Determination of Verdet constant from combined ac and dc measurements

Two methods of determination of the Verdet constant (V) for an optically transparent medium are described. These methods use the same apparatus in which the intensity of a monochromatic beam of light is modulated by passing it, successively, through a polarizer, the medium under test (contained within a solenoid which carries ac of frequency f in its windings), and an analyzer. The emergent beam is incident on a detector which produces a steady output voltage Uo for the special conditions of the optical system set for maximum transmittance and, simultaneously, zero modulation. Methods I and II, which were tested by determining V for water for the wavelength 643.3 nm, are based, respectively, on the ratios u1/Uo and u2/Uo, where u1 is the rms value of detector output voltage varying at frequency f and u2 is the corresponding output varying at frequency 2 f. The three mean values of V from method I, method II, and a literature survey agree to within 1%. The standard deviation in the values of V by method I (eight determinations) is 0.8% of the mean and by method II (16 determinations) is 1.4%, leading to respective standard errors of the mean (attributable to random errors) of 0.3% and 0.4%. By either method there is, additionally, 0.4% systematic uncertainty in V arising from calibration accuracy of the instrumentation. The total range of Faraday rotation angles studied spanned the range 2×10−4–0.24 deg rms.