4. Absorption and scattering

The transmission

Lambert's law is applied in physics and biology, in environmental and geosciences in this form:

Chemists reformulate the law so that they derive the Lambert-Beer law, which enables them to measure the concentration of absorbing substances.

The transparency or transmission T on the way from 0 to $x$ is given by:

It takes on values from 0 for opaque materials to 1 for completely transparent materials, and it might be indicated in % as well.

The highest value $T=1$ practically does not exist. Glass windows of a sample cuvette reflect about 10% of the light at vertical incidence. The window transmission thus is not more than 90%. Moreover, radiation is always scattered by atoms and molecules of matter to a certain degree. The following diagram shows the relevance of scattering and absorption for the transmission of the atmosphere. It is the result of a model calculation in which it was assumed that light passes the atmosphere vertically (what means the shortest distance possible) on a day of perfect view and typical concentrations of greenhouse gases.

Transmission of the atmosphere over the wavelengths from 200 nm to 70 μm on a logarithmic scale. The increasing decline in transmission from VIS to UV is caused by Rayleigh scattering of the gas molecules and by ozone (O₃) absorption. The drops in the red range and in IR are mostly evoked by absorption through greenhouse gases, and to a minor extent by oxygen (O₂) and ozone. In a following paragraph we will explore in more detail the absorbance of gases in the atmosphere.
Source: Wikimedia, modified

The diagram shows that $T=0$ is found at many points of the spectrum. Ozone protects us from dangerous UV on the one hand and greenhouse gases evoke the absence of transmission in several absorption bands in the IR on the other hand. In these spectral ranges the atmosphere is a black body. In spectral ranges with variable transmission it is a coloured body. In one of the next paragraphs, it is shown which gases cause this absorption.

The high transmission values in the visible spectrum make the atmosphere become transparent for sunlight. This holds also for the 10 μm temperature radiation emitted by the earth's surface. These spectral ranges are the atmospheric windows that are of importance for the radiation budget and in consequence for the temperatures on earth.

At most times the atmosphere's transmission is by far lower than shown in the diagram on the left. The following foto taken from space shows how dust, haze and especially clouds inhibit a clear view of the earth's surface. Not only do they diminish the transparency in the visible spectrum, but they also close the optical window in the infrared due to the high absorption of water. Besides other greenhouse gases, the water in the atmosphere thus plays an important role regarding the weather and climate.

Foto of the Pacific Ocean taken from the International Space Station ISS. Illuminated by the back-light of the sun, there are manifold cloud structures to be seen which inhibit the view on the earth's surface. The Pacific Ocean is perceptable only in the very centre of the foto by the sunlight which is reflected by the water. The higher air layers show up as a fine, blue glowing ribbon on the horizon.
Source: NASA - Johnson Space Center

On the following pages it will be illustrated, how transmission data and absorption coefficients can be determined experimentally. We will have to narrow down the atmosphere and deal with liquid samples only.