JEE Main · 2005 · 08 May 2005 · Offline · Modern Physics

Absorption follows $I=I_0{e}^{-\mu x}$. At $x=36$ mm the intensity is $\frac{I_0}{8}=2^{-3}{I}_0$, so $e^{-36\mu }=2^{-3}$, giving $36\mu =3\ln 2$ and $\mu =\frac{\ln 2}{12}$ per mm. To halve the intensity, $e^{-\mu x}=\frac{1}{2}$ needs $\mu x=\ln 2$, so $x=\frac{\ln 2}{\mu }=12$ mm. The same result follows at a glance from noting that three equal layers each halve the intensity, and $\frac{36}{3}=12$ mm.