ON THE THEORY OF OPTICS. 4J7 



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 cal- 

 culations, 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 surface 

 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 cither causes them to diverge, or lessens their convergence. (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 dif- 

 ference. 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 substance, 

 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-i, we must divide the radius by ^, or increase it one half, for 

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

 water. 



When a radiant point is at twice the distance of the principal fOcus from 

 a convex lens, the image is at an equal distance on the other side; when the 



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