Reflection of Radiation from An Infinite Series of Equally Spaced Planes

Reflection of Radiation from an Infinite Series of Equally Spaced Planes.—If the fractions of the incident radiation upon any plane which are absorbed, reflected and transmitted by that plane are constant and denoted by $a$, $r$ and $t$ respectively, and if all possible internal reflections are taken account of, the coefficient of reflection is shown to equal ($\frac{1}{2r}$) {$1-t^2-r^2-\sqrt{[1-2\mathrm{}{t}^2-r^2+{(t^2-r^2)}^2]}$}. When both $a$ and $r$ are very small, as in the case of the reflection of X-rays from a crystal surface, the expression becomes [$1+\frac{a}{r}-\sqrt{(\frac{a^2}{r^2}+\frac{2a}{r})}$]; thus the proportion reflected depends only on the ratio of absorption to reflection per plane.