar to atomic hyperthesis and classic theromal dynamics. Just because nature is it, no deeper reason. However, K&K reconsider a more macroscopic quantity, intensity from a more macroscopic varible, total cross section. The formula become so straightforward that once you wrote it down, everything just show up in the exact place you want. Then, they require these two to be the same, bam! optical theorm.

A second way to do it is drawing Feymann diagram, you will soon notice you are doing something stupid —- you forgot the simplest case! Write it down, read it, you got optical theorm.