32G LECTURE XXXV. 



observed : and the same is true of the foci produced by refracting sur*ces. 

 (Plate XXVII. Fig. 377, 378.) 



When a ray of light passes through two surfaces forming an angle with 

 each other, including a denser medium, as in the case of a prism of 'glass, 

 it is always deflected from the angle in which the two surfaces meet. A 

 greater number of surfaces, placed in different directions, constitute what 

 is sometimes called a multiplying glass, each of them bending the rays of 

 light into a different direction. (Plate XXVII. Fig. 379, 380.) 



A lens is a detached portion of a transparent substance, of whic^ the 

 opposite sides are regular polished surfaces, of such forms as may be 

 described by lines revolving round a common axis. These lines may be 

 portions of circles, of ellipses, hyperbolas, or of any other curves, or they 

 may be right lines. But in general, one of the sides is a portion of a 

 spherical surface, and the other either a portion of a spherical surface or 

 a plane ; whence we have double convex, double concave, planoconvex, 

 planoconcave, and meniscus lenses. The figures of all these are suffi- 

 ciently described by their names, except that the term meniscus, which 

 properly implies a little moon or crescent, is applied in general to all lenses 

 which are convex on the one side and concave on the other, although they 

 may be thicker at the edges than in the middle. Sometimes, however, a 

 lens of this kind is distinguished by the term concavoconvex. A lens is 

 generally supposed, in simple calculations, to be infinitely thin, and to be 

 denser than the surrounding medium. (Plate XXVII. Fig. 381.) 



The general effect of a lens may be understood, from conceiving its sur- 

 face to coincide at any given point with that of a prism ; for if the angle 

 of the prism be external, as it must be when the lens is convex, the rays 

 will be inflected towards the axis ; but if the base of the prism be external, 

 and the lens concave, the rays will be deflected from the axis : so that a 

 convex lens either causes all rays to converge, or lessens their divergence, 

 and a concave lens either causes them to diverge, or lessens their conver- 

 gence. (Plate XXVII. Fig. 382.) 



The principal focus of a double convex or double concave lens, of crown 

 glass, is at the distance of the common radius of its surfaces ; and the focal 

 length of a planoconvex lens is equal to the diameter of the convex surface. 

 If the radii of the surfaces are unequal, their effect will be the same as if 

 they were each equal to the harmonic mean between them, which is found 

 by dividing the product by half the sum ; or, in the meniscus, by half the 

 difference. Thus, if one of the radii were two inches, and the other six, the 

 effect would be the same as that of a lens of three inches radius ; and if it 

 were a meniscus, the same as that of a lens of six inches. (Plate XXVII. 

 Fig. 383, 384.) 



The focal length of a lens of flint glass, of water, or of any other sub- 

 stance, may be found, by dividing that of an equal lens of crown glass by 

 twice the excess of the index of refraction above unity. Thus, the index 

 for water being 1, we must divide the radius by f, or increase it one half, 

 for the principal focal distance of a double convex or double concave lens 

 of water. 



