By Sunil Bhardwaj

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Beer-Lambert's Law states that “Equal fractions of incident light are absorbed by successive layers of equal thickness and equal concentration of absorbing medium.” We know that Lambert's Law is $$2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K'l$$ And Beer's Law is $$2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K''c$$ On combining both, we get Beer-Lambert's Law which is, $$2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = K'l K''c$$ $$2.303\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = Kcl$$ $$\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = \frac { K }{ 2.303 } cl$$ $$\log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = \varepsilon cl$$ where $$\epsilon$$ is constant and $$\epsilon = \frac { K }{ 2.303 }$$ is known as molar extinction coefficient Or molar absorptivity and it is defined as “the reciprocal of the thickness which produces transmitted ray $$\frac { 1 }{ 10 }$$ of its incident rays if the concentration of the absorbing species in the solution is 1mole.”

The unit is $${ dm }^{ 3 } { mole }^{ -1 } { m }^{ -1 }$$.

But Optical density is defined as logarithm of ratio of $${ I }_{ 0 }$$ to $${ I }_{ t }$$. Therefore, $$\boxed { \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = Optical \ density \ (O.D.) = \ Absorbance \ (A) }$$ OD has no unit and its value lies between 0 to 1. Also Transmittance T is defined as the fraction of the light transmitted. $$T = \frac { { I }_{ t } }{ { I }_{ 0 } }$$ The value of T is always small to convert in to appreciable it is always expressed in percentage.

Thus Beer-Lambert's Law becomes, $$\boxed { O.D = A = \log { \frac { { I }_{ 0 } }{ { I }_{ t } } } = -\log { T } = \varepsilon cl }$$

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