Answer to Question #250820 in Algebra for ggss

Question

Suppose that lo and I denote the light intensity before and after going through a material. Then according to Beer-Lambert's law"', x = -In () where k is a constant that depends on the material. If k = 0.03 and lo = 15 lumens, find the line intensity at a depth of 30 feet.

Answer 1

According to Beer-Lambert’s law;

x=-(1/k)In(I/I₀)

Given that I₀=15 lumens

k=0.03

Light intensity at a depth of 30 feet

x=30ft

In(I/I₀)=-k x

e ^In(I/I₀⁾=e^{-k x}

(I/I_O)=e^{-k x}

I(x)=I₀e^-kx

I(x)=I₀e^-0.03*10

=0.7408