A method for analyzing fluids, particularly the solute concentration in liquids which are dense or viscous and are only slightly transparent to light, which utilizes an attenuated total reflectance cell with a curved-path optical wave guide, particularly an optical fiber, the wave guide having a portion of its surface interfacing with the fluid to be analyzed. The wave guide has selected dimensions and properties including bend radius, waveguide radius, index of refraction, and effective light path which optimize the measurement. The optimum wave guide dimensions and wavelength of light are selected through calibration of the ATR device with a plurality of fluids of known composition. Light is transmitted through the wave guide and is attenuated by partial reflectance within the wave guide due to absorbance by the fluid being analyzed. The attenuated transmittance is related to optical absorbance, which is correlated directly to concentration of solute.