Visibility Phenomena with Interference by Multiple Reflections

Visibility of interference fringes due to multiple reflections of approximately monochromatic light.—Approximate expressions are developed for the intensity and visibility of interference fringes for both transmitted and reflected light when any number of multiple reflections exist and the source of light is one of small width. Where the number of reflections is large, the visibility is $V=\frac{2b^{2}C}{P}$ and $V=\frac{(1-b^2)C}{P}$ respectively, $C$ and $P$ depending on the distribution of intensity in the source and having the significance which was given them by Michelson and Rayleigh $b$ is the coefficient of reflection at the first reflecting surface. The effects of the coefficients of reflection and absorption are examined and it is indicated that the method of visibility with interferometers which depend on multiple reflection may be used to advantage in the study of the fine structure of such spectra as those of hydrogen and helium, not only in order to obtain the components but also to determine the character of each component. It is also indicated that the development may be extended to x-ray spectra in which series of multiple reflections from numerous planes exist.