Chapter 20, Problem 17P

The thickness of the retina changes during certain eye diseases. One way to measure retinal thickness is to shine a low-energy laser at the retina and record the reflections on film. Because of the optical properties of the eye, the reflections from the front surface of the retina and the back surface of the retina will appear as two lines on the film separated by a distance. The distance between the lines on the film is proportional to the thickness of the retina. Below are data taken from the scanned film. Fit two Gaussian-shaped curves of arbitrary height and location to these data and determine the distance between the centers of the two peaks. A Gaussian curve has the form

$f\left(x\right)=\frac{k{e}^{-k^2{\left(x-a\right)}^2}}{\sqrt{\pi }}$

wherek and a are constants that relate to the peak height and the center of the peak, respectively.

Position	Light Intensity	Position	Light Intensity
0.17	5.10	0.31	25.31
0.18	5.10	0.32	23.79
0.19	5.20	0.33	18.44
0.20	5.87	0.34	12.45
0.21	8.72	0.35	8.22
0.22	16.04	0.36	6.12
0.23	26.35	0.37	5.35
0.24	31.63	0.38	5.15
0.25	26.51	0.39	5.10
0.26	16.68	0.40	5.10
0.27	10.80	0.41	5.09
0.28	11.26	0.42	5.09
0.29	16.05	0.43	5.09
0.3	21.96	0.44	5.09