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Beer-Lambert law

For a better perspective, it is advisable to read the following sections:
What happens to light falling on an object?
What happens to light absorbed by an object?
The Born-Oppenheimer approximation

Beer-Lambert law: When light is passed through a medium and comes out at the other side, its intensity will be reduced, because part of the light will be absorbed by the medium. The actual amount of light absorbed by the medium is governed by the Beer-Lambert law. The derivation of the law is as follows: 

Lambert’s law: (This law was actually observed by Pierre Bouguer in 1729. Its origin is wrongly attributed to Johann Heinrich Lambert, who only quoted from Bouguer’s work in 1760). This law says that the decrease in intensity (dI) when light passes through a medium of thickness ‘dx’ is directly proportional to (a) the intensity of the incident radiation ‘I’ and (b) the thickness of the medium. This may be mathematically expressed as: 

-dI a I.dx        or         -dI = k1.I.dx

 where ‘k’ is the proportionality constant. The minus sign indicates that the intensity decreases as light passes through the medium.

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