Laser Extinction Method Lab Report

The laser extinction method was developed based on the work of Piere Bouger (1729), August Beer (1852) and Johann Heinrich Lambert (1760). The diminishing intensity of the light passing through a given medium was estimated by Piere Bouger. He was the first person to define the law known as Beer-Lambert law. Later on, Lambert presented the results of his experiments using white light which stated that absorbance is directly proportional to the thickness of the sample. Beer concluded that the absorbance of the light by the substance is proportional to the concentration of the substance in the sample. The modern definition of absorbance correlates the Beer-Lambert law as a function of concentration to the path length of the light travelled through

The Lambert-Beer law can be better understood by the following equation

where $E_{lambda}$ is the extinction, $I_0$ and $I$ are respectively the light intensities before and after the light passed through the measurement volume, $K_{ext}$ is the extinction coefficient and $L$ is the length of the probe volume. The extinction coefficient $K_{ext}$ within the measurement volume is supposed to be constant. For a discrete wavelength, the extinction coefficient is defined by

where $N_V$ is the number density distribution of the soot particles, $ Q_ {ext} $ is the absorption efficiency, which is the sum of the absorption efficiency, $ Q_ {abs} $ and the scattering efficiency $ Q_ {st} $, $N(d_P)$ is the number of particles and $d_p$ is the particle diameter variable of integration. Practically, the scattering can be neglected for particles in nanoscale, without producing significant errors in LE. Thus, the extinction efficiency may be approximated by Eq. ef {lambertbeer}. $E_{lambda}$ is described as