Mathematical and Physical Journal
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# Problem P. 4790. (December 2015)

P. 4790. The refractive index of the material of a triangular prism of apex angle $\displaystyle \varphi=45^\circ$ is $\displaystyle n_1=1.3$. The base of the prism is an isosceles triangle of height $\displaystyle H=20$ cm. Another prism of apex angle $\displaystyle \varphi/2$ is attached to the previously described one as shown in the figure. A beam of light enters to the first prism, parallel to the base of the isosceles triangle at a distance of $\displaystyle h=12~$cm from it.

$\displaystyle a)$ What should the refractive index of the second prism $\displaystyle n_2$ be in order that the light beam emerges parallel to the original beam?

$\displaystyle b)$ By what distance $\displaystyle d$ is the emerging beam displaced with respect to the entering ray?

$\displaystyle c)$ How long does a wave-front of the light-beam take to travel through the double prism?

(5 pont)

Deadline expired on January 11, 2016.

### Statistics:

 53 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Bartók Imre, Bekes Nándor, Blum Balázs, Csorba Benjámin, Di Giovanni András, Elek Péter, Fajszi Bulcsú, Forrai Botond, Hornák Bence, Horváth Péter, Iván Balázs, Kasza Bence, Kopitkó Tünde, Kormányos Hanna Rebeka, Kovács Péter Tamás, Körmöczi Dávid, Mándoki László, Marozsák Tóbiás , Nenezic Patrick Uros, Olosz Adél, Páhoki Tamás, Pázmán Előd, Sal Kristóf, Simon Dániel Gábor, Szántó Benedek, Szentivánszki Soma , Tibay Álmos, Tófalusi Ádám, Tomcsányi Gergely, Tóth Adrián. 4 points: Büki Máté, Csenger Géza, Juhász 326 Dániel, Németh Flóra Boróka, Sallai Krisztina, Stein Ármin, Szick Dániel, Szőke Dániel, Wiandt Péter. 3 points: 4 students. 2 points: 7 students. 1 point: 1 student.

Problems in Physics of KöMaL, December 2015