Absorbum

Meet Absorbum, a stack of shielding slabs that each take the same share of a beam.

When a beam of X-rays or gamma rays passes through a material, some of it is absorbed or scattered away. Each thin layer removes the same fraction of whatever reaches it, so the intensity falls exponentially with thickness, I = I₀e^(−μx). The attenuation coefficient μ depends on the material and the energy of the rays.

Take a material with μ = 0.5 per cm. After 2 cm the intensity is e^(−1) ≈ 0.37 of the starting value. Each 1 cm layer lets through about 61% of what reaches it. The half-value layer, which halves the beam, is ln 2 / μ ≈ 1.4 cm.

The beam never quite reaches zero. Extra layers keep cutting it by the same fraction, so shielding is designed to bring the level down far enough to be safe.

Dense materials such as lead have large attenuation coefficients, which is why they are used for radiation shielding in hospitals.