The six forms shown in fig. 9 are all used in optical constructions. It may be stated fairly generally that lenses which are thicker at the middle are collective, while those which are thinnest at the middle are dispersive.
| Fig. 10. |
Different Positions of Object and Image.—The principal points are always near the surfaces limiting the lens, and consequently the lens divides the direct pencil containing the axis into two parts. The object can be either in front of or behind the lens as in fig. 10. If the object point be in front of the lens, and if it be realized by rays passing from it, it is called real. If, on the other hand, the object be behind the lens, it is called virtual; it does not actually exist, and can only be realized as an image.
| Fig. 11. |
When we speak of “object-points,” it is always understood that the rays from the object traverse the first surface of the lens before meeting the second. In the same way, images may be either real or virtual. If the image be behind the second surface, it is real, and can be intercepted on a screen. If, however, it be in front of the lens, it is visible to an eye placed behind the lens, although the rays do not actually intersect, but only appear to do so, but the image cannot be intercepted on a screen behind the lens. Such an image is said to be virtual. These relations are shown in fig. 11.
| Fig. 12. |
By referring to the equations given above, it is seen that a thin convergent lens produces both real and virtual images of real objects, but only a real image of a virtual object, whilst a divergent lens produces a virtual image of a real object and both real and virtual images of a virtual object. The construction of a real image of a real object by a convergent lens is shown in fig. 3; and that of a virtual image of a real object by a divergent lens in fig. 12.
| Fig. 13. |
The optical centre of a lens is a point such that, for any ray which passes through it, the incident and emergent rays are parallel. The idea of the optical centre was originally due to J. Harris (Treatise on Optics, 1775); it is not properly a cardinal point, although it has several interesting properties. In fig. 13, let C1P1 and C2P2 be two parallel radii of a biconvex lens. Join P1P2 and let O1P1 and O2P2 be incident and emergent rays which have P1P2 for the path through the lens. Then if M be the intersection of P1P2 with the axis, we have angle C1P1M = angle C2P2M; these two angles are—for a ray travelling in the direction O1P1P2O2—the angles of emergence and of incidence respectively. From the similar triangles C2P2M and C1P1M we have
C1M : C2M = C1P1 : C2P2 = r1 : r2.