50 



SIR DAVID BREWSTER ON THE PHENOMENA OF THIN PLATES 



If we now calculate by these formulae the values of x for the different angles of inci- 

 dence in the preceding Table, and subtract them from 90°, we shall have the numbers 

 in the third column of the Table, which agree with those observed within the limits 

 of the errors of observation. In the case of water and glass, too, where the azimuth 

 of disappearance was observed to be about 79° or 11°, the formula gives 79° 28', or 

 10° 32', at an incidence of 56° 45'. 



In order to ascertain the relation between the mutual inclination of the planes of 

 polarization of the interfering pencils when they produced hlack-centred or white- 

 centred rings, I have computed the following Table for an incidence of 56° 45'. 



Azimuth of Polarized Light. 



+ 



O I 



90 



74 43 



49 30 



28 26 



15 28 



5 45 



4 3 



2 6 







Film of water and glass. 

 Inclination of Planes and 0'". 



90 

 82 45 

 75 4 

 61 34 

 43 19 

 18 57 

 13 3 



7 7 

 



180 0" 

 157 28 

 124 34 

 90 

 58 47' 

 24 42 

 17 6 

 9 13 

 0. 



JVhite-cenivQA 

 rings. 



No rings. 

 Black-centred 



> 



rings. 



By taking ^ positive, or on the right-hand side of the plane of reflexion, then (p"' must 

 be negative, or on the left-hand side of that plane* ; hence -f (p, — (p'" will be the mu- 

 tual inclinations of the planes of polarization of the interfering pencils, and we obtain 

 the important law. 



That when two polarized pencils reflected from the surfaces of a thin plate lying on 

 a reflecting surface of a different refractive power interfere, half an undulation is not 

 lost, and wuiTE-centred rings are produced, provided the mutual inclination of their 

 planes of polarization is greater than 90° ; and that when this inclination is less than 

 90°, half an undulation is lost, and BhACK-centred rings are produced; when the inclina- 

 tion is exactly 90°, the pencils do not interfere, and no rings are produced. 



At an incidence of 45° upon water and glass, where the signs of (p and (p'" are the 

 same, the maximum ditference in the planes of polarization is 23° 12', which takes 

 place in azimuth 70° 30'; and at an incidence of 10° the greatest difference is 2° 16', 

 which takes place at an azimuth of about 45°. 



In the case of soap and plate glass, where the black-centred rings appear beyond 

 the incidence of 71° 45', the difference of inclination in the planes of the two pencils 

 is also less than 90°. 



I was now desirous of examining the phenomena of a perfect system of rings when 

 the film had a greater refractive power than the substance upon which it was laid ; 



* See Philosophical Transactions, 1830, p. 70, fig. 1. 



