The general direct and inverse problems of turbidity of spheroids which are monodisperse in size and shape and fall in the Rayleigh-Debye-Gans (RDG) and Rayleigh scattering regimes are solved analytically. The theory applies to single and independent scattering from nonabsorbing optically isotropic particles. From turbidity measurements at one incident direction, one wavelength, and three incident polarizations, it is shown that three functions or moments of the orientation distribution functions can be obtained for both regimes. For RDG particles, use of turbidity spectra (at multiple wavelengths) can recover more information, i.e., more moments. The complete orientation distribution function, with no empirical fits, can in principle be obtained from turbidity spectra at many incident directions for the RDG regime, but not for the Rayleigh regime. The approach used is more general, and should provide potentially much more orientation information than measurements of conservative linear dichroism.