70 



OF DIOPTRICS AND CATOPTRICS. 



SECTION YII. 

 I 



OF mOPTKICS AND CATOP- 

 TRICS. 



402. Definition. Light is an influence 

 capable of entering the eye, and of aflFecting 

 it with a sense of vision. A ray of hght is 

 considered as an evanescent element of a 

 stream of light ; and a pencil as a collection 

 of such rays accompanying each other. 



403. Definition. Light is distinguished 

 by its effect on the sense of vision, into white 

 and coloured light; and coloured light into 

 a great number of various hues : but they 

 may all be referred to the three primitive 

 colours, red, green, and violet. 



404. Definition. Those substances, 

 through which light passes uninterrupted in 

 straight lines, are called homogeneous trans- 

 parent mediums. 



405. Phenomenon. When rays of light 

 arrive at a surface, which is the boundary of 

 two mediums not homogeneous, they con- 

 tinue in the same planes ; but a part of 

 them, and sometimes nearly the whole, is 

 reflected, making with the perpendicular an 

 angle of reflection equal to the angle of in- 

 cidence; and another part is transmitted, 

 making such an angle of refraction, that at 

 the same surface, and for rays of the same 

 kind, the ratio of the sines of incidence and 

 refraction is constant, whatever may be their 

 magnitude. 



406. Phenomenon. If the same re- 

 fracted ray return to the surface in an oppo- 

 site direction, it will be transmitted back in 

 the direction of the incident ra3^ 



406. Definition. ITie medium, in which 

 the ray is nearer to the perpendicular, is said 

 to have the greater refractive density ; and a 

 ray of light being supposed to pass from an 

 empty space into a transpaient medium, the 



index of the refractive density of the medium 

 is that number which is to unity as the sine 

 of incidence to the sine of refraction. 



408. Phenomenon. When, between 

 two transparent mediums, a third is in- 

 terposed, terminated by parallel surfaces, 

 the whole angular refraction remains un- 

 changed. 



Scholium. The proportions of the sines of the angles 

 of incidence and refraction may be deduced from the me- 

 chanical laws of motion, whether we consider refraction 

 as produced by a constant attractive force, acting in a given 

 small space on the. particles of light as projected corpuscles, 

 or by the change in the velocity with which an undulation 

 is transmitted through mediums of different densities. For 

 when a moving body approaches a surface obliquely, its ve- 

 locity may be resolved into two parts, one In a direction 

 parallel, and the other perpendicular to the surface ; and 

 the attractive force, being supposed to be perpendicular to 

 the surface, will not affect its lateral motion. Now, since 

 the fluxion of the square of the velocity varies as the flux- 

 ion of the space, and as the force, conjointly (23S), the space 

 and the force remaining the same, the finite increments of 

 the squares of any two perpendicular velocities will also be 

 equal. Calling the whole velocity in the hypotenuse a, 

 and the perpendicular velocity x, the lateral velocity will 

 be ■/(aa — xx) ; and after refraction, we have ,i/{xx+ll) 

 for the perpendicular velocity, and v" (aa+ib) for the whole 

 velocity, which is therefore in a constant ratio to the former 

 velocity a. But the lateral velocity remaining, in any one 

 refraction, constant, may be made radius, and the virhole 

 velocities will be the cosecaiUs of the angles, which, bysi- 

 milar triangles, are inversely as the sines of the same angles, 

 and the ratio of the sines is therefore constant. In the un- 

 dulatory system, the distance 

 between any two points of 

 the surface being made radius, 

 the perpendicular distance 

 which the same undulation 

 passes over, while it travels 

 from the first to the second, 

 is the sine of the respective 

 angle in each medium, and # 



thesedistances,beingdescribed 



in the same time, must be in the constant ratio of the Telo- 

 cities appropriate to the mediums. 



409. Theorem. The index of refraction 



