CH. //.] LIGHTING AND FOCUSING. 51 



meant unless otherwise stated. For example, when the index of refraction of wa- 

 ter is said to be 1.33, and of crown glass 1.52, etc., these figures represent the ab- 

 solute index, and the incident ray is supposed to be in a vacuum. 



\ 93 b. Relative Index of Refraction. — This is the index of refraction between 

 two contiguous media, as for example between glass and diamond, water and glass, 

 etc. It is obtained by dividing the absolute index of refraction of the substance 

 containing the refracted ray, by the absolute index of the substance transmitting 

 the incident ray. For example, the relative index from water to glass is 1.52 di- 

 vided by 1.33. If the light passed from glass to water it would be, 1.33 divided by 

 1.52. 



By a study of the figures showing refraction, it will be seen that the greater the re- 

 fraction the less the angle and consequently the less the sine of the angle, and as the 

 refraction between two media is the ratio of the sines of the angles of incidence and re- 

 fraction I s 1 it will be seen that whenever the sine of the angle of refraction is 



/ sin l '\ it will 

 \siii r/ 



increased, by being in a less refractive medium, the index of refraction will show 

 a corresponding decrease and vice versa. That is the ratio of the sines of the 

 angles of incidence and refraction of any t?oo contiguous substances is inversely as 

 the refractive indices of those substances. The formula is : 



/ Sine of angle of incident ray\ /Index of refraction of refracting medium \ 



V Sine of angle of refracted ray/ V Index of refraction of incident medium/ 



Abbreviated | — ) = I = — =— — ; 1 . By means of this general formula one can solve 



Ism r/ \ index / / 



any problem in refraction whenever three factors of the problem are known. The 



universality of the law may be illustrated by the following cases : 



(A) Light incident in a vacuum or in air, and entering some denser medium, as 



water, glass, diamond, etc. 



(Sin of angle made by the ray in air \ /Index of ref. of denser med. \ 



Sin of angle made by ray in denser medium / \ Index of ref. of air ( 1 ) / ■ 



If the dense substance were glass : | . -1 = 1 — — I . If the two media were 



V sin r) \ 1 ) 



water and glass, the incident light being in water the formula would be : I — 1 = 



\sm r) 



(I - If the incident ray were in glass and the refracted rav in water : I -. ) 

 1.33/ J fi " \sin r) 



And similarly for any two media ; and as stated above if any three of 



(m) 



the factors are given the fourth may readily be found. 



\ 93 d. Critical Angle and Total Reflection. — In order to understand the 

 Wollaston camera lucida {\ 171, p. in) and other totally reflecting apparatus, it 

 is necessary briefly to consider the critical angle. 



The critical angle is the greatest angle that a ray of light in the denser of two 

 contiguous media can make with the normal and still emerge into the less refrac- 

 tive medium. On emerging it will form an angle of 90 with the normal, and if 

 the substances are liquids, the refracted ray will be parallel with the surface of the 

 denser medium. 



Total Reflection. — In case the incident ray in the denser medium is at an angle 

 with the normal, greater than the critical angle, it will be totally reflected at the 

 surface of the denser medium, that surface acting as a perfect mirror. By consult- 

 ing the figures it will be seen that there is no such thing as a critical angle and 

 total reflection in the rarer of two contiguous media : 



