Mathematical and Physical Journal
for High Schools
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Problem P. 4454. (May 2012)

P. 4454. The volume of a cubic aquarium, which is filled with water halfway, is V=8 litres. Salt is carefully dissolved in the water such that the refractive index of the water, with respect to light which illuminates the water from below, changes with the height h measured from the bottom of the aquarium as a function of n(h)=n0-kh2, where n0=1.35 is the refractive index at the bottom and k=2 m-2 is a constant.

The aquarium is illuminated by a light-beam perpendicularly to one of its side. On the other side a screen is moved. The screen always remains parallel to that side of the aquarium which is illuminated by the light. How far is the screen from the aquarium, when only a thin sharp, horizontal line of light can be observed on it?

(6 pont)

Deadline expired on June 11, 2012.


Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. Az akvárium

f=\frac{1}{2k\sqrt[3]{V}}=1{,}25\,\rm m

fókusztávolságú hengerlencseként viselkedik, tehát az akváriumból ilyen távol levő ernyőn jelenik meg az éles fénycsík.


Statistics:

29 students sent a solution.
6 points:Agócs Fruzsina, Balogh Tamás, Bolgár Dániel, Bősze Zsófia, Czipó Bence, Demeter Dániel, Fehér Zsombor, Filep Gábor, Fonyó Viktória, Győrfi 946 Mónika, Horicsányi Attila, Janzer Barnabás, Janzer Olivér, Juhász Péter, Kollarics Sándor, Medek Ákos, Öreg Zsombor, Papp Roland, Sárvári Péter, Szabó 928 Attila, Szász Norbert Csaba, Szélig Áron, Szigeti Bertalan György, Takács 737 Gábor, Ürge László, Varju Ákos, Wiandt Péter.
5 points:Laczkó Zoltán Balázs.
3 points:1 student.

Problems in Physics of KöMaL, May 2012