Half thickness

A constant chance

Put more and more slices of an absorber between source and detector. Each slice is identical for each photon: there is a constant chance that each photon gets absorbed. Therefore, a constant fraction of the photons are absorbed by each slice.

A constant fraction

This constant chance gives a constant fractional decay. This is an exponential pattern: each step takes out a constant fraction of the photons. What that fraction is depends on the photon energies and the absorber.