Magyar Information Contest Journal Articles

# Problem P. 4646. (May 2014)

P. 4646. What is the shape of the rounded end of that glass rod, which converges all the light rays entering onto the round glass surface parallel to the axis of the rod to one point inside the rod? Determine the equation of the surface as a function of the refractive index of the glass $\displaystyle n$ and the focal length $\displaystyle f$.

(5 pont)

Deadline expired on 10 June 2014.

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

Megoldásvázlat. Olyan forgásellipszoid, amely vezérgörbéjének kistengelye $\displaystyle f\sqrt{\frac{n-1}{n+1}},$ nagytengelye $\displaystyle f\frac{n}{n+1}$.

A megoldás kulcsa: a Fermat-elv.

### Statistics:

 11 students sent a solution. 5 points: Antalicz Balázs, Dinev Georgi, Fehér Zsombor, Horicsányi Attila, Janzer Barnabás, Juhász Péter, Morvay Bálint, Sal Kristóf. 4 points: Berta Dénes. 3 points: 2 students.

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