REFRACTION. 



Alcohol 



White of an egg 



jEther 



Vitreous humour of an eye 



Water 



Atmofpheric air (Haukfbee) 



1.36 

 '•358 



'•336 

 1.00032 



See Phil. Tranf. vol. xcii. for 1802. art. 12. See Dis- 

 persion of Light. 



From the law kid down in the beginning of this article, it 

 follows, that one angle of inclination, and its correfponding 

 refrafted angle, being found by obfervation, the refratted 

 angles, correfponding to the feveral other angles of in- 

 clination, are eafdy computed. Now, Zahnius and Kir- 

 cher have found, that if the angle of inclination be 70°, 

 the refrafted angle will be 38° 50'; on which principle 

 Zahnius has conftrudVed a table of refraftions out of air 

 into glafs, for the feveral degrees of the angle of inclination ; 

 a fpecimen of which follows : 



Hence it appears, that if the angle of inclination be lefs 

 than 20'', the angle of refraftion out of air into glafs is al- 

 moft one-third of the angle of inclination ; and, therefore, a 

 ray is refradled to the axis ol refraftion, by almolt a third 

 part of the quantity of its angle of inclination. And on 

 this principle it is that Kepler, and raoit other dioptrical 

 writers, demonftrate the refraftions in glafles ; though in 

 eftimating the law of thefe refractions, he followed the 

 example of Alhazen and Vitellio, and lought to difcover 

 it in the proportion of the angles, and not in that of the 

 tines. 



The true law of refraftion was firft difcovered by Wille- 

 brord Snellius, profeflbr of mathematics at Leyden ; sn\\o 

 found by experiment that the fecants of the complements, 

 or co-fecants, of the angles of incidence and refraftion, are 

 always in the f^me ratio. It is vulgarly attributed, how- 

 ever, to Defcartes ; who having feen it in Snellius's MS., 

 firft publifhed it in his Dioptrics, without naming Snellius ; 

 as we are informed by Huygens. The form in which 

 Defcartes gives this law is different from that of Snellius, 

 and in general more commodious ; but it might have been 

 eafdy deduced from it. According to him, the fine of the 

 angle of refraftion always bears the fame proportion to the 

 line of the angle of incidence. Indeed, as the rays of light 

 are not all of the fame degree of refrangibility, this conilant 

 ratio mull be different in different kinds. The ratio, there- 

 fore, obferved by authors, is to be underllood of rays of the 

 mean refrangibility, i. e. of green rays. The difference of 

 refraftion betv/een the Icaft and moft refrangible rays, that 

 is, between violet and red rays, fir Ifaac Ne\yton (hews is 

 abo>at the 27^th part of the whole refraftion of the mean 



refrangible ; which ditfercnce he owns is fo fraail, that there 

 leldom needs to be any regard paid to it. 



3. When a ray paps out of a denfer into a rarer medium, 

 e.gr. out of glafs into air, it is refraded from the perpen- 

 dicular, or from the axis of ref radian. And hence the angle 

 ot refraftion is greater than the angle of inclination. 



lience, alfo, if the angle of inclination be lefs than «o°, 

 MiiC (Pto^ XVIII. Optics, fig. II.) is nearly equal to 

 onc-lhird oi M B E ; therefore MBC is one-half of C B E; 

 confoquently, if the refraftion be out of glafs into air, and the 

 angle of inclination lefs than 30°, the ray isrefrafted from the 

 axis of refraftion by almolt one-half part of the angle of in- 

 clination. And this is the other dioptrical principle ufed bv 

 moll authors after Kepler, to demonftrate the refraftion o'f 

 glafles. 



If the refraftion be out of air into glafs, the ratio of tlic 

 fine of inclination to tiic fine of the refrafted angle is as 

 3 to 2, or, more accurately, as 17 to 11 ; if out of air 

 into water, as 4 to 3 : therefore, if the refraftion be the 

 contrary way, r«. out of glafs or water into air, the ratio 

 of the fines, in the former cafe, will be as 2 to 3, or 11 to 

 1 7, and in tlie latter as 3 to 4. 



Hence, if the refraftion be from water or glafs into air, 

 and the angle of incidence or inclination be greater than 

 about 481° in water, or greater than about 40"^ in glafs, the . 

 ray will not be refrafted into air, but will be reflcfted into 

 a line, which makes the angle of refleftion equal to the angle 

 of incidence ; becaufe the fines of 485° and 40° are to the 

 radius as 3 to 4, and as ii to 1 7 nearly, and therefore when 

 the fine has a greater proportion to the radius than as above, 

 the ray will not be refrafted. 



4. A ray falling on a curve furf ace, -whether concave Or con- 

 vex, is refraded after the fame manner as if it fell on apian: 

 which is a tangent to the curve in the point of incidence. 



For tlie curve and plane furface touching it, have an infi- 

 nitely fmall part common to them both (each being originally 

 generated by the flux of a point). But a ray isrefrafted 

 m fuch a little part ; therefore it is the fame as if it were re- 

 frafted in fuch a plane. 



5. If a right line EF {Plate XVIII. Optics, fg. 14.) 

 cut a nf raffing furface, G H, at right angles ; and if from 

 any point in the denfer medium, as D, he draiun D C parallel 

 to the incident ray A B : this luill meet the refraded ray in C ; 

 and "Mill be to it as the fine of the refraded angle to the fine of 

 the angle of inclination. 



For = X ; but if B C pifs out of a denfer medium into 

 a rarer, y > x; and out of a rarer into a denfer, y Kx; 

 therefore, in the former cafe, y > 0, in the latter _y < o ; 

 confequently, in the former, -\- u < y + u ; in the latter 

 y -\- u <. + u. But in the one cafe + u, and in the 

 other y f u, are equal to two right angles ; therefore, 

 -r u m this, a.ndiy 4- u in the other, are lefs than two 

 right angles, and_ confequently D C will meet B C. But 

 fince = X, or the angle of inclination, and_>r is the re- 

 frafted angle, it is evident that C B is to C D as the fine 

 of the angle to the fine of the angle y, or in the ratio of 

 the fine of the angle of inclination to the fine of the re- 

 frafted angle. 



Hence, if B C pafs out of glafs into air, it is in a fub- 

 feiquialterate ratio to G D ; if, on the other hand, it 

 paffe;-, out of air into glafs, it is in a fefquialterate ratio to 

 CD. 



Hence, alfo, if light pafs out of water into airi C B is in 

 a fubfefquitertian ratio to C D ; if out of air into water, 

 in a fefquitertian. &csf.gs. 14 and 15. 



Rls.FR\criON in plane fmfaces, laivs of . I. If parallel rays 

 be refrafted out of one traiifparent medium into another of 



a dif- 



