 The absorption of radiation can be described by the Beer-Lambert law, sometimes just called Beer's law. Note that any change to the radiance equals the product of the amount of radiance, the absorption cross-section of matter, whether they be atoms or molecules through which the radiation is passing, the number of concentration of the absorbing molecules or atoms, and the path length. Note that this cross-section is wavelength dependent and may be pressure and temperature dependent as well. You should be able to easily integrate this equation to get the exponential form of Beer's law. Remember that e to the minus one is just 0.37, only about one-third left, e to the minus two is just 0.13. In the example photograph, the green laser is shining into a dye solution that absorbs the green laser radiation and then fluoresces in the yellow color. As the green radiation penetrates further into the dye solution, more of it gets absorbed and less gets transmitted, until we see that there is too little green radiation left to make the dye solution fluoresce. For the atmosphere, the absorbers are often arranged in atmospheric layers. The stratospheric ozone layer is one example. In this case, the layer thickness is called DZ. For sun directly overhead, the path length through the layer is a minimum, which means that the greatest amount of radiation should be able to pass through. However, as the sun is at higher solar zenith angles, where the solar zenith angle is the angle from the vertical, then the path length through the layer increases, so we would expect more absorption. And because the decrease in radiation is exponential with path length, we should expect the amount of radiation absorbed at high solar zenith angles to be great compared to the case of the overhead sun.