Monthly MI ical ° 
SE en, of Immersion Lenses. 137 
TABLE II. 
Loitine ANGLES OF REFRACTION oR ANGLES OF ToTaL INTERNAL REFLEXION. 
Angle of Total 
Moutvat REFRACTIONS. TuiterrialiReflosion 
ae Se ae 
Oo ! 
From plate glass into air rie or! L gets Fs oe 41 48 
a FS WAWE | Bo) Ga. od. | Sac 62 57 
» flint glass into crown glass sou) at 56 50 
“ 5 Canada balsam .. .. 78 23 
a 5 forpentiney J. sa) (2: 78ST | 
These angles are the extreme semi-apertures of the transmitted pencils nascent from 
the brilliant particle; all rays of greater obliquity being internally reflected. 
In the case of water versus air the quantity of defining rays 
nascent from the brilliant particle immersed in balsam varies as the 
square of the angles of total internal reflexion in each case; or, 
denoting these quantities by Q and Q’ for water and air respectively, 
and the angles by 8, 6’, 
QE BOR* Ot CG) 3 \622°7| as (ates) 
:: 22 3 1 very nearly. 
Tn other words, the water film possesses the advantage of trans- 
mitting a quantity of defining rays nascent from the brilliant 
spherule immersed in balsam two and one-fourth greater than that 
transmitted by the air film to the eye through the objective, or in the 
proportion of 9 to4. In other words, the definition accomplished 
vid water exceeds that vid air by more than a double brilliance of 
effective rays. 
As these limiting angles of refraction represent semi-apertures, 
by doubling them it will be seen that no nascent pencil can reach 
the objective wid air and vid water respectively greater than 
ce) fo} ' 
Forair .. .. 84 (2x 41 48 nearly) 
FAKE on. an WS (CA eer Gye) 
showing the advantage of the employment of a water film com- 
pared with air. 
The battle of the glasses is by no means yet fought out. The 
combinations for their construction have by no means been ex- 
hausted. 
The deviation caused by using Canada balsam in contact with 
the covering glass is slight. 
The amount is readily found by subtracting the angle of inci- 
dence from that of refraction. In all these questions, it at a great 
L 
