A swimmer enters a gloomier world (in one sense) on diving to greater depths. Given that the mean molar absorption coefficient of sea water in the visible region is 6.2 x 10-5- L moI-1 cm-1, calculate the depth at which a diver will experience (a) half the surface intensity of light, (b) one-tenth the surface intensity

(a) The depth at which a diver will experience half the surface intensity of light is 0.81 m.

(b) The depth at which a diver will experience one-tenth the surface intensity is 2.69 m.

Explanation:

(a)  We know that Lambert-Beer's law is as follows.

As it is given that,

and,  

We know that molarity of sea water is 599 mM.

       l =

        = 81 cm

        = 0.81 m

Therefore, the depth at which a diver will experience half the surface intensity of light is 0.81 m.

(b)  We are given that,

                l =

                  = 269 cm

or,               = 2.69 m       (as 1 m = 100 cm)

Therefore, the depth at which a diver will experience one-tenth the surface intensity is 2.69 m.

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