The absorption of light in a uniform water column follows an exponential law; that is

Chapter 1, Problem 91

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The absorption of light in a uniform water column follows an exponential law; that is, the intensity I (z) at depth z is I (z) = I (0)ez where I (0) is the intensity at the surface (i.e., when z = 0) and is the . (We assume here that is constant. In reality, depends on the wavelength of the light penetrating the surface.) (a) Suppose that 10% of the light is absorbed in the uppermost meter. Find .What are the units of ? (b) What percentage of the remaining intensity at 1mis absorbed in the second meter? What percentage of the remaining intensity at 2 m is absorbed in the third meter? (c) What percentage of the initial intensity remains at 1 m, at 2 m, and at 3 m? (d) Plot the light intensity as a percentage of the surface intensity on both a linear plot and a log-linear plot. (e) Relate the slope of the curve on the log-linear plot to the attenuation coefficient . (f) The level at which 1% of the surface intensity remains is of biological significance. Approximately, it is the level where algal growth ceases. The zone above this level is called the . Express the depth of the euphotic zone as a function of . (g) Compare a very clear lake with a milky glacier stream. Is the attenuation coefficient for the clear lake greater or smaller than the attenuation coefficient for the milky stream?