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?

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?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 59PQ

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Concept explainers

Interference of sound

Seiche

A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water including bays and lakes. A seizure can happen in any enclosed or semi-enclosed body of water.

Question

100%

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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