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.
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.
Fig. 53.