Mathematical and Physical Journal
for High Schools
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Problem P. 3971. (March 2007)

P. 3971. In 1611, before the law of refraction was discovered by Snell, Kepler published the book Dioptrice in which he describes his investigation about the refraction of light entering from air into a rock-crystal. He found that the angle \varepsilon between the extension of the incident ray and the refracted ray is proportional to the angle of incidence \alpha: \varepsilon=k\,\alpha, where k is a constant (in case of the rock crystal k=\frac{1}{3}).

a) Verify Kepler's formula for small angles.

b) Aim a beam of monochromatic light to a rock crystal prism the apex angle \varphi of which is small, such that the beam is nearly perpendicular to the surface of the prism. Using Kepler's formula determine the angle between the incident ray and the ray which leaves the prism.

(5 pont)

Deadline expired on April 11, 2007.


44 students sent a solution.
5 points:Almási 270 Gábor András, Balogh Máté, Blázsik Zoltán, Bodosi Eszter, Csató Bertalan, Dudás János, Fülöp Bálint, Hegyi Ádám, Lovas Lia Izabella, Nagy 224 Csaba, Pálovics Róbert, Para Attila, Roósz Gergő, Sebők Tamás, Sümegi Károly, Szerző 147 Péter, Szolnoki Lénárd, Tihanyi Benedek, Tolner Ferenc, Tüzes Dániel, Varga Bonbien, Vőfély Róza.
4 points:Bogár 560 Péter, Nagy 897 Zsolt, Takács 484 Marcell.
3 points:6 students.
2 points:5 students.
1 point:2 students.
0 point:2 students.
Unfair, not evaluated:4 solutions.

Problems in Physics of KöMaL, March 2007