## Estimate M and find the uncertainty in the estimate.

1.  The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3 , L = 1.2 ± 0.1 cm, and A = 1.30 ± 0.05.

a.  Estimate M and find the uncertainty in the estimate.

b.  Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm3 , reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?

2.    In the article “Temperature-Dependent Optical Constants of Water Ice in the Near Infrared: New Results and Critical Review of the Available Measurements” (B. Rajaram, D. Glandorf, et al., Applied Optics, 2001:4449–4462), the imaginary index of refraction of water ice is presented for various frequencies and temperatures. At a frequency of 372.1 cm −1 and a temperature of 166 K, the index is estimated to be 0.00116. At the same frequency and at a temperature of 196 K, the index is estimated to be 0.00129. The uncertainty is reported to be 10 −4 for each of these two estimated indices. The ratio of the indices is estimated to be 0.00116/0.00129 = 0.899. Find the uncertainty in this ratio.

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