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In 1760 Lambert has given the statement which is known as Lamberts Law. It states that “Equal fraction of Incident Light is absorbed by equal thickness of absorbing medium.” Or “When monochromatic light is incident on a medium the rate of decrease of intensity of light with thickness of the medium is proportional to the intensity of light incident on it.”
If \({ d }_{ i }\) is the decrease in intensity of light or absorbed intensity of light by the thickness \({ d }_{ l }\) and \(I\) is the intensity of light incident on it, then, $$- \frac { { d }_{ i } }{ { d }_{ l } } \propto I $$ The negative sign is for decrease in intensity of incident light. $$ - \frac { { d }_{ i } }{ { d }_{ l } } = K'I $$ OR $$ - \frac { { d }_{ i } }{ I } = K'{ d }_{ l } $$ On integrating the equation between limits when \(l = 0\) then \(I = { I }_{ 0 }\) and when \(l = l\) then \(I = { I }_{ t } \) $$ \int _{ { I }_{ 0 } }^{ { I }_{ t } }{ - \frac { { d }_{ i } }{ I } } = \int _{ 0 }^{ l }{ K'{ d }_{ l } } $$ $$ \int _{ { I }_{ 0 } }^{ { I }_{ t } }{ - \frac { { d }_{ i } }{ I } } = K'\int _{ 0 }^{ l }{ { d }_{ l } } $$ $$ - \ln { \frac { { I }_{ t } }{ { I }_{ 0 } } } = K'l $$ $$ \ln { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K'l $$ $$ \boxed { 2.303 \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K'l } $$ Where \({ I }_{ o }\) is the intensity of incident radiation and \({ I }_{ t }\) is intensity of transmitted radiation. Equation is known as Lamberts Absorption Equation.
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