2. When a ray passes through a triangular prism _a b c_, the inclination of the faces _a c_ and _c b_ causes the emergent ray _r′_ to be bent towards _a b_, the base of the prism, in a measure depending on the inclination of the sides of the prism and the obliquity of the incident ray to the first surface. [Illustration: Fig. 50.] 3. When parallel rays fall on a concave lens, they will, at their emergence, be divergent. The section of the diaphanous body _a b c d_ may be regarded as composed of innumerable frusta of prisms, having their apices directed towards the centre line _x r_; and the rays which pass through the centre, being normal to the surface, will be unchanged in their direction, while all the others will (as shewn in the figure) suffer a change of direction, increasing with their distance from the centre, owing to the increasing inclination of the surfaces of the lens as they recede from its axis. [Illustration: Fig. 51.] 4. Lastly, when divergent rays fall on a convex lens _a b_, from a point _f_, called the principal focus, they are made parallel at their emergence; while, _conversely_, parallel rays which fall on the lens are united in that point.[54] This effect, which is the opposite of that caused by the concave lens, may be explained in a similar manner, by conceiving the section _a b_ of the convex lens to be composed of innumerable frusta of prisms, arranged with their _bases_ towards the centre of the lens. [54] It is, of course, to be understood that only rays incident near the axis of the lens are refracted accurately to a focus. [Illustration: Fig. 52.] Now, it is obvious, that we can derive no assistance, in economising the rays of a lamp for Lighthouse purposes, from concave lenses, whose property is to increase the dispersion of the rays incident on them. With concave lenses, therefore, we have no concern; and we shall confine ourselves to the consideration of the convex or converging lenses. The lens always used in Lighthouses is (for reasons already noticed) plano-convex, and differs from the last only by having a plane and a curve surface, instead of two curve surfaces, whose radii are on opposite sides of the lens. The plano-convex is generally regarded, by writers on optics, as a _case_ of the double convex having one side of an _infinite_ radius. Both forms cause parallel rays to converge to a focus. We commence with a general view of the relations which exist between the position of the _radiant_ and the focus. [Illustration: Fig. 53.]