On a Systematic Error in the Measurement of Optical Constants

Abstract

The optical constants of opaque materials are frequently determined by measuring the principal angle of incidence, ø¯, and the principal azimuth ψ¯. The approximation furnished by Brewster’s law is examined. The slope at ø¯ of the graph of Rp/Rs, against ø is ½ cot3ø¯ sin4ψ¯; previous investigations omitted the factor ½.The variation of ψ with ø in the neighborhood of ψ¯ and ø¯ is expanded in the form ψ-ψ¯=a(ø-ø¯)+b(ø-ø¯)2+c(ø-ø¯)2. The parabolic term is the most important in the infrared. Therefore, whether ø-ø¯ be positive or negative, ψ-ψ¯ will be positive. Such a systematic error in ψ¯ leads to a positive error in the measurement of refractive index. The magnitude of such an error depends on the signal to noise ratio. It is not significant in the visible region but is relevant in the infrared. Experimental values are examined and a graphical chart enables a ready estimate to be made in any practical case.