## Abstract

In internal reflection spectroscopy effective thickness is defined as the thickness of material required to give a spectrum of the same contrast in a transmission measurement as that obtained via internal reflection. Simple expressions for effective thickness are given for bulk materials and for thin films which are useful as guide lines in determining the optimum conditions required to record internal reflection spectra. Depending on angle of incidence and index of refraction, the effective thickness for bulk materials may be much greater or much less than the wavelength of light. Similarly for thin films the effective thickness may be much greater or much less than the actual thickness.

© 1966 Optical Society of America

Full Article |

PDF Article
### Equations (6)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$\frac{{d}_{e\perp}}{{\mathrm{\lambda}}_{1}}=\frac{{n}_{21}\hspace{0.17em}\text{cos}\theta}{\pi (1-{{n}_{21}}^{2}){({\text{sin}}^{2}\theta -{{n}_{21}}^{2})}^{1/2}}$$
(2)
$$\frac{{d}_{e\left|\right|}}{{\mathrm{\lambda}}_{1}}=\frac{{n}_{21}\hspace{0.17em}\text{cos}\theta (2\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{21}}^{2})}{\pi (1-{{n}_{21}}^{2})[(1+{{n}_{21}}^{2})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{21}}^{2}]{({\text{sin}}^{2}\theta -{{n}_{21}}^{2})}^{1/2}}.$$
(3)
$${d}_{e\perp}=[4{n}_{21}\hspace{0.17em}d\hspace{0.17em}\text{cos}\theta /(1-{{n}_{31}}^{2})]$$
(4)
$${d}_{e\left|\right|}=\frac{4{n}_{21}\hspace{0.17em}d\hspace{0.17em}\text{cos}\theta [(1+{{n}_{32}}^{4})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{31}}^{2}]}{(1-{{n}_{31}}^{2})[(1+{{n}_{31}}^{2})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{31}}^{2}]}.$$
(5)
$${E}_{\left|\right|}=2\hspace{0.17em}\text{cos}\theta /{(1-{{n}_{31}}^{2})}^{1/2}$$
(6)
$${E}_{\perp}=\frac{2\hspace{0.17em}\text{cos}\theta {[(1+{{n}_{32}}^{4})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{31}}^{2}]}^{1/2}}{{(1-{{n}_{31}}^{2})}^{1/2}{[(1+{{n}_{31}}^{2})\hspace{0.17em}{\text{sin}}^{2}\theta -{{n}_{31}}^{2}]}^{1/2}}.$$