A researcher investigates refraction at the interface between methanol (index ) and…
PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction
Problem
A researcher investigates refraction at the interface between methanol (index 1.33) and diamond (index 2.42). A laser beam travels inside the methanol and is incident upon the flat surface of the diamond. The incident angle is measured to be 52.0∘±1.0∘ relative to the normal. The refracted beam is photographed inside the diamond, and its angle is determined to be 27.9∘±0.8∘ relative to the normal.
Using the reported measurements and their uncertainties, perform the following analysis. All uncertainty calculations should be carried out using maximum–minimum (worst-case) propagation and reported to an appropriate number of significant figures.
(a) Compute a value for the ratio sinθdiamondsinθmethanol using the central (best-estimate) angles.
(b) Determine the maximum and minimum possible values of the ratio found in part (a) that are consistent with the stated experimental uncertainties.
(c) Compare the best-estimate ratio and its uncertainty range with the theoretical value nmethanolndiamond. State whether the experimental results are consistent with theory and justify quantitatively.
(d) Using the central angles, predict the refracted angle inside the diamond for an incident beam in methanol that approaches at 40.0∘ relative to the normal, and comment on how the propagated uncertainty in part (b) would affect the precision of this prediction.