Chapter 3.4, Problem 10E

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.