312 



OPTICS. 



Index qf Refraction. 



2-974 

 . 2-755 

 2-224 

 2-028 

 1-987 



ix table of such numbers showing the lengths of the 

 sines of the angle of incidence, the length of the 

 sine of the angle of refraction, being always regarded 

 as one, is called a table of refractive powers, and the 

 numbers l-.'i.'i, 1-5, &c., are denominated the indices 

 of refraction. The following is a specimen of such 

 tables : 



Mttfcte 

 Chromate of lead 



Diamond 



Phosphorus .... 

 Glass ilead 3 flint 1) ... 

 (lead 2, saud l) 



Flint gloss 1-605 



Copal 1-549 



Crown glass . . ' 1-525 



Dutch plate glass 1-517 



Oil of turpentine . 1-475 



Sulphuric acid 1-440 



Alcohol 1-37 



Water ........ 1*33 



Although, in most cases, there is a connexion 

 between the refractive power and the density of 

 bodies, yet refraction does not invariably increase 

 with their density. In the case of oily substances 

 and inflammable bodies, such as hydrogen, phos- 

 phorus, sulphur, diamond, bees' wax, amber, spirit 

 of turpentine, linseed oil, olive oil, camphor, their 

 refractive powers are from two to seven times greater, 

 in respect to their density, than those of most other 

 substances. Sir Isaac Newton observed this fact 

 with respect to the last five substances, which, he 

 says, are " fat, sulphureous, unctuous bodies," and, 

 as he observed the same high refractive power in the 

 diamond, he inferred that it was probably an unctu- 

 ous substance coagulated. This law, however, at 

 one time, seemed to be overturned by an observation 

 of doctor Wollaston, that phosphorus, one of the 

 most inflammable substances in nature, had a very 

 low refractive power ; but doctor Brewster, confid- 

 ing in the truth of the law, examined the refractive 

 power of phosphorus by forming it into prisms and 

 lenses, and he found it to be nearly as high as dia- 

 mond, and fully twice that of diamond compared 

 with its density an observation which re-established 

 and extended the general principle respecting the 

 refractive power of inflammable substances. In fig. 

 2 we have represented side sections of the most com- 

 mon kinds of lenses, or optical glasses, fg is a line 

 drawn through their centre ; a represents a plano- 

 convex lens, being plane on the one side and convex 

 on the other ; b is a plano-concave, being plane on 

 the one side and concave on the other ; c is a double 

 convex lens, or convex on both sides ; el is a double 

 concave lens, or one with two concave sides ; e is a 

 concavo-convex or meniscus lens, being concave on 

 the one side and convex on the other. We now 

 proceed to show the action of these lenses in refract- 

 ing light, and first we shall explain the effect of the 

 plano-convex lens. 



In fig. 3 we have represented a plano-convex lens 

 with the parallel rays a c, b n, m d, falling upon its 

 convex surface. Now, not one of those rays, ex- 

 cepting the middle one b n, falls perpendicularly 

 upon the surface of the glass, but that ray will pass 

 directly on in the straight line b n C without chang- 

 ing its course. The rays a c and m d fall obliquely, 

 and will therefore be refracted in contrary directions, 

 and meet in the point C. So will all the other rays, 

 excepting the middle one, which never deviates from 

 its original course, but meets them in the point C. 

 The point C, at which the rays meet, can be shown 

 both by geometry and experiment, to be in the cir- 

 cumference of the circle of which the curvature of 

 the lens forms a part. The point C is called the 

 focus of the lens. Had the other side been also cur- 

 ved, the effect of refraction would have been still 

 greater, for then th rays would have passed out of 



the glass more obliquely than if it had been plane. 

 In fig. 4 we have shown two conv< x glasses. Sup- 

 pose the parallel rays A B, fig. 4, fall upon the lens 

 D E, which is doubly convex, they will be converged 

 into the focus/, which is situated in the centre of the 

 circle, whose radius is the same as that of the 

 curves of the surfaces. The same holds of the lens 

 F G, upon which the parallel rays b c fall. We are 

 supposing that the surfaces of the lens are of equal 

 curvature, but when they are not, the distance of 

 the focus from the centre of the circle will be found 

 by using this simple proportion as the sum of the 

 radii of both curves is to the radius of either, so is 

 double the radius of the other to the distance of the 

 focus from the middle point ; thus, if the one radius 

 be 4 and the other 3 inches, then 3 + 4=7 and 

 7:4: : 6 : 3 f inches. These remarks, respecting 

 the place of the focus, only hold true when the rays 

 which fall on the lens are parallel ; when they are 

 not, the place of the focus will be nearer to or far- 

 ther from the lens, according as the rays are conver- 

 gent or divergent before they reach the surface of 

 the glass. Thus, in fig. ~5, the rays before they 

 reach the lens are convergent, and would meet in 

 a point on the other side of the lens, even if it were 

 not interposed ; but the effect of the lens is to con- 

 verge the rays, and this added to the natural con- 

 vergence, which they possess before they reach the 

 lens, will cause them to converge sooner after they 

 pass through it, than if they had been parallel ; so 

 that, instead of meeting in the point/, which is the 

 centre of the circle of curvature, and which would 

 have been the focus had the rays been previously 

 parallel, they meet in the point g nearer to the lens, 

 which point is therefore the focus. On the othei 

 hand, if the rays proceed from an object x which is 

 near the lens, and diverge before they meet it, this 

 divergence will partly destroy the converging power 

 of the lens, and the rays will not meet so soon after 

 passing through it as if they had been previously 

 parallel ; they will meet in a point g, fig. 6, beyond 

 the centre of curvature / of the lens. Where the 

 rays meet, or in the focus of the convex lens, they 

 form an inverted image of any object, the rays of 

 light proceeding from which pass through it, for at 

 that point the rays cross each other. Let a b c, fig. 

 7, represent an arrow placed in the front, and beyond 

 the focus g of a double convex lens d ef, some rays 

 will flow from every point of the arrow, and fall 

 upon the lens : but we shall regard only those which 

 flow from the ends a and c, and the middle point *. 

 From the point a the rays a d, a e, and af issue, 

 and will be refracted by the lens, and meet in A. 

 The rays which come from the middle point b will 

 diverge, and passing through the lens will meet in 

 the point B and the rays which are emitted from c 

 will be converged into the point c at the top of the 

 image which is formed in the focus of the lens. 

 This may be easily proved by experiment. Hold a 

 convex lens at a distance from the window, and 

 place behind it a piece of paper, exactly in the focus, 

 it will be found that a distinct image of the window 

 and the objects beyond it will be formed on the paper, 

 but the image will be inverted, or the houses and 

 trees will appear at the top instead of the bottom. 



The action of a concave lens on rays of light is 

 quite different from that of a convex. If parallel 

 rays fall upon a concave lens, they will diverge after 

 refraction, and continue to deviate farther from one 

 another the farther they proceed. The form of the 

 concave lens being the reverse of the convex, its 

 effect may easily be conceived to be the reverse. In 

 fig. 8, A B represents a concave lens with parallel 

 rays entering it from the points a b c, &c. ; these rays 

 will, after passing through it, diverge in the directions 



