State and explain Beer-Lambert's Law.

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 $$2.303\log \frac{I_0}{I_t}=K^{\prime }l$$ 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, $$2.303\log \frac{I_0}{I_t}=K^{\prime }l{K}^{″}c$$ $$2.303\log \frac{I_0}{I_t}=Kcl$$ $$\log \frac{I_0}{I_t}=\frac{K}{2.303}cl$$ $$\log \frac{I_0}{I_t}=\epsilon cl$$ where $ϵ$ is constant and $ϵ=\frac{K}{2.303}$ 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, $$\boxed{{\displaystyle \log \frac{I_0}{I_t}=Opticaldensity(O.D.)=Absorbance(A)}}$$ 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, $$\boxed{{\displaystyle O.D=A=\log \frac{I_0}{I_t}=-\log T=\epsilon cl}}$$