Half-value layer ($x_{1/2}=\ln 2/\mu$)

The half-value layer is the thickness reducing the specified transmitted signal by one half. For constant monoenergetic linear attenuation coefficient $\mu$, solving $e^{-\mu x_{1/2}}=1/2$ gives $x_{1/2}=\ln 2/\mu$. The stipulated $\mu =0.40\mathrm{m}{\mathrm{m}}^{-1}$ gives $x_{1/2}\simeq 1.73\mathrm{mm}$; two such layers transmit one quarter. A broad frequency spectrum need not retain the same half-value layer after filtering.