Double scattering correction in the interpretation of Rayleigh scattering data near the critical point of a binary liquid

Double-scattering contributions to the intensity of Rayleigh-scattered light near the critical point of a binary liquid are calculated for 90\ifmmode^\circ\else\textdegree\fi{} scattering. We consider a family of sample geometries, namely cylinders with arbitrary length-to-radius ratio and cuboids with square cross sections and arbitrary length-to-side ratio. For binary liquids with nearly matched refractive indices, these terms can be sufficiently large that they affect the interpretation of data with respect to the value of the critical exponent $\ensuremath{\eta}$ and the deviation of the correlation function from Ornstein-Zernike form, yet small enough that higher-order contributions can be neglected. Numerical results are presented for all temperatures above ${T}_{c}$ together with analytical results in certain limiting cases. Near the critical point, the double-scattered intensity is comparable with that lost through extinction and these two effects cancel in leading order. Some analytical results are also obtained for the depolarization ratio. For example, if the height of the sample seen by the detector is small, the depolarization ratio is proportional to the differential cross section and to the sample height. The proportionality constant is $\frac{\ensuremath{\pi}}{4}$. Numerical results are presented for more general cases.