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GEOMETRICAL OPTICS. 



1595. There are three plane mirrors whose lines of intersec- 

 tion are parallel; a ray is incident on one of them in a plane 

 perpendicular to all the mirrors in such a direction that after 

 reflexion at the three mirrors its course is parallel to its original 

 direction : prove that, after another reflexion at each of the 

 three mirrors in the same order, it will return on its original path, 

 and that the whole length of its path between the first and third 

 reflexions at any mirror is independent of the point of incidence. 



1596. A ray of light whose direction touches a conicoid is 

 reflected at any confocal conicoid : prove that the reflected ray 

 will also touch the conicoid. 



1597. In a hollow ellipsoidal shell, small polished grooves are 

 made coinciding with one series of circular sections, and a bright 

 point is placed at one of the umbilici in which the series termi- 

 nate : prove that ,the locus of the bright points seen by an eye in 

 the opposite umbilicus is a central section of the ellipsoid ; and 

 that the whole length of the path of any ray by which a bright 

 point is seen is constant. 



1598. A ray proceeding from a point on the circumference of 

 a circle is reflected n times at the circle; prove that its point of 

 intersection with the consecutive ray similarly reflected is at a 



distance from the centre equal to ^ = *Jl + 4n(n+ 1) sin'tf, 



6 being the angle of incidence of the ray and a the radius. 



1599. If a ray of light be reflected at two plane surfaces, its 

 direction before incidence being parallel to the plane bisecting the 



