Main Concept

Visibility in water is something of great interest to scuba divers. The amount of light reaching a given depth depends on several factors. The most important factors are the light absorption of the water and the intensity of the original light source (which is above the water—for a scuba diver this would normally be sunlight). If we reformulate the problem as that of determining the proportion of the original light reaching a given depth, then the intensity of the original light source drops out of the problem.

The proportion, p, of light reaching a depth, $x$, through water with absorption coefficient $c$ is given by $p\&equals;{\&ExponentialE;}^{-c\cdot x}$. Typical values for the coefficient $c$ for water are in the range $0< c<0.1$, with smaller values representing clearer water and larger values indicating more opaque water.

Using the sliders, select the values of $p$ and $c$. The diagram shows the depth, $x$, to which the proportion $p$ of source light reaches through water with absorption coefficient $c$.

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