18 



REFRACTION 



cmwn -giant it in nearly 3 : 2. Now olwervation 

 show- that light passing from wntr into crown- 

 glam U so refracted that the sines have the ratio 

 I : |, or 9 : 8, to that the rays are less hent than 

 when they pass from air into any of these media. 



fig. L 



The ratio of these sines when at'r is one of the pair 

 of media involved is called the refractive index of 

 the other medium ; thus, water has, for sodium 

 monochromatic light and at 18 C. , a refractive 

 index of 1 '.'f.'t.'iti, and crown-glass one of 1 5396 ; anil 

 the ratio of these refractive indices, ascertained 

 with respect to air, governs the ratio of the sines, 

 whether air be one of the pair of media experi- 

 mented on or not. A direct consequence of this is 

 that, if light pass successively, say, through air, 

 glass, ami water, the ultimate deviation will be 

 i he same as if the glass had been absent: and so 

 for any number of intervening terms, it being 

 always assumed that the Imunding surfaces are 

 parallel to one another ; and if a parallel beam of 

 light, passing through air, come to traverse any 

 numlif] of parallel refracting-surfaces, and if it 

 if gain the air, it will )>e found to travel parallel to, 

 if not directly in, its original course. 



The observed fact that light is differently bent in 

 its course by different refracting media shows that 

 there is a difference lietween bodies in their power 

 of receiving light through their bounding surfaces. 

 Newton, in accordance with his corpuscular theory 

 (see LIGHT), interpreted this as showing that when 

 the luminous corpuscles come very near the surface 

 of a denser sultstance they are as it were jerked 

 or made to swerve out of an oblique path and 

 hurried in by the attraction of the denser substance 

 so as to enter that substance more directly ; and 

 that when the light quits the denser substance it 

 is retarded by a similar attraction. The conse- 

 quence of this would be that light would travel 

 in the denser medium perhaps not appreciably 

 faster than in air, but with a mean velocity cer- 

 tainly not less. On the undulatory theory, how- 

 vcr. refraction is a necessary consequence of a 

 slower travel of ether-disturbances in the denser 

 medium. 



In fig. 2 A is a plane wave-front, advancing 

 ibli'jiiely towards B, the surface of a denser 

 medium. At the end of a certain time the wave- 

 i nint is at A' ; after an equal interval it is at A", 

 liming the next equal interval a gradually diminish- 

 ing breadth of the wave is traversing (lie original 

 medium with the original velocity; out a steadily 

 widening portion of the wave-front enters the 

 denser medium and is there hampered. At the 

 en. I of the interval the aggregate disturbance, that 

 in to nay, the wave-front, will be found to have 



swung round into the position and direction repre- 

 sented by a, just as a line of soldier- would tend to 

 tlo on obliquely entering more difficult ground. 

 During the next equal interval the wave-front 

 advances parallel to itself, but traverses smaller 

 distances in equal time-, so that an' is less than 

 \ \ To this explanation it is essential that in 

 optically denser media light should travel more 

 -lowly : and it has been absolutely established that 

 this is the case. Optical density, so called, does 

 not, however, always coincide with mass-density : 

 bisulphide of carbon, which is lighter than gla--, 

 has for sodium light a refractive index of 1 -63, 

 while crown-glass has an index about 1'5, and flint- 

 glass one about 1*6. If the course of any ray 

 between any two points 'in the two respective 

 media be studied, it will be found that no other 

 path lift ween the two points could have been 

 traversed in HO short a time. 



If we go back to fig. 1, and assume the rays to 

 pass from A', B', &c. towards O, we find the ravs 

 emerging from the denser medium more nearly 

 parallel to SS' ; a ray from C', so far as it is 

 refracted at all, emerges parallel to SS' ; and for 



Fig. 2. 



rays approaching O from points between C and S' 

 the construction for the refracted ray becomes 

 impossible. The angle C'ON' is the critical angle, 

 beyond which there is no refraction, but total 

 reflection (see REFLECTION). This angle is such 



that its sine is equal to -, where /< is the ratio 



between the refractive indices of the denser and 

 the rarer medium. For water ami air it i-. tor 

 sodium monochromatic light, 48 27' 40". Where 

 this ratio u. (the 'relative index of refraction') is 

 high, this critical angle is small and total reflection 

 i- well marked, as in the sparkle of the diamond. 



When a spherical wave impinges on a plane 

 surface it is modified into a hyperboloid, the centre 

 of curvature of the central portion <>f which is 

 farther away than or nearer than the centre of the 

 sphere in the ratio of the refractive index of tin; 

 -frond medium to that of the first. An eye within 

 a rarer medium will thus see the image of a point, 

 situated within the denser medium as if it were 

 nearer than it really is ; hence a stick appears bent 

 when partly immersed obliquely in water: and, 

 owing to differences in the amount of refraction at 

 different angles, the bottom of a tank looked down 

 upon appears sunk in the middle. 



In lig. :i light starts from a point X, and impinge* 

 directly 11 IHIII a spherical surface of a denser medium; 

 the centre of curvature of the spherical surface is 

 at C. During a certain interval of time the front 

 of the wave advances from A' to A ; during the 

 next equal interval it would, but for the denser 



