July 11, 1884.] 



• KNOWLEDGE • 



33 



century. We have said above that had we sent our beam 

 of light perjiendicularly into the water it would have 

 pursued a rigidly rectilinear jiath throughout. If, though, 

 light struck its surface at all obliquely, refraction would 

 occur at once. As we have had ocular demonstration by 

 the aid of 'our bottle, when light passes from a rarer 

 medium into a denser one it is bent towards a perpendicular 

 to the refracting surface. On the othfr hand, when it 

 passes from a denser medium into a rarer one it is 

 bent from the perpendicular. And this brings us to the 

 incidental mention of the principle of reversibility. 

 By whatever path light travels from air into water, by 

 that same path will it return from water into air. So, again, 

 in Figs. (!, 10, 11, the object and its reflected image may be 

 regarded as interchangeable in their respective positions. 

 We shall probably have occasion to reiterate and insist 

 upon this law, lying as it does at the root of numerous 

 optical jihenomena. Reverting, however, to our figure. 

 The law discovered by Snell was this — that when light 

 passes from any medium to another of different density the 

 sine of the angle of incidence always bears a fixed and de- 

 finite ratio (or proportion) to the sine of the angle of refrac- 

 tion. The sine of an angle is defined in old niathematical 

 books — in a way much more intelligible to the learner than 

 that employed in more modern ones — as a line drawn from 

 one extremity of an arc at right angles to the diameter 

 from the other extremity. Thus, in Fig. 15, PiS is the sine 

 of the angle R C P ; R' S' the sine of the angle R' C P ; m 

 the sine of the angle rCP', and r's' the sine of the angle 

 '/•' C P'. A little attention will show how these conform to 

 the definition just given. Then, Snell's law says this : if 

 (as we shall find to be the case) RS is 1 J times the length 

 of r s, R' S' will be 1^ times the length of r' s', and so on 

 for any angle of incidence we may select. Now, here we 

 will pause to call attention to a very remarkable circum- 

 stance. We have said that light passing from air into 

 water will be refracted, if it do so, " at any angle of inci- 

 dence ; " but, if the student has followed us attentively so 

 far, he will see that the converse of this will not hold 

 good, and that our choice of angles of incidence in the 

 passage of light from vater to air is not unlimited. 

 For it is easy to see that the angle of incidence might be 

 so great that the sine of the angle of refraction being \\ 

 times as large must be greater than CW, the radius of the 

 circle, which is impossible ; or, to put it another way, he 

 may select such an angle of incidence in water that the 

 light must emerge parallel with the surface, and when we 

 increase such angle the light cannot get out of the icater at 

 all, and is totally reflected. The incidental angle at which 

 the emergent ray is parallel to — or, rather, in — the surface 

 of the water, is known technically as " the critical angle." 

 Total reflection may be observed by looking obliquely 

 upwards at the inner surface of the water in a clear glass 

 tumbler at the image of a candle, a silver spoon, or other 

 bright object held on the other side of the tumbler. It 

 may also often be noticed in aquaria, such as the one at 

 Brighton, in which the surface of the water seen at the 

 proper angle from beneath reflects the fish near it, and 

 shines like molten silver. Or, by turning our card, which 

 covers the side of the bottle in Fig. 14, upside down, so that 

 the slit in it is below the level of the water, we may reflect 

 our beam of light upwards to its inner surface, and trace 

 its reflection visibly. The " mirage " of the desert is 

 believed to have its origin in total reflection from the sur- 

 face formed by two adjacent strata of air of different tem- 

 peratures and densities. We have spoken of the sine of 

 the angle of incidence of a ray of light passing from air into 

 water being 11 times the length of the fine of refraction. 

 It is more accurately 1-336 times that length; and this 



number 1-33G is called " the index of refraction " of waterj 

 The denser a body the higher its index of refraction. 

 Thus it is I'.'iT") in flint glass, and sometimes as high 

 as 2-75 in the diamond. Hence the incomparable 

 lustre of this stone. Numerous illustrations of refraction 

 will occur to the reader. One of the most familiar is none 

 the less instructive. Let him get a pie-dish, and put a 

 sixpence at the bottom of it. Now, let him walk back- 

 wards until the side of the dish just hides the sixpence, 

 and remain perfectly still while some one else pours water 

 into the dish. The effect will be to bring the sixpence into 

 view again. Fig. 1.") will show how the water bends the 

 r.iys of light from the coin over the rim of the dish. Or 

 he may vary the experiment by so placing a lamp that the 

 side of the pie-dish casts a long shadow on the bottom of 

 it when empty. Then, as before, on pouring in water, the 

 shadow will be seen to shorten perceptibly, and to approach- 

 the side casting it. So an oar or a stick partly immersed 

 in water seems broken or bent at the surface ; and a fisher- 

 man looking obliquely at the bottom of a clear lake from 

 its bank sees it apparently only about three-quarters of its- 

 real depth. Or, instead of water, we may employ a thick 

 piece of plate-gla.ss to produce refraction ; and, hiding some 

 writing behind the edge of a thin book lying flat on a table, 

 as we did the sixpence with the edge of the pie dish, bring 

 it into view again by placing our piece of plate-glass upon 

 it. And the mention of jilateglass suggests to us here 

 to investigate the course of a ray of light passing, 

 through such a medium. In Fig. 16, G G is a sectioa 



Fig. IG. 



or edgeways view of a window-pane ; R P, a ray 

 (suppose from a tree-top) incident on the outside of the 

 glass at P. Then, as we have seen above, this ray 

 will be bent towards the perpendicular in the glass. 

 On reaching the other surface, however, at p, it will be 

 bent from the perpendicular, and will follow the direction 

 pE, parallel to RP, and will be seen by an eye at E as 

 though it emanated from R', thus slightly raising our ima- 

 ginary tree-top. Inasmuch, however, as the whole land- 

 scape is equally raised, ybr the same obliquity of vision, no 

 sensible distortion is apparent. Quite obviously, objects 

 from which rays fall square on to the surface of the glass suffer 

 no apparent change of position whatever. It must be pretty 

 evident that the higher the refractive index of any sub- 

 stance, the greater the displacement of a ray of light passing 

 through it ; so that if we could conceive a window formed 

 of sheets of diamond, and one pane to be left open, the 

 landscape would be very notably raised as viewed through 



