## Abstract

The validity of effective thickness expressions for sample films used in internal reflection spectroscopy is obtained by comparing them to exact computer calculations for various refractive indices, angles of incidence, extinction coefficients, and film thicknesses.

© 1971 Optical Society of America

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### Equations (7)

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(1)
$$I/{I}_{0}={e}^{-\alpha d}.$$
(2)
$$I/{I}_{0}\simeq 1-\alpha d.$$
(3)
$$R=1-\alpha {d}_{e},$$
(4)
$$\frac{{d}_{e}{}_{\perp}}{{\mathrm{\lambda}}_{1}}=\frac{{n}_{21}\hspace{0.17em}\text{cos}\theta}{\pi (1-{{n}_{21}}^{2}){({\text{sin}}^{2}\theta -{{n}_{21}}^{2})}^{{\scriptstyle \frac{1}{2}}},}$$
(5)
$$\frac{{d}_{e\parallel}}{{\mathrm{\lambda}}_{1}}=\frac{{n}_{21}\hspace{0.17em}\text{cos}\theta (2\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{21}}^{2})}{\pi (1-{{n}_{21}}^{2})[(1+{{n}_{21}}^{2})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{21}}^{2}]\hspace{0.17em}{({\text{sin}}^{2}\theta -{{n}_{21}}^{2})}^{{\scriptstyle \frac{1}{2}}}},$$
(6)
$${d}_{e\perp}=[4{n}_{21}d\hspace{0.17em}\text{cos}\theta /(1-{{n}_{31}}^{2})],$$
(7)
$${d}_{e\parallel}=\frac{4{n}_{21}d\hspace{0.17em}\text{cos}\theta [(1+{{n}_{32}}^{4})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{31}}^{2}]}{(1-{{n}_{31}}^{2})[(1+{{n}_{31}}^{2})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{31}}^{2}]}.$$