Page:Elementary Text-book of Physics (Anthony, 1897).djvu/431

§ 340] and larger than the object. Convex mirrors produce only virtual images, which are erect and smaller than the object.

339. Images formed by Lenses.—Let us suppose an object in front of a double-convex lens, which may be taken as a type of the converging lenses. The point $$c$$ (Fig. 106) will have an image at the conjugate focus on the principal axis, $$a$$ and $$b$$ will have images on secondary axes drawn through those points respectively, and a point called the optical centre of the lens. So long as these secondary axes make but a small angle with the principal axis, definite foci will be formed at the same distances as on the principal axis, and an image $$a'b'$$ will be formed which will be real and inverted, or virtual and erect, according to the distance of the object from the lens. The formula $$\frac{1}{p} + \frac{1}{p'} = (\mu - 1) \left( \frac{1}{r} + \frac{1}{r'} \right) = \frac{1}{f}$$ shows that when $$p$$ increases $$p'$$ diminishes, and conversely. It shows also that when $$p$$ is less than $$f, \, p'$$ is negative, and the image virtual. It is plain from the figure that the sizes of image and object are in the ratio of their distances from the lens. Diverging lenses, like diverging mirrors, produce only virtual images smaller than the object.

340. Optical Centre.—It was stated in the last section that the secondary axes of a lens pass through a point called the optical centre. The position of this point is determined as follows: In Fig. 107, let $$C, C'$$ be the centres of curvature of the two surfaces of the lens, and let $$CA$$ and $$C'B$$ be two parallel radii. The tangents at $$A$$ and $$B$$ are also parallel, and light entering at $$B$$ and emerging at $$A$$ is light passing through a medium with parallel surfaces (§ 334), and suffers no deviation.