In optics and spectroscopy, transmittance is the fraction of incident light (electromagnetic radiation) at a specified wavelength that passes through a sample. The terms visible transmittance (VT) and visible absorptance (VA), which are the respective fractions for the spectrum of light visible radiation, are also used. The natural radiation of the cuvette corresponding to the temperature of the cuvette remains ignored - see radiative transfer equation.
In equation form, the transmittance is:
where is the intensity of the radiation coming out of the sample and is the intensity of the incident radiation. In these equations, scattering and reflection are considered to be close to zero or otherwise accounted for. The transmittance of a sample is sometimes given as a percentage.
Note that the term "transmission" refers to the physical process of radiation passing through a sample, whereas transmittance refers to the mathematical quantity.
Relation to absorbance
Relation to optical depth
From the above equation for the inverse problem the transmittance is thus given by:
If one want to express optical depth in decibels:
In plane geometry:
where, when the plane parallel assumption is invoked, with the angle of propagation of the ray from the normal of the surface.
In case of uniform attenuation optical depth is simply:
for example if there is a strong temperature or pressure nonuniformity in a material, the concentration is nonuniform but the cross section is uniform, so:
Another equation that can be useful in solving for is the following:
Where is a measure of absorbance. By manipulating the equation you can generate the more direct form of the equation:
- "Electronic warfare and radar systems engineering handbook".
- IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Transmittance".
- Verhoeven, J. W. (1996). "Glossary of terms used in photochemistry (IUPAC Recommendations 1996)". Pure and Applied Chemistry 68 (12): 2223–2286. doi:10.1351/pac199668122223. ISSN 0033-4545.
- IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorbance".
- "CRC Dictionary of pure and applied physics, CRC Press, Editor: Dipak Basu (2001)".
- "Molecular Spectroscopy — Beer's Law". Sheffield Hallam University, Faculty of Health and Wellbeing, Biosciences Division, On-Line Learning.