Chapter 8, Problem 32P

The transmission of light through a transparent solid can be described by the equation:

$I_T=I_0{(1-R)}^2{e}^{-\beta L}$where I_Tis the transmitted intensity, I₀is the intensity of the incident beam. is the absorption coefficient, I. is the length of the transparent solid, and R is the fraction of light which is reflected at the interface, lithe light is normal to the interface and the beams are transmitted through air, $R={\left(\frac{n-1}{n+1}\right)}^2$ where n is the index of refraction for the transparent solid.

Experiments measuring the intensity of light transmitted through specimens of a transparent solid of various lengths are given in the following table. The intensity of the incident beam is 5 W/m².

L(cm)	0.5	1.2	1.7	2.2	4.5	0.6
IT(W/m2)	4.2	4	3.8	3.6	2.9	2.5

Use this data and curve fitting to determine the absorption coefficient and index of refraction of the solid.