## Friday, April 29, 2022

### How the Attenuation of Light Depends on Wavelength

 Air and Water,by Mark Denny.
In Chapter 14 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the absorption of light by water. Our Figure 14.14 shows that the absorption coefficient of water increases with the wavelength of light over the range from 600 to 750 nanometers, which is the red end of the visible spectrum.

To examine this behavior in more detail, let’s turn to Mark Denny’s book Air and Water: The Biology and Physics of Life’s Media. Denny has an entire section on the consequences of the attenuation of light. Below I present a modified version of his Figure 11.13B, plotting the attenuation coefficient as a function of wavelength. The most important point is that the attenuation of air is much less than that of water. The difference doesn’t look too striking in this figure, because the attenuation is plotted on a logarithmic scale, but the attenuation of water is at least a hundred times greater than the attenuation of air, and for large wavelengths (red light) the difference is far greater. On the right I added a scale for the penetration depth, which is just the reciprocal of the attenuation coefficient. For air, the penetration depth is at least ten kilometers, and often much more. This is good, because we definitely want sunlight to pass through the atmosphere and reach the earth’s surface.

For water, the attenuation coefficient has a minimum around 470 nm, which is in the blue part of the visible spectrum. It then rises as the wavelength increases into the green, yellow, and red parts of the spectrum. Again, don’t let the logarithmic plot fool you. Between blue and red the attenuation coefficient increases by a factor of a hundred. Red light can only penetrate a few meters into water, but blue light reaches depths of hundreds of meters. Except very near the surface, aquatic animals live in a blue world. No sunlight reaches the bottom of the ocean, ten kilometers down.

I’ll let Denny describe more ramifications of the strong dependence of attenuation on color.

The attenuation coefficient of water varies with wavelength… Attenuation is high in the UV [ultraviolet] and IR [infrared], and is minimal for light at visible wavelengths. Given that life initially evolved in an aqueous medium, it may not be a coincidence that “visible” light corresponds to those wavelengths for which water is most transparent. The same argument can be applied to the pigments used by plants to capture light for photosynthesis. All of the major photosynthetic pigments (chlorophylls, carotenoids, and phycobilins) absorb light in the range of 400 to 700 nm, the range at which water is least attenuating…

Even within the visible range, the attenuation coefficient of water varies substantially (fig. 11.13B); red light is attenuated much more strongly than blue light. Again this effect is well known to SCUBA divers, who note that the apparent color of objects changes rapidly with depth. For instance, a camera case that is bright red at the surface appears gray at a depth of only a few meters because all of the available red light has been absorbed by water above… The rapid absorption of red light has had evolutionary consequences for plants. Because chlorophyll a (the most common photosynthetic pigment) absorbs strongly at a wavelength of 680 nm (red light), it is a relatively ineffective means for gathering light at depth. However, plants which live deep beneath the water’s surface have accessory pigments (carotenoids and phycobilins) that absorb at shorter wavelengths.