PARABOLIC REFLECTORS. ] 



UNDULATORY FORCES. LIGHT. 



43 



of our readers, werj we to enter into an exact analysis of 

 the different curv<jd surfaces which might be employed 

 to overcome this tendency to aberration. There is, how- 

 ever, one curved surface, called the parabola, which, 

 employed as the reflective curve of any mirror, enables 

 us to get rid of aberration, and so to effect the reflection 

 of incident rays in a far more perfect manner. The 

 curve called an ellipse answers a similar purpose. 

 Without, therefore, entering into any mathematical dis- 

 quisition on the subject, we may state, that, obeying the 

 law of reflection the angle of incidence and reflection 

 being always equal to each other rays of light incident 

 on a parabolic or elliptic reflector, will, owing to the pro- 

 perties of these curves, be converged to one focus ; and, 

 vice vend, all rays passing from the foci of these curves 

 to the reflecting surface, will be equally reflected there- 

 from to the other foci of similar curves. The value of 

 this law will be at once seen when we have to refer to the 

 use of mirrors in various optical instruments. 



That the non-mathematical student may understand 

 the difference existing between the curvature of a sphere, 

 an ellipse, and a parabola, we annex a diagram illustrat- 

 ing each of these curves. (See Fig. 9). 

 Kg. 9. 



1. J. 3. 



In Fig. 9, No. 1 represents a portion of a sphere ; 

 No. 2, of an ellipse ; No. 3, of a parabola. In each of 

 these, a e is the axis of the curve, and e the focus of 

 incident rays. The lines d t show the direction of a 

 reflected ray from its source to the focal point. 



Having thus endeavoured to explain the laws of reflec- 

 tion of concave curved surfaces, we proceed to examine 

 the effect on a ray of light incident on surfaces of a 

 convex nature. We may state, generally, that exactly 

 opposite results are produced by convex to concave re- 

 flectors, the incident rays being always diverged from 

 those of a convex form. Thus, in Fig. 10, we have 

 . 10. a portion of a sphere, a b e, 



on which rays of light, d e, f g, 

 are incident. Instead of con- 

 , verging to a point in front of 

 the mirror, the real focal point 

 would be found at h, or that 

 place which would be the focus 

 of rays incident on a curved 

 surface of a concave form, hav- 

 ing the same centre of curva- 

 ture. The ray thus incident will take the direction e i 

 and >j H, if not in the same line with the axis of the mirror. 

 The ray in the axis of the mirror will be reflected back 

 in the same line as that of incidence, for reasons which 

 we have already frequently explained. The same re- 

 marks apply to a parabolic reflector, the internal or con- 

 cave focus being also that point from which rays incident 

 on its convex surface will be diverged. This is illustrated 



Fig. ll. 



in Fig. 11, where/ is the focus 

 of the parabola a 6 e, and d a 

 ray of light, which is incident 

 on its convex exterior, and 

 diverged in the direction a e. 



Having thus pointed out 

 some special laws affecting the 

 reflection of light from surfaces 

 of different curved forms, we 

 shall leave their extended ap- 

 plication as in the case of reflecting telescopes to the 

 subject of Optical Instruments, when the variety of uses 

 to which reflectors are adapted will bo fully dealt with. 

 We shall next proceed to examine the phenomena of 

 refraction, which are produced in bodies capable of allow- 

 ing the passage of light through them ; and shall deal 

 with those change* to which a ray is thus subjected. 



REFRACTION OF LIGHT, OR DIOPTRICS. 



HAVINO examined the results which take place when a 

 ray of light falls on a reflecting surface, we proceed to 

 investigate the phenomena of refraction, or the effects 

 produced when light passes through transparent media of 

 different densities. 



If a ray of light pass perpendicularly through any 

 medium of equal or homogeneous character in every 

 part, it will do so in a straight line. If, however, the 

 medium vary in its density, then the ray will be bent out 

 of its straight course ; and, to use philosophical terms, we 

 say that it is "refracted." If the ray pass obliquely, 

 the same effect will occur. We shall be better under- 

 stood if we give instances wherein this refraction takes 

 place. Amongst them are the following. 



On looking from the banks of a river at a fish swim- 

 ming in the water, we see the fish at some distance 

 from its real place, owing to the rays of light passing 

 from its body being bent or refracted from a straight 

 line. 



A stick introduced obliquely into a pail of water, 

 appears broken, because the rays of light from that 

 portion in the water, and from that remaining in the air, 

 do not reach the eye at the same angle. 



In looking down a long trough of water, the bottom of 

 the trough seems to touch the surface of the liquid at 

 that end furthest from the eye of the spectator. Again, 

 if a coin be placed in a basin, and the observer retreats 

 until he just loses sight of it, the piece of money will 

 reappear on water being poured into the vessel ; because, 

 by the refractive power of the liquid, the rays of light are 

 bent upwards, and so reach the eye. 



On looking through a piece of window-glass of different 

 thicknesses, all straight lines so observed will appear 

 curved. A similar effect is observed when the eye is 

 placed in a line with the surface of a wall strongly heated 

 by the sun's rays. Objects viewed through the heated 

 air arising from the surface, will appear to assume most 

 fantastic shapes, owing to the refraction of light thus 

 produced. 



The refraction of light causes the heavenly bodies to 

 appear, if viewed by the naked eye, much larger when 

 near the horizon than when at the zenith. Tlu's effect is 

 often noticed at those seasons of the year when moisture 

 is abundant in the air, or when the atmosphere is 

 heated. The apparent position of the sun is thus 

 altered by refraction ; and we therefore observe the disc 

 of that body some time before it has actually risen. 

 This effect is illustrated in the following engraving (Fig. 

 12), wherein the in- Fi 12 _ 



ner circle represents 

 the earth, and the 

 outer one the at- 

 mosphere. The up- 

 per line points to the 

 apparent position of 

 the sun before ris- 

 ing; the sun actually 

 being below the ho- 

 rizon, as shown in 

 the second line, al- 

 though visible to the 

 spectator by the re- 

 fraction which its rays undergo whilst they pass through 

 the air. 



Having thus given familiar instances of the effects of 

 the refraction of light, we proceed to investigate the 

 laws in accordance with which its phenomena are mani- 

 fested. 



For this purpose, we annex diagrams which illustrate 

 the progress of a ray of light from a rare to a compa- 

 ratively dense medium, and vice versa ; and at the same 

 time they indicate the refraction or bending of the rays 

 duringtheir progress. 



In Fig. 13 we observe the progress of a ray from c, at 

 an oblique position to the perpendicular line o 6. On 

 arriving at the surface of the water, / g, the ray does 



