Page:Elementary Text-book of Physics (Anthony, 1897).djvu/433

§ 343] as one of a group parallel to the axis. All such rays must, after passing through the lens, pass through the principal focus. $$LA',$$ passing through $$F,$$ is therefore the emerging ray, and its intersection with $$AA'$$ locates the image of $$A.$$ Hence, to construct the image of a point, draw from the point two incident rays, and determine the corresponding emergent rays. The intersection of these will determine the image. The rays most convenient to use are the ray through the optical centre and the ray parallel to the axis or through the principal focus. Fig. 109 gives another example of an image determined by construction.

342. Thick Lenses.—When a lens is of considerable thickness, the formula derived in § 337 does not give the true position of the conjugate foci. A formula involving the thickness of the lens may be derived without difficulty, but for practical purposes it is usual to refer all measurements to two planes, called the principal planes of the lens. The determination of the position of these planes involves a discussion which does not come within the scope of this book.

343. Mirrors and Lenses of Large Aperture.—The equations derived in §§ 336, 337 are only approximations, applying with sufficient exactness to mirrors and lenses of small aperture. But for large apertures, terms containing the higher powers of $$x$$ cannot be neglected, $$x$$ will not disappear from the expression of $$p',$$ and $$p'$$ will, therefore, not have a definite value. In other words, the reflected or refracted wave is not spherical, and there is no one point $$l$$ where the light will be concentrated. Surfaces may, however, be constructed which will, in certain particular cases, produce by reflection or refraction perfectly spherical waves. If we desire to find a surface such that light from $$L$$ (Fig. Fig. 110. 110) is concentrated by reflection at $$l,$$ we remember that the sum $$LB + Bl$$ must be constant, and that this