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In this case, there is no phase change due to reflection at A and B because, in both cases, light is travelling from a denser to a rarer medium. Thus, the effective path difference between transmitted rays is also 2µt cos r. For constructive interference, (2n + 1) λ / 2 = 2μt Cos r. 2t = mλ n. For destructive interference, nλ = 2μt Cos r
effective path difference between the interfering waves in reflected light for a film is 2ut cosr - /2. When the film is excessively thin such that its thickness t is very small compared to the wavelength of light then 2ut cos r is almost zero. Hence the effective path difference becomes /2. This is condition for minimum intensity.
If only one of the reflections results in an inversion, however, the effective path-length difference is 2t plus or minus (it doesn't really matter which) half a wavelength. Once we've determined the effective path-length difference between the two waves, we can set that equal to the appropriate interference condition.
I believe that "the effective path length" is an oversimpliification to describe a real system. The refs you provided are not from the top journals. "The effective path length" is not well defined ...
of depth of penetration, effective penetration, and effective path length for typical combinations of crystal materials, angles of incidence, and number of reflections shown in Table 1. With the thin penetration of the evanescent wave into the sample, it is obvious that intimate contact of the sample be made onto the surface of the ATR crystal.
Jul 5, 2024 · The effective optical path length, however, was found to be 5.3 ± 0.2 mm, notably larger than the geometric average path length of 2.0 mm. Employing this effective optical path length, an initial ...
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Mar 15, 2008 · Attenuated total reflection (ATR) spectroscopy is now the most popular sampling technique for the measurement of infrared spectra of condensed phase samples. Most practitioners of ATR spectroscopy use the equation for depth of penetration, dp, to estimate the path length of the evanescent wave through the sample. However, the effective path length, de, of the evanescent wave in an ATR measurement, i.e., the equivalent path length in a transmission measurement that would lead to an absorption ...
