REFRACTION. 



a diflc'reiit denfity, tlicy will coiiiiime parallel after refiaftion. 

 The pliyfical reafon is, that, being parallel, their obliqiiity, 

 or angle of incidence, is the fame ; but, at equal obliquities, 

 we have (hewn the refradlion is equal ; confequently the 

 ])arallclifm, which they had before the refraftion, will be 

 retained after it. 



But this may be alfo demonflrated geometrically : thus, 

 if tlic rays be perpendicular to the refrnfting furface, they will 

 pafs without any refraftion ; confequently being parallel be- 

 fore their paffage, they will be lo after it. If they fall 

 obliquely, as A B and C D (/i'. 1 6.), the angles of incidence 

 and u, and, confequently, alfo the angles of inclination 

 X and J', will be equal. But the fines of the angles of in- 

 clination s and y have the fame ratio to the fines of the re- 

 fracted angles m and » ; therefore the refrafted angles m and 

 «, and alfo the angles s and r, are equal ; confequently the 

 refrafted rays are parallel. 



Hence a glafs, plane on both fide, bein^ turned direftly 

 to the fun, the light paffing through it will be propagated 

 after the fame manner as if the glafs were av\'ay ; for the rays 

 being perpendicular, will pafs without rcfraclion. If the 

 glafs be turned obliquely to the fun, the light, after refrac- 

 tion, will be of the fame intenfity as before, the intenfity 

 depending on the fpiifitude or clofeiiefs of the rays, and on 

 the angle with which they llrike the objeft, or the eye ; both 

 which are here unvaried. 



2. If two rays D C and C P [Jig. 17.) proceeding from 

 the fame radiant C, and falling on a plane furface of a dif- 

 ferent dcnfity, fo that the points of refrattion D and P are 

 equally diftant from the cathetus of incidence G K, the re- 

 fraftcd rays D F and P Q have the fame virtual focus, or 

 the fame point of difperfion G. 



Hence, i. Since, in rays very near each other, the diitance 

 from the cathetus is the fame as to fenfe, very near rayi 

 will diverge from the fame point G, i. e. tkey will have the 

 fame virtual focus G. 



And hence, 2. When refrafted rays, falling on the eye 

 placed out of the cathetus of incidence, are either equally 

 diftant from the cathetus, or very near each other, they will 

 flow upon the eye, as if they came to it from the point G ; 

 confequently the point C will be feen by the refradled rays 

 as in G. 



3. If a ray C D fall obliquely out of a thinner into a 

 dcnfer medium, having a plane furface, the diitance of the 

 radiant point C K will have a lefs ratio to the diftance of the 

 point of difperfion, or virtual focus, K G, than the fine of 

 the refradted angle to the fine of the angle of inclination. 

 But if the diftance of the point of refraftion, from the 

 cathetus of incidence K D, be lefs than the eleventh or 

 nineteenth part of the diftance of the radiant point C K ; 

 and if in the former cafe the tenth, and in the latter the 

 hundredth, part of it be fo fmall, that it cannot be 

 afligiied, or need not be minded, then will C K be to K G, 

 as to fenfe, in the ratio of the fine of the refrafted angle, 

 to the fine of the angle of inclination. 



Hence, i. If the refraftion be out of air into glafs, the 

 diftance of the point of difperfion of rays near the cathetus 

 is fcfquialteratc of the radiant point ; of more remote rays 

 greater than fefquialterate. But if the refraftion be out of 

 air into water, the diftance of the fame point will be fefqui- 

 tertian, when the rays arc near the cathetus ; and when more 

 remote, greater than fefquitertian. 



Hence, 2. If the eye be placed in a denfe medium, objefts 

 in a rarer will appear more remote than they arc ; and the 

 place of the image, in any given cafe, may be determined 

 from the ratio of the ref:aftion. Thus, iojifius J'-wimmlng under 



nuater, ohjeHs out of the nualtr muJI appear farther diftant than 

 in reality they are. 



4. If a ray D G fall obliquely out of a denfcr into a rarer 

 medium A B, the diftance of the radiant point G K has a 

 greater ratio to the diftance of the point of difperfion K C, 

 than the fine of the refradted angle has to the fine of the 

 angle of inclination. In the other cafe of the preceding 

 theorem, K G will be to K C, as to fenfe, in the ratio of 

 the fine of the refrafted angle, to the fine of the angle 

 of inclination. 



Hence, i. If the refraftion be out of glafs into air, the 

 diftance of the point of difperfion of the rays near the cathetus 

 of incidence ij; fubfcfquialtcrate of the diitance of the ra- 

 diant point ; that of the more remote rays is lefs than fubfef- 

 quialterate. 



But, 2. If the refraftion be out of water into air, the 

 diftance of the point of difperfion of rays near the cathetus 

 is fubfefquitertian ; of thofe more remote, lefs than fubfef- 

 quitertian. 



And, 3. The eye, therefore, being placed in a rarer me- 

 dium, objefts, placed in a denfer, appear nearer thai) they 

 are ; and the place of the image may be determined in anv 

 given cafe by the ratio of refraftion. Hence, the bottom 

 of a veftel full of water is raifed by refraftion to a third part 

 of its height, with refpeft to an eve perpendicularly over 

 the refracting furface ; and hence fi/hes, and other todies under 

 water, appear nearer than they really are. 



5. If the eye be placed in a rarer medium, an objeft 

 feen in a denfer medium, by a ray refrafted in a plane fur- 

 face, will appear larger than it really is. If the objeft be 

 in a rarer, and the eye in a denfer medium, the objeft will 

 appear lefs than it is. And, in each cafe, the apparent 

 magnitude is to the real one in a ratio compounded of the 

 diftance of the point to which the rays tend before refrac- 

 tion, from the refrafting furface D £ (jfj . 18.) lo the 

 diftance of the eye G L from the fame, and of the diftance 

 G M of the objeft A B from the eye, to its diftance F M 

 from a point F, to which the rays tend before refraftion. 



Hence, i. If the objeft A B be very remote, F M will 

 be phyfically equal to G M ; and, therefore, the real mag- 

 nitude M B is to its apparent one M H, as G L to F L, 

 or the diftance of the eye G from the refrafting plane to 

 the diftance of the point of convergence F from the fame 

 plane. 



Hence, 2. Objecls und^r ivalcr, to an eye in the air, appcir 

 larger than they are ; and tojtjhes under •water, ohjeSs in the 

 air appear lefs than they are, 



Refraction, Latvs of, in fpherical furfaces, both concave 

 and convex. I. A ray ot light DE {Jig. 19.) parallel 

 to the axis of a denfer fphere, after a fingle refraftion 

 in E, falls in with the axis in the point F, beyond the 

 centre C. 



For the femidiameter C E, drawn to the point of refrac- 

 tion E, is perpendicular to the furface K L, and is there- 

 fore the axis of refraftion ; but a ray out of a rarer into a 

 denfer medium, we have (hewn, is refrafted towards the per- 

 pendicular, or the axis of refraftion ; therefore the ray D E 

 will converge to the axis of the fphere A F ; and will, there- 

 fore, at length concur with it, and that beyond the centre C, 

 in F ; becaufe the angle of refraftion F E H is lefs than the 

 angle of inclination C E H. 



2. If a ray D E fall on a fpherically convex furface of a 

 denfer medium, parallel to its axis A F ; the femidiameter 

 C E will be to the refrafted ray E F in the ratio of the fine 

 of the angle of refraftion, to the fine of the angle of incli- 

 nation ; but the diitance of the focus, or point of concur- 

 rence from the centre C F, is to the refrafted ray F E, in the 



ratio 



