In the article “Temperature-Dependent Optical Constants of Water Ice in the Near Infrared: New Results and Critical Review of the Available Measurements”, 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.
What will be an ideal response?
Let 
be the estimated index at a temperature of 166 K, let 
be the estimated index at a temperature of 196 K, and let
be the ratio. Then 
.
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