**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 =45^{o} and the diameter of the water drop is 1 mm.

(5 points)

**Deadline expired on 13 February 2006.**