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Problem P. 3862. (January 2006)

P. 3862. A ray of light enters into a spherical water drop. After refraction it is reflected at the internal boundary of the drop, and then it leaves the drop at another point. a) Prove (numerically) that if the angle of incidence is greater than a certain ``critical'' angle, then there exists another ray parallel to the original ray, and after leaving the drop the two rays remain also parallel. Find this ``critical'' angle. b) What is the distance between the two parallel incident rays if the refractive index of water is n=4/3, the angle of incidence of one of the rays is \alpha=45o and the diameter of the water drop is 1 mm.

(5 pont)

Deadline expired on 13 February 2006.


Statistics:

16 students sent a solution.
5 points:Bogár 560 Péter, Csire Gábor, Engedy Balázs, Kónya 495 Gábor, Nagy 224 Csaba, Nagy 317 Péter, Pálovics Róbert, Pásztor Attila, Széchenyi Gábor, Werner Miklós.
4 points:K. Gergely, Konczer József.
3 points:1 student.
1 point:2 students.
0 point:1 student.

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