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Consider media with magnetic permeability of a medium, µ ≈ µ0, where µ0 is the magnetic permeability of vacuum, also referred to as the magnetic constant. This criterion is satisfied by many media, including water (for example, Mätzler C et al 2006b). It follows from Eq. 3 in Irradiance and the Poynting vector that the ratio of irradiances due to a plane electromagnetic wave in two such media, can be expressed as follows:
| E2 / E1 ≈ ( m'2 / m'1 ) ( < Ê2 2> / < Ê1 2> ) | (1) |
where m'1 and m'2 are, respectively, the refraction indices of these media, < x > is the time average of x over a period much longer than that of the electromagnetic wave in question, and Ê1 and Ê2 are, respectively, the time-dependent magnitudes of the electrical vector of the electromagnetic wave in each of these media.
Given Eq. 3 in Irradiance and the Poynting vector, this ratio can also be expressed by using a Fresnel transmission coefficient, t (Eq. 3 and Eq. 4 of Fresnel coefficients, see also Hecht E 1987, p. 96):
| E2 / E1 ≈ ( m'2 / m'1 ) t 2 | (2) |
for either of the two orthogonal polarizations of the incident electromagneric wave, where t for each polarization is a function of the the complex refractive index, m, of one medium relative to the other, and of the incidence angle. Thus, for each polarization, the relationships between the irradiances incident at, reflected from, and transmitted through the interface depend on the incidence angle of the plane wave and on the relationship between the refractive indices of the two media, due to the dependencies of the Fresnel coefficients on these factors.
In particular, at incidence angles greater than the angle of total internal reflection, which exists when m'1 > m'2 and the radiation is incident at the interface from the side of medium 1, the transmitted power (and irradiance) equals 0. The total internal reflection (TIR) occurs for the angle of incidence greater than the incidence angle at which the refraction angle equals 90°. Hence, the TIR angle, also referred to as the critical angle, is expressed as follows:
| γC | = arcsin( m'2 / m'1 ) | |
| = arcsin( 1 / m'12 ) | (3) |
where m'12 = m'1 / m'2 > 1 is the real refractive index of medium 1 (dense) relative to that of medium 2 (less dense).
| CITATION: Jonasz M. 2006. Radiometry: Transmission of irradiance through an interface (www.tpdsci.com/Tpc/RdmIrdTsm.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 06-Mar-2008 Modified: 02-Feb-2009 Peer-reviewed: PENDING |
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