Decoupling refractive index and geometric thickness from interferometric measurements of a quartz sample using a fourth-order polynomial

A Michelson interferometer setup was used to determine refractive index and thickness of a fused-quartz sample with no knowledge of either parameter. At small angles, < 10 degrees, the interferometer equation follows a fourth-order polynomial in the sample refractive index alone, effectively decoupling the sample thickness from the equation. The incident angle of the He-Ne laser beam versus fringe shift was fitted to the polynomial, and its coefficients obtained. These were used to determine refractive index to within 6 x 10(-4) of the known value with an accuracy of +/- 1.3%. Sample thickness was determined to an accuracy of +/-2.5%. Reproducibility of the rotating table was determined to be +/-2 x 10(-3) degrees.