46 
SIR DAVID BREWSTER ON THE PHENOMENA OF THIN PLATES 
than 78° 4' the system of rings with the black circumference will again appear as at 
incidences below 53° 11',, and will be visible up to 90° of incidence, the interfering 
pencils being now both reflected at angles above the polarizing angle of the surfaces 
which reflect them. 
This experiment with vapour and fluor spar I have not made ; and it may be diffi- 
cult to see the rings at such an oblique incidence. If the rings are formed by soap 
upon plate glass, or by alcohol upon Jhior spar, the second disappearance of the rings 
may be seen : 
Plate glass m 1*510 
f “ i — — 1 0154. 
soap m 1*487 
Polarizing angle at second surface of the soap .... 45° 26' 
Angle of incidence on the first surface 71 ° 45' 
Fluor spar m 1*487 1 mrkAn 
alcohol m! “ 1*370 — 1049 " 
Polarizing angle at second surface of alcohol 46° 22' 
Angle of incidence on the first surface 82° 32' 
If we call m, m! the indices of refraction of the two substances, viz. the Jilm and 
the surface upon which it rests, m being the larger index, then a ray incident at 90° 
will fall upon the common surface of the two media at the polarizing angle of that 
surface, when the angle of refraction at the first surface is equal to the tangent, or 
cotangent of the polarizing angle, according as the refractive power of the film is less 
or greater than that of the body upon which it rests. 
Hence we have sin i! — — or 
lib lib 
and 
and 
.,771 .771 
tan i = — 7 , or cot i = —> 
77V , 7m! 
m = 
777 , . 771 
> and m = v=t 
V 771 12 — 1 
when a ray incident at 90° is polarized at the second surface, or falls upon it at the 
polarizing angle. 
These formulae enable us to discover between what limits of refractive power the 
second disappearance of the rings can take place, and consequently what substances 
we should employ in order to observe it. In this manner we obtain the following 
results for the mean rays of the spectrum : — 
Values of m ! . 
V m' 2 — 1 ’ 
or m. 
3*000 
2-500 
2*000 
1-900 
1-061 
1-090 
1*154 
1-176 
Values of 
