226 



THE AMERICAN MONTHLY [October, 



Divide the length o m by the length p n, you obtain a certain 

 quotient ; in like manner divide m o by p' n\ in each case you 

 obtain the same quotient. This is a constant quantity for each 

 particular substance, though it usually varies for different sub- 

 stances when compared with each other. This constant is the 

 index of refraction of the substance. The perpendiculars o fu 

 and p ti are the sines of the respective angles 7n Yj o and nY.p^ 

 hence calling the angle of incidence {m E o) V and the angle of 

 refraction {n E /) X, we have the expression, index of refraction 



cirip yJ 



= ~. The following apparatus (shown at figure 3) is well 



devised to demonstrate the laws of refraction ; it consists of a grad- 

 uated vertical circle to which is attached a glass receptacle having 

 the shape of a half cylinder and containing a liquid whose upper 

 surface passes through the centre of the circle. Abeam of light 



3 



0) 



Fig. I. Fig. 2.* 



is reflected from the mirror I through the diaphragm D toward 

 the centre O. The alidade O a gives exactly the value of the 

 angle of incidence, the beam is refracted when it passes through 

 the liquid, and the angle it now makes is measured by the alidade 

 O R ; this is done by moving it until the beam emerges through 

 the diaphragm tube Z. As the beam emerges in a perpendicular 

 direction to the medium it is not again refracted, so the alidade 

 gives the true value of the angle of refraction. The value of the 

 angles, in degrees, can now be read from the graduated circle, and 

 the sines compared, and it will be found that the relationship be- 

 tween the sines of the angles of incidence and refraction are 

 always the same for the same liquid ; this relationship is, as before 

 stated, the index of refraction. 



In the case just examined the beam is supposed to travel from 

 the rarer to the denser medium ; the apparatus can, however, be 



* By an oversight, the beam O L is not represented in the figure. A line drawn about midway 

 between A O and R" O will represent the beam O L referred to in the text. 



