CH. //] LIGHTING AND FOCUSING 63 



tained when the incident ray passes from a vacuum into a given medium. As 

 the index of the vacuum is taken as unity, the absolute index of any substance 

 is always greater than unity. For many purposes, as for the object of this 

 book, air is treated as if it were a vacuum, and its index is called unity, but in 

 reality the index of refraction of air is about 3 ten-thousandths greater than 

 unity. Whenever the refractive index of a substance is given, the absolute 

 index is meant unless otherwise stated. For example, when the index of 

 refraction of water is said to be 1.33, and of crown glass 1.52, etc., these figures 

 represent the absolute index, and the incident ray is supposed to be in a 

 vacuum. 



\ no. Relative Index of Refraction. — This is the index of refraction be- 

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

 water and glass, etc. It is obtained by dividing the absolute index of refrac- 

 tion 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 divided 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 refraction 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 refraction ( — I , it will be seen that whenever 



\sm rj 



the sine of the angle of refraction is 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 two contiguous substances is inversely as the refractive indices of those sub- 

 stances. The formula is : 



(Sine of angle of incident ray \ / Inedx of refraction of refracting medium \ 

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



Abbreviated ( — I = I : — ; — ) . By means of this general formula one 



\sinr/ \ index z / J ° 



can solve 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. 



V Sine of angle made by the ray in air \ _ / Index of ref.of denser med \ 



\ Sine of angle made by ray in denser med. / — \ Index of ref . of air ( 1 ) / 



If the dense substance were glass ( ^-^ ) = ( ^T^ ) ' If the two media were 



weter and glass, the incident light being in water the formula would be ; 



/ sin t \ _ / 1.52 \ _ jf tlle i nc ident ray were glass and the refracted ray 

 \sin rj \ 1.33 / 



in water- / sin * \_/JL33_ \ And similarly for any two media ; and as 



\sin rj \ 1.52 / 

 stated above if any three of the factors are given the fourth may be readily 

 found. 



