REFRACTION. 



ratio of the fine of the refraftedanglL', to tlie fine of the an- 

 gle of inclination. 



3. If a ray D E fall on a donfer fphcrical convex fur- 

 face K L, parallel to the axis A F, the didance of the fo- 

 cus from the refracting furface F B mult be to its dillance 

 from the centre F C, in a ratio greater than that of tlie 

 fine of the angle of inclination, to the fine of the refradted 

 angle. But if the rays be very near the axis, and the angle 

 of inclination B C E be only of a few degrees, the diilaiices 

 of the focus from the furface, and the centre, F B and F C, 

 will be nearly in the ratio of the fine of tlie angle of incli- 

 nation, to the fine of the refrafted angle. 



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

 th? cafe of rays near the axis, BF : FC :: 3 : 2. And 

 in the cafe of rays remote from the axis, B F : F C > 3 : 2. 

 Confequently, in the former cafe, B C : B F :: i 13; and 

 w the latter, B C : B F < 1:3, 



And, 2. If the refraftion be out of air into water ; in the 

 former cafe, B F : F € :: 4 : 3 ; and in the latter, B F : 

 FC > 4 : 3. Confequently, in the former, B C : B F :: 

 1:4; and in the latter, B C : B F < i : 4. 



Hence, 3. Since the fun's rays are parallel as to fenfe, if 

 they fall on the furface of a folid glafs fphere, or of a 

 fphere full of water, tliey will not concur with the axis 

 within the fphere ; fo that Vitcllio was millaken, when he 

 imagined, that the fun's rays, falling on the furface of a 

 cryilalline fphere, were refrafted to the centre. 



4. If a ray D E {fg. 20.), parallel to the axis FA, fall 

 out of a denfer into a rarer fpherical medium, after refraction, 

 it will diverge from the axis ; and the diilance of the point of 

 difperfion, or the virtual focus from the centre of the fphere 

 F C, will be to its femi-diameter C E in the ratio of the 

 fine of the refrafted angle, to the fine of the angle of re- 

 fradlion ; but to the portion of the refradfed ray drawn 

 back, F E, it will be in the ratio of the fine of the re- 

 frafted angle, to the fine of the angle of inclination. 



5. If a ray E D fall parallel to the axis A F on the 

 fpherically convex furface K L of a rarer medium, out of a 

 deafer, the dillance of the point of difperfion from the cen- 

 tre F C, is to its diftance from the furface F B, in a ratio 

 greater than that of the fine of the refrafted angle to the 

 fine of the angle of inclination. But if the rays D E be 

 very near the axis F A, the ratio will be very nearly the 

 fame with that of the line of the refrafted angle to the fine 

 of the angle of inclination. 



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

 the cafe of rays near the axis, F C : F B :: 3 : 2. Confe- 

 quently B C : F B :: I : 2. Therefore, in the cafe of rays 

 more remote from the axis, F C : F B > 3 : 2. 



2. If the refraftion be out of water into air ; in the for- 

 mer cafe FC : F B :: 4 : 3. Confequently, B C : F B :: 

 I : 3 ; in the latter cafe therefore, F C : F B > 4 : 3. 



3. Since then the point of difperfion F is more remote 

 from the refrafting furface K L, if the rays proceed out of 

 water, than if they pafs out of glafs into air ; parallel 

 rays are lefs difperfed in the former cafe than in the 

 latter. 



6. If a ray H E {fg. 19.) fall parallel to the axis F A, 

 out of a rarer, on the furface of a fpherically concave denfer 

 medium ; the refrafted ray E N will be driven from the 

 point of the axis F ; fo that F E will be to F C in the ra- 

 tio of the fine of tlie angle of inclination, to the fine of the 

 refrafted angle. 



7. If a ray E H fall parallel to the axis F B on the con- 

 cave furface K L of a fpherical denfer medium, from a 

 rarer ; the diilance of the point of difperfion from the re- 

 frafting furface F B, is to its diftance from the centre F C, 



Vol. XXIX. 



in a ratio greater than that of the fine of the angle of incli- 

 nation, to the fine of the refrafted angle. But if the rays 

 be very near the axis, and the angle B C E be very fmall, 

 B F will be to C F very nearly in the ratio of the fine 

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

 angle. 



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

 the cafe of rays near the axis, F B : F C :: 3 : 2 ; in the 

 cafe ot rays more remote from the axis, F B : F C > 3 : 

 2 ; confequently, in the former, B C : F C :: i : 2. And 

 hence, in the latter, B C : F C < 1 : 2. 



Hence alfo, 2. If the refraftion be out of air into water; 

 in the cafe of rays near the axis, F B : F C :: 4 : 3. In 

 the cale of rays more remote from the axis, F B : F C > 4 

 :3; confequently, in the firft cafe, BC:FC::i:3. 

 And hence, in the latter, B C : F C > i : 3. 



And iience, 3. Since the point of difperfion F is farther 

 from the centre C, if the refraftion be in water than in air ; 

 rays will be lefs difperfed in the latter cafe than in the 

 former. 



8. If the ray H E {fg. 20. ) fall parallel to the axis A F, 

 from a denfer upon the furface of a fphcrical concave rarer 

 medium, the refrafted ray will concur with the axis A F, 

 in the point F ; fo that the diilance of the point of con- 

 courfe from the centre C F, may be to the refrafted ray 

 F E, in the ratio of the fine of the refrafted angle, to the 

 fine of the angle of inclination. 



9. If a ray H E fall parallel to the axis A F on the con- 

 cave lurface of a rarer medium out of a denfer, the diftance 

 of the tocus from the centre F C will be to its diftance from 

 the refrafting furface F B in a greater proportion than the 

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

 nation. But if the rays be very near the axis, F C will be 

 to F B in the proportion of thefe fines. 



Hence, \. If the refraftion be out of glafs into air ; ia 

 the cafe of rays near the axis, FC:FB:;3:2; in the 

 cafe of rays more remote from the axis, F C : F B > 3 : 2. 

 Whence, in the former cafe, B C : F B :: I : 2. 



2. If the refraftion be out of water into air ; in the cafe 

 of rays near the axis, FC:FB::4:3; in the cafe of 

 rays more remote, F C ; F B > 4 : 3. Whence, in the for- 

 mer cafe, B C : F B :: I : 3. For the demonftration of 

 thefe feveral laws of refraftion, we refer to Wolfius's Ekm. 

 Mathef. &c. torn. iii. p. 179, &c. See alfo Lens. 



Refraction in a glafs prifm. If a ray of light D E 

 (;ff . 21.) fall obliquely out of air on a prifm ABC; being 

 refrafted towards the perpendicular, inftead of proceeding to 

 F, it will decHne to G, /. e. towards a line H I, drawn per- 

 pendicular to the furface A B in the point of refraftion E. 

 Again, fince the ray E G, pafiing out of the glafs into air, 

 fails obliquely on C B, it will be refrafted to M, fo as to re- 

 cede from the perpendicular N G O. And hence arife the va- 

 rious phenomena of the prifm. See Colour and Refrangi- 



BILn V. 



Refraction in a convex lens. If parallel rays, A B, C D, 

 and E F {Jig. zz.) fall on the furface of a lens 2 B 3 K, the 

 perpendicular ray A B will pafs unrefrafted to K, where 

 emerging into air perpendicular, as before, it will proceed 

 ftraight to G. But the rays C D and E F, falling obhquely 

 out of air into glafs, in D and F, will be refrafted towards 

 the axis of refraftion ( i. e. towards lines H I and L M, drawn 

 perpendicular to the refrafting furface in the points of .re- 

 fraftion D and F) and dechne to Q and P. Again, emerg- 

 ing obliquely out of the glafs into the furface of the air, 

 they will be refrafted from the perpendicular, and, therefore, 

 D Q will not proceed to X, but to G ; and F P, not to V, 

 but to G ; thus, likewife, might all the other rays, falling on 

 4F the 



