- #1

creative_wind

- 7

- 0

## Homework Statement

Light in the near-infrared (close to visible red) can penetrate surprisingly far through human tissue, a fact that is being used to "illuminate" the interior of the brain in a noninvasve technique known as near-infrared spectroscopy (NIRS). In this procedure an optical fiber carrying a beam of infrared laser light with a power of 1.5 mW and a cross-sectional diameter of 1.4 mm is placed against the skull. Some of the light enters the brain, where it scatters from hemoglobin in the blood. The scattered light is picked up by a detector and analyzed by a computer.

(a) According to the Beer-Lambert law, the intensity of light, I, decreases with penedtration distance, d, as I=I

_{0}e

^{-µd}, where I

_{0}is the initial intensity of the beam and µ = 4.7 cm-1 for a typical case. Find the intensity of the laser beam after it penetrates through 3.5 cm of tissue.

Answer should be in mW/m

^{2}

(b) Find the electric field of the initial light beam.

Answer should be in kV/m

## Homework Equations

I

_{0}=P/A

I=I

_{0}e

^{-µd}

I=c[tex]\epsilon[/tex]

_{0}E

^{2}(I think this is the equation I need to answer b)

[tex]\epsilon[/tex]

_{0}=8.85*10

^{-12}

## The Attempt at a Solution

a)

Step 1) Solve for I

_{0}(I'm assuming the cross-sectional area refers to a circle)

I

_{0}=P/A = 1.5mW/(pi*(1.4*10

^{-4}m/2)

^{2}= 9.744*10

^{5}mW/m

^{2}

Step 2) Solve for I

I=I

_{0}e

^{-µd}= (9.744*10

^{5}mW/m

^{2})*e

^{(-0.047m-1*0.035m)}= 9.728*10

^{5}mW/m

^{2}

This answer gets me "Your answer differs from the correct answer by orders of magnitude." Since the e term is about 0.998, my I

_{0}must be incorrect. The math is correct (as far as me quadruple-checking can affirm ) so is there a different equation I should be using to determine I

_{0}?