total internal reflection
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total internal reflection[′tōd·əl in′tərn·əl ri′flek·shən]
Total Internal Reflection
When electromagnetic radiation, such as light or radiowaves, in a transparent medium with a higher refractive index meets the boundary of a transparent medium with a lower refractive index at an angle of incidence i greater than a certain critical angle iCr, total internal reflection occurs. When i > icr, refraction into the second medium ceases.
Total internal reflection was first described by J. Kepler. After the discovery of Snell’s law of refraction, it became clear that within the framework of geometrical optics total internal reflection follows directly from this law, since the angle of refraction j cannot exceed 90° (Figure 1). The quantity icr is given by the condition sin icr = 1/n, where n is the relative refractive index of the first and second media. Because of dispersion, the values of n and, consequently, of icr differ somewhat for different wavelengths (frequencies) of radiation.
In total internal reflection the electromagnetic energy is completely returned— hence the term “total”—to the optically denser medium, that is, the medium with the higher refractive index. The reflection coefficient in total internal reflection is greater than in specular reflection from polished surfaces and is practically equal to unity. Moreover, for total internal reflection, unlike specular reflection, the coefficient is independent of the wavelength of the radiation, provided that total internal reflection occurs for the wavelength; even in the case of repeated total internal reflection the spectral composition (“color”) of complex radiation does not change. For this reason, extensive use is made
of total internal reflection in many optical instruments and experiments (see Figures 2 and 3). It should be noted, however, that the energy of electromagnetic waves during total internal reflection partially penetrates into the second medium (the medium with the lower refractive index) but then returns. The depth of this penetration is extremely slight and is of the order of the wavelength of the reflected light.
REFERENCELandsberg, G. S. Optika, 4th ed. Moscow, 1957. (Obshchii kurs fiziki, vol. 3.)
Born, M., and E. Wolf. Osnovy optiki, 2nd ed. Moscow, 1973. (Translated from English.)
Tolansky, S. Udivitel’nye svoistva sveta. Moscow, 1969. (Translated from English.)