When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I (t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I0 of the incident beam. What is the intensity of the beam 12 feet below the surface

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Social Studies

Zackery

16 February, 07:24

When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I (t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I0 of the incident beam. What is the intensity of the beam 12 feet below the surface

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Mollie Mueller · Answer 1

Intensity of 0.039

Explanation:

The intensity of the initial beam is 10; 3 feet below it's 2.5 (25% of 10); at 6 feet (I = Intensity decreases proportional to t = thickness in feet) it's 0.625 (25% of 2.5); at 9 feet it's 0.15625 and at 12 feet the intensity has shrinken to a mere 0.039.