322 Address by the President. [Sess. 



will be shown farther on. Meanwhile we may point out 

 shortly how the refractive index of the medium is to be 

 ascertained. The measure of the angle of incidence and of 

 the angle of refraction can be found by experiment. You 

 find then from a table of natural sines the sines of these 

 respective angles, and dividing the sine of the angle of in- 

 cidence by the sine of the angle of refraction, you obtain the 

 refractive index of the medium. Thus in the foregoing 

 example the angle of incidence is 42°, the sine of which by 

 the table is 6691, and the angle of refraction in water is 30°, 

 the sine of which is 5000 : thus f§0^= 1'33, the refractive 

 index of water. Again, in the case of oil the angle of re- 

 fraction is 26°, the sine of which by the table is 4384: 

 thus |4§¥~ 1'52, the refractive index of oil and of crown- 

 glass. The smaller the angle of incidence in air, the smaller 

 the angle of refraction in the medium, until the ray of light 

 coincides with the normal, in which case it passes through 

 the medium without any refraction. 



If the bounding sides of the medium through which the 

 ray passes are parallel, then the refracted ray after emergence 

 proceeds in a direction parallel to the incident ray : it is 

 otherwise if the sides of the medium are curved, — and in the 

 case of lenses, one or both sides are always curved. In lenses, 

 then, the direction of the emergent ray depends upon the 

 nature of the curve. If one or both sides are convex, the 

 parallel rays of light, after passing through the lens, are 

 brought to a focus or point at a shorter or greater distance 

 from the lens, according to the intensity of the curve ; while 

 if the lens is concave, the emergent rays of light tend to 

 separate more and more. It is upon these principles that the 

 construction of microscopic lenses proceeds. 



Before proceeding farther I would like to draw your atten- 

 tion to an important point in optics. When rays of light pass 

 from a denser medium into a rarer medium, as crown-glass 

 into air, all the rays which entered the glass do not pass out 

 into the air, — a number of them are reflected back into the 

 medium. The angle at which this reflection takes place is 

 called the critical angle. The sine of this critical angle is the 

 reciprocal of the refractive index. Thus the refractive index 

 of glass is 1'52 and of air is 1. Thus 1-^1'52 = 658, and 



