It is taken for granted that usual interference experiments provide information about phase of monochromatic light. However, monochromatic light is not realizable. We will elucidate the meaning of the phase that is measured.
We show, both analytically and experimentally, that under common experimental conditions the interference pattern produced in a classic Young's double-slit experiment is indistinguishable from that generated by means of a doubly refracting uniaxial crystal whose optic axis makes a skew angle with the light propagation direction. The equivalence between diffraction and crystal optics interference experiments, taken for granted by Arago and Fresnel in their pioneering research on the interference of polarized light beams, is thus rigorously proven.
Introduction W hen there is interference of light, the width of the resulting bands, measured for example from darkness to darkness, is usually a function of the colour of the light employed. Thus, in the case of Fresnel's well-known interference-experiment, in which light reflected from two slightly inclined mirrors illuminates a screen, the width of the bands is proportional to the wave-length of the light. In order that a considerable number of bands may be visible, it is necessary that the light be highly homogeneous; otherwise it is impossible that the various band-systems can fit one another over the necessary range. If the light could be supposed to be absolutely homogeneous, there would be no limit to the number of observable bands: and, what is especially to be remarked, there would be nothing by which one band could be distinguished from another,—in particular there could be no central band recognizable. When, on the other hand, the light is white, there may be a central band at which all the maxima of brightness coincide; and this band, being white, may be called the achromatic band. But the system of bands is not usually achromatic. Thus, in Fresnel's experiment the centre of symmetry fixes the position of the central achromatic band, but the system is far from achromatic. Theoretically there is not even a single place of darkness, for there is no point where there is complete discordance [opposition] of phase for all kinds of light.