Remarks:

• The relationship between the optical path length and refractive index can be derived from the consideration of the speed of light as follow. For a light ray (2) traveling in the medium compared to one traveling in vacuum (1), one can write

where and is a coordinate along the direction of propagation of light.

• The expression for the optical path length assumes that rays travel is straight lines. In a more general setting, light rays could refract and the path of light propagation would be a curve . The optical path length is then evaluated along this curve as

with evaluated from Figure 4.5 as:

Figure 4.6: Two-beam Mach-Zehnder Interferometer with adjustable Optical Components. BS is beam splitter, M is mirror, L is a plano-convex lens, SF is spatial filter, C is a CCD camera connected to a computer, and TC is the test cell. Ray 1 is the reference beam that passes through vacuum while ray 2 is the test beam that asses through the thermally disturbed zone.