78 Immersion Lenses and New Refradometers. 



substances, the angles between tbose sides and the base exactly 

 represent the angles of refraction and incidence between the two 

 substances. The diagram represents the angles {jp and (p') of inci- 

 dence and refraction, when //. = 1"500; and for air, /x = 1*00 

 nearly. When the angle i;3 at A becomes 90'^, the angle B or <p' 

 represents the angle of total internal reflexion 42^ 48', and so for 

 any other example. 



The logarithmic refractometer consists of a slide rule, the upper 

 lines of which represent the refractive indices ; and the lower lines 

 and divisions give any angles from 90^ down to 30'. 



The angles of total internal reflexion are given at sight oppo- 

 site 90'^ by merely setting the refractive indices of the two media 

 proposed opposite to each other. 



Further examjdes. — Find the angles of total internal reflexion 

 for the following substances, the ray passing into them from air, 

 refractive index taken = 1 • 000. 



The refractive index is placed on B under 1 ' 000, on A under 

 QQr'. The answers must then be interpreted. 



Find the aberration into air of a " jplaie " of each of these sub- 

 stances as given in the note, page 69, ^ x -, «'. e. ^ -f- />t,' 



Sines I Sin. 64° .. 42^° .. 40° .. 34i° .. 261° 



Values 0-90 .. 0-675 .. 0-643 .. 0-565 .. 0-44 



From which it appears that the lower is the refractive index of a 

 film or cover, the greater effect has the thickness of it upon the 

 primary aberration into air of the pencil radiating from the illu- 

 minated particle under view ; another reason for preferring the water 

 film. 



The above example is simply worked by placing 10 B or 90" 

 over the angle whose sine is desired, and reading oiS" the numbers 

 under 1 on A : as 1 -r- /^^ = sine of the angle of total reflexion in 

 each case. 



