COJTCAVB LSSSES.] 



UNDULATORY FORCES. LIGHT. 



47 



T*rallel position, provided that II is a homogeneous 

 substance, or of equal size in every part. But 1 1 forms 

 part of a spherical refracting medium, such as glass, <fcc. ; 

 and, as such, the rays passing through it will, with the 

 exception of 6', which is in its axis, all fall upon it 

 obliquely, and will therefore be refracted, or bent, from 

 their straight course. Instead, therefore, of continuing 

 on towards a a,', itc., they will incline towards each 

 other, and at last meet in one focus /, which is the 

 focus of the lens under examination. This focal point is 

 found, in the case of the plano-convex lens, to be of a 

 distance, from the centre of the lens I I, equal to the 

 diameter of the sphere or circle, of which the curved 

 surface of the lens forms part. This will be observed in 

 our diagram, where / is placed at the extremity of the 

 diameter of the circle including the curvature of the lens. 



In the double convex lens, the focus is found at the 

 centre of the circle of curvature, and will, therefore, be 

 at only half the length of the diameter of the circle, from 

 the centre of the lens ; in other words, the extremity of 

 the radius of the circle, drawn from the glass, will be the 

 focal point of this class of lens. As an illustration of 

 this and the previous rule of finding the foci of these two 

 kinds of lenses, wo may add, that presuming the curva- 

 ture of a plano-conrex lens to be part of a circle three 

 feet in circumference, then its focal point would be found 

 about twelve inches behind it. If, however, we take the 

 case of a double convex lens, we should find the focus six 

 inches behind it, which is about the length of the radius 

 of a circle thirty-six inches in circumference. 



As e are confining our attention to the course of 

 parallel rays through lenses, we will next examine the 

 effect thereon when they pass through a double concave 



I:.'. U, 



a 



a 



Fig. 10 represent* a lens where both surfaces are con- 

 cave :aba are three parallel rays of light, incident on 

 one surface of the lens 1 1. We shall find that the centre 

 ray b will continue its straight course to 6', being in the 

 axis of the lens, and passing through its centre. In the 

 case of the rays a a, we find that they are refracted dur- 

 ing their passage, falling as they do on the curved surface 

 of the lens ; and on emission on its opposite side, we 

 observe that they diverge, as shown in the lines a' a'. 

 The focus of this lens will be found at /, or at such a 

 point as would be arrived at on the line 6, by the re- 

 fracted rays a and a, if they were produced backwards 

 through the lens to /, which is the centre of the cavity of 

 tii'- u'l ;"< 



It will bo found that / will be distant from the centre 

 of the lens to the extent of the length of the radius of 

 the circle of curvature. If, however, the lens is plano- 

 concave, then, like the plano-convex, its focus will be 

 distant from the centre of the glass to the extent of the 

 diameter of the circle, of which the curve of the lens is a 

 portion. 



By following the above rules, the foci of a meniscus 

 and concavo-convex lens may be found : as, however, 

 these are not likely to engage the attention of the reader, 

 we shall not enlarge on the matter. 



Having thus examined the effects produced on rays of 

 light passing through lenses of various forms, we shall 

 now refer to other results, which are more especially con- 

 nected with their practical uses. 



If the rays of light passing from an object placed at 

 some distance beyond the focal point of a convex lens, 

 are viewed after their passage through the glass, an in- 

 verted imago of the object may be seen by placing a piece 

 of ground-glass, oiled paper, <tc., BO as to receive the 

 transmitted rays near the focus, on the opposite side to 

 that of the object. The inversion of the image is 'caused 

 by the rays crossing each other. This is illustrated in 



Fig. 20, where o represents the object, 6 the lens, and c 

 the inverted image. 



20. 



Now, if the rays pass from d in the object a, they will 

 be found refracted as passing obliquely through the lens, 

 and their image will be seen at d' , on the screen c ; and 

 so with the rays passing from the object at e, their imago 

 will appear on the screen c at e', of course inverted. 



One of the simplest methods of illustrating this pro- 

 perty of convex lenses, is that of allowing the rays of a 

 candle, whose flame is placed beyond the focus of a 

 double convex lens, to pass through the glass on to a 

 sheet of paper placed on the other side. The inverted 

 imago of the flame will be at once observed. If a lens, 

 again, is held towards a window, and the rays of light 

 passing from external objects be received on paper or 

 ground-glass, as before mentioned, a complete but inverted 

 representation of them will be seen. On this principle 

 the camera-obscura is constructed, an instrument of 

 which we shall give a full description under the head of 

 Optical Instruments. 



On placing a piano or double convex lens batween tho 

 eye and an object, the latter will present a magnified 

 image, if at about a distance from the lens equal to its 

 focal length : this effect is called the magnifying power 

 of a lens, and varies in proportion to the difference of 

 focal lengths in lenses, when compared with each other. 

 The shorter the distance of the focus from the centre of 

 the lens, the greater will be the magnifying power of the 

 instrument.- This effect in convex lenses is owing to 

 our being enabled to view any object at a larger angle, 

 by their assistance, than could be done by the eye alone. 



Perhaps the most ready mode of illustrating this law, 

 will be that of referring the student to the apparent 

 diminution of an object as wo recede from it. The 

 further we are from any form, the less angle does it 

 subtend to tho eye : the nearer we approach to it, the 

 larger this angle of vision becomes ; and thus the object 

 appears of greater size. Now the effect of a lens is to 

 collect the rays passing from an object placed at its focal 

 point ; and, by refraction, these rays reach the eye, 

 subtending a greater angle on the retina than that exist- 

 ing from the centre of the unassisted eye itself ; hence, 

 of course, the image is enlarged. The effect of concave 

 lenses is directly tho reverse of this, for they diminish tho 

 angle at which an object is seen ; and hence the apparent 

 size is also lessened. 



We have thus endeavoured to give an explanation of 

 the laws of lenses, and of many phases of single refraction. 

 We shall enlarge on tho various uses of lenses under the 

 head of Optical Instruments, in respect of the micro- 

 scope, telescope, <tc. Wo shall defer the consideration of 

 double refraction to tho subject of Polarisation, with 

 which it stands so intimately connected ; and shall now 

 attempt to show the application of these laws of lenses, 

 so far as they refer to the structure and use of the eye. 



THE EYE AND ITS STRUCTURE. 



Fig. 22. 

 Fif. 51. 



a, the cornea, cmUlning th aquwm humour; I, the pupil; c, the 

 crystalline U-n; /, the irU; y, chamber of the vitreous humour; A, 

 the optic mrrc ; i i, the tclcrotica ; X k, the choroidea ; I /, the retina. 



