A numerical method for determining refractive index of a glass sample from its implicit transcendental function

The refractive index of a glass sample was determined from an implicit function of its optical path within the sample arm of a Michelson interferometer.On rotation of the sample from normal incidence, the light beam suffers increasing refraction, causing the optical path for air to decrease whilst that for the glass sample increases. This is observed as a shift in the number of fringes, which were captured and counted in real time on a computer, as rotation proceeded. The angle of rotation and the fringe shift were entered into an implicit function of optical path versus refractive index written to an Excel worksheet. A refractive index matching the wavelength of the He–Ne laser light source was read-off to three decimal places. A new source of uncertainty has been identified, misalignment on a micrometer scale of the laser normal to the sample surface. Whilst driving the sample to find normal incidence a finite angular region of insensitivity (dead space) occurs due to misalignment of the laser normal to the sample surface by a few micrometers. A linearization technique was employed to compensate for this offset and hence reduce its uncertainty contribution.