Bouguer’s law

The factor 7 is also known as the turbidity or attenuation coefficient. Equations 16.3 through 16.5 are all forms of what is sometimes known as Beer s law but should more properly be called Bouguer s law, in honor of the person who empirically established it in 1760. 

To verify the dependence of the optical density on foam layer thickness, standard rectangular optical cuvettes of various sizes were used (without electrodes and a manometer). The cuvette was filled up with foam and when it became sufficiently transparent its optical density was measured with a spectrophotocolourimeter. The measurements were performed at two different foam layer thicknesses by an abrupt rotation of the cuvette to 90°. The experimental results obtained (Table 8.2) indicate that for one and the same foam Bouguer s law holds. The D/H(l/nr) dependence was also studied. For that purpose the cuvette was filled... 

Each rocket motor type was fired a number of times (see table 1) and the IR emission spectra were recorded for each test as replicate measurements. The total set of recorded IR emissionspectra thus comprised 420 measurements. The spectra were recorded by Roodt (1998) using a spectral radiometer at varying distances, i.e. 500 m, 350 m, 250 m and 200 m The data were preprocessed in order to compensate for the varying absorbance path lengths and atmospheric conditions (Bouguer s law) as described in Roodt (1998). 

Lambert s laws (1) The illuminance of a surface illuminated by light falling on it perpendicularly from a point source is inversely proportional to the square of the distance between the surface and the source. (2) If the rays make an angle 6 with the normal to the surface, the illuminance is proportional to cose. (3) (Bouguer s law) The luminous intensity (J) of light (or other electromagnetic radiation) decreases exponentially with the distance d that it enters an absorbing medium, i.e. 

An absolute method of checking a spectrophotometer s photometric linearity exists. It combines the use of Bouguer s law and the superposition of optical fields (17). A simple example of this technique from Hawes paper explains the method clearly. Two neutral density filters are measured separately and then together. If the transmittance of one is 57.19 and the other is 48.66, the transmittance of the two together, separated by an air space, would be 57.19-0.4866 = 27.83. Other filters can be measured separately and combined in multiple stacks to check various photometric levels. 

A. Bouguer s law [ ] is, in a sense, the first important event in the history of spectrophotometry. It was formulated in 1729 and states that each layer of equal thickness absorbs an equal fraction of the radiant energy which traverses it (this applies to the special case of a parallel beam of monochromatic radiation passing rectilinearly through a homogeneous absorbing medium). 

It is incorrect to call it Lambert s law since the latter merely rediscovered Bouguer s law in 1760. 

For a parallel beam of light, such as that shown in Fig. 16.1, the ratio of the light intensity traversing the aerosol, I, to that incident on the aerosol, /o, is given by Bouguer s law (also known as the Lambert-Beer law). 

It is of interest to express Bouguer s law, Eq. 16.7, in terms of the particle mass concentration C for monodisperse aerosols. 

You observe the visual range in urban air. If you assume that the range depends solely on the fine-particle mode and that it can be represented by an equivalent nonabsorbing monodisperse aerosol, what is its particle size Assume that Qt = Q,= and the particle density is 1500 kg/m [1.5 g/cm ]. [Hint Use the empirical expression relating visual range to hne-particle mass concentration and Bouguer s law expressed in terms of mass concentration.] ANSWER 0.3 pm. 

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