Physics Cup – TalTech 2019, Problem 5

• Problem 5 with intermediate results
• Problem 5 with the first hint and intermediate results
• Problem 5 with two hints and intermediate results
• Problem 5 with three hints and intermediate results
• Problem 5 with four hints and intermediate results

Results and best solutions

Fifth problem turned out to be far more difficult than I expected, there were only 5 fully correct solutions and 5 more qualitatively correct ones(out of the 20 solutions submitted in total). There was not much choice about to whom the best solution award should go as there were only four fully correct solutions submitted before the publication of the first hint. Oliver Lindström , Johanes Suhardjo, and Thomas Foster will all recieve one third of the bonus, and Oliwier Urbański the solution of whom was somewhat less reader-friendly than the other three will receive 1.1-factor bonus, primarily for writing a script to calculate numerically the positions of the brightest spots.
As a matter of fact, out of the five solutions which were qualified as “fully correct”, only the solution Thomas Foster is entirely correct. The other contestants overlooked two details in the same way as I did when I composed the problem. Namely, depending on the direction of light propagation after being reflected by a mirror, a small part of light rays may be shaded by the edge of the neighbouringt step of this echelle grating. Second, the size of the pattern on the screen depends on the focal length of the used lens. None of the contestants got penalized for these omissions, because the effect of shading by the edges of the steps is a really subtle effect and can be easily overlooked (it is also conceptually much easier than the rest of the problem); the same applies to a careful handling of the effect of the converging lens. The fact that Thomas Foster noticed these two details is really praiseworthy! (Hadn’t he sent a partially incorrect solution during the first week, his bonus would have been bigger than one third.)
Finally, it should be clarified, what kind of solutions were qualified as “qualitatively correct”. These were solutions for which the pattern on the screen was composed of a set of slanted lines (as it should be), but the geometry (starting and ending points of the lines) was incorrect. In the table below, the date and time refers to the submission of the fully correct solution unless it is in parentheses in which case it refers to the submission of the qualitatively correct solution.

Results for Problem 5, university and high school students together