The intensity of light I through a lake at a depth of x meters is given by the following formula.   dI/dx=(−1.31)I   ​(a) At what depth is the intensity of the light half that of the intensity at the​ surface, I0​? ​(b) At 5 meters​ deep, what is the intensity of the light as a fraction of I0​?

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter25: Reflection And Refraction Of Light
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Problem 7OQ: Light traveling in a medium of index of refraction n1 is incident on another medium having an index...
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The intensity of light I through a lake at a depth of x meters is given by the following formula.
 
dI/dx=(−1.31)I
 
​(a) At what depth is the intensity of the light half that of the intensity at the​ surface, I0​?
​(b) At 5 meters​ deep, what is the intensity of the light as a fraction of
I0​?
c) At what depth will the intensity of the light be 11% of the light at the surface?
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