Specular Reflections in Scintillation Frustums

A method of analysis previous developed by Williamson for calculating the light output of conical light pipes is extended to end-window scintillators whose surfaces are specularly reflecting. If the larger base of the scintillation frustum adjoins a photodetector of greater index of refraction than the scintillator, all of the generated light can be collected in four or less reflections for a wide range of frustum geometries. Light collection properties are tabulated as a function of tapering angle, ratio of base diameter to altitude, and surface reflectivity with an accuracy of better than 80% over a wide range of parameters by assuming all of the light to be generated at the center of the median altitude.