The Reflection of theKαLine of Carbon from Quartz and its Relation to Index of Refraction and Absorption Coefficient

Abstract

Measurements were made of the ratio of the intensity of the reflected ray to that of the incident ray in the case of the $K\alpha$ line of carbon reflected from a mirror of fused quartz for glancing angles of incidence between 1° 30′ and 8°. The atomic absorption coefficients of carbon, nitrogen, oxygen, and neon were experimentally determined by the writers as described in the preceding article. This gave the value of the oxygen coefficients directly and data from which the atomic absorption coefficient of silicon could be calculated. The linear absorption coefficint, $\mu$, of quartz was then computed from its density, percentage composition, and the atomic absorption coefficients of its constituents. Then from the relation $\kappa =\frac{\mu \lambda }{4\pi }$, the absorption index $\kappa$, was found to be 1.68×${10}^{-3\mathrm{}}$. The value of $\delta =1-n$ was computed from the Drude-Lorentz formula and found to be 4.8×${10}^{-3\mathrm{}}$. Convenient methods for the calculation of the intensity of either the parallel or perpendicular components of the reflected ray are derived from the Fresnel equations relating to absorbing media. A curve computed with the above values of $\delta$ and $\kappa$ predicts somewhat higher reflectivity than found experimentally. Use of the value $\kappa =2.5\mathrm{}\times {10}^{-3\mathrm{}}$ yields a computed curve agreeing well with the experimental one. On the other hand, assuming values of $\delta$ other than that given above leads to less satisfactory agreement.