Problem 12.2. As light from the surface pene- trates water, its intensity is dim
ID: 2870854 • Letter: P
Question
Problem 12.2. As light from the surface pene- trates water, its intensity is diminished. In the clear waters of the Caribbean, the intensity is decreased by 15 percent for every 3 meters of depth. Thus, the intensity will have the form of a general exponential function.
(a) Iftheintensityoflightatthewater’ssur- face is I, find a formula for I(d), the in- tensity of light at a depth of d meters. Your formula should depend on I and d.
(b) At what depth will the light intensity be decreased to 1% of its surface intensity?
Explanation / Answer
A)I=I0 e^(kd) where k is constant , d is depth , I0 is intensity at surface
at 3m depth
(100/100 -15/100)=100/100 *(e^k*3)
==>0.85=e^(3k)
3k =ln(0.85)
k=-0.054
therefore I=I0 e^(-0.054d) is required equation
b)I=I0 e^(-0.054d)
1/100 =100/100 *e^(-0.054d)
(-0.054d)=ln(0.01)
d=85.28
d=85.3 meters light intensity is decreased to 1% of its surface intensity