CH. II] LIGHTING AND FOCUSING 53 



dence divided by the sine of the angle of refraction equals the index of refraction. 



In the figures, —. — _ „ „ T , = index of refraction. Worked out completely in 

 s Sm CBN' 



Fig. 54, A B N=4o°, CB N'= 28° 54' and _? in *° ° - =-^^^ = 1.33, i.e., 

 °*' H ' °^ Sin 28 54' 0.48327 °° 



the index of refraction from air to water is 1.33. (See \ 33.) In Figs. 55-56, 



illustrating refraction in crown glass, the angles being given, the problem is easily 



solved as just illustrated. (For table of natural sines see third page of cover ; for 



interpolation, \ 32). 



I 98. Absolute Index of Refraction. — This is the index of refraction obtained 

 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. 



§ 99. 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 sub- 

 stance containing the refracted ray, by the absolute index of the substance trans- 

 mitting 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 



/ sin i \ 



and refraction ( — ) , it will be seen that whenever the sine of the angle of refrac- 



\sm r / 



tion 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 substances. The formula is : 



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



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



Abbreviated ( -. ) = ( ; — z . ) • By means of this general formula one can 



\sin rj \ index z/ 



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. 



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



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



/ gin i \ / 1 o \ 



If the dense substance were glass I I I 1 • If the two media were 



\sin r J — \ 1 / 



