(A) If a luminous body is at a great distance at the left, its light is brought to a focus at P, or its image is formed at P. (B) As the object approaches the lens the image gradually recedes until the object and image are at S and S´, equally distant from O and of equal size (as in Fig. 383). The object and image are now said to be at the secondary foci of the lens. (C) As the object moves from S to P the image recedes, rapidly increasing in size until (D) when the object is at P the rays become parallel and no image is formed. (E) When the object is between P and the lens, the rays appear to proceed from points back of the object, thus forming an erect, larger, virtual image of the object. (See Fig. 384.) This last arrangement illustrates the simple microscope.
With a concave lens but one case is possible, that corresponding to the one last mentioned with convex lenses; since the rays from a body are divergent after passing through a concave lens they appear to proceed from points nearer the lens than the object and hence a virtual, erect, smaller image of the object is formed. This virtual image may be seen by looking through the lens toward the object. (See Fig. 385.)
Fig. 384.—Construction of a virtual image by a convex lens.
Fig. 385.—Construction of a virtual image by a concave lens.
388. The Lens Equation.—The location of either the object or of the image upon the principal axis of the lens may be calculated if the position of one of these and the focal length are known. This is accomplished by the use of a formula 1/F = 1/D0 + 1/D1 in which F represents the focal length and D0 and D1 the distance from the lens of the object and the image respectively. Thus if an object is placed 30 cm. from a lens of 10 cm. focal length, where will the image be formed? Thus: 1/10 = 1/30 + 1/D and 3D1 = D1 + 30, or 2D1 = 30 D1 = 15. This result indicates that a real image will be 15 cm. from the lens. A minus value would indicate a virtual image.
Important Topics
(A) Lenses: convex, concave, six forms, center and radius of curvature.
(B) Principal focus, focal length, virtual focus, conjugate foci.