Spectroscopy is an important tool to measure light wavelengths pertaining to a variety of chemistry, physics, biochemistry, material and chemical engineering, and clinical applications. Beer- Lamberts law relates the transmitted light intensity, I, to the incident light intensity, I0, according to the following relationship:

= # 10()*+

where a is a wavelength-dependent constant called the extinction coefficient of the sample, b is the light path length (i.e., path distance) through the sample, and c is the sample concentration. Experimental measurements of the path distance at 0.1-cm intervals are given in the following

table. The extinction coefficient is ,### - and the concentration is 18 mM. Note that path length

(b) is the variable in this question.

.01

Distance (cm)	Intensity (arbitrary units)
0.0	1000.0
0.1	990.8
0.2	981.7
0.3	972.7
0.4	963.8
0.5	954.9
0.6	946.2
0.7	937.5
0.8	928.9
0.9	920.4
1.0	912.0

This above equation can be rewritten as follows:

log5#() = log5#(#) which could result in a straight line with slope and intercept log5#(#).

1. (a) Plot the measured data (as shown in table) as red circles.

2. (b) Carry out a first-order polynomial fit to model the measured data. Find the slope and intercept

   of the straight line.

3. (c) Calculate the slope based on your curve fitting results. Compare your results to (given above).

4. (d) Calculate the value of I0 based on your curve fitting results.

5. (e) Calculate new values of based on your polynomial fit, over a range 0.0 1.0.

6. (f) In a new plot, plot the logarithm (base 10) of on the y-axis and b on the x-axis using (i) measured data as red circles, and

   (ii) linear polynomial fit as a blue solid line.

Label the axes and give an appropriate title to the plot. Include appropriate legend showing measured data and linear fit.