12 



two reflexions at an angle of 62 30', 

 which is above the polarising angle, and 

 50 26', which is below it, will also po- 

 larise the incident ray, or it may be 

 done by several reflections, each reflec- 

 tion being made at a different angle. 

 Dr. Brewster likewise determined that 

 the same law prevailed at the separating 

 surface of glass and water. 



On the State of Light partially 



Polarised by Reflexion. 

 When a ray of light is incident on a polar- 

 ising medium, at an angle greater or less 

 than the angle of complete polarisation, a 

 portion of it is completely polarised, and 

 this polarised portion diminishes from the 

 polarising angle on one side to of inci- 

 dence ; and on the other to 90, when it 

 disappears. The other portion of light has 

 been regarded by Malus, Biot, Arago, 

 Fresnel, Dr. Young, and others, as in the 

 state of common light, and this opinion 

 has been deduced from speculative views 

 and some insulated experiments, the re- 

 sults of which are incompatible with the 

 preceding facts respecting the polarisation 

 of light by successive reflexions. The 

 character of common light is, that it 

 cannot be polarised by one reflexion at 

 any other angle of incidence than one, 

 viz., the maximum polarising angle, 

 which for glass is 56 45'. But the light 

 under our consideration has received a 

 physical change, which enables it to be 

 polarised by a second or a third reflexion 

 at a greater and a less angle than 56 45'. 

 For example, a pencil of light reflected 

 from glass at an angle of 70, contains 

 a small quantity of polarised light, which 

 we may call p, and a large quantity of 

 other light, which we may call P. The 

 light P will, after six reflexions, have 

 suffered such a physical change, that it 

 is capable of being wholly polarised by 

 ONE reflexion at 70, whereas such a 

 reflexion is not capable of polarising 

 one-fifth of common light. The original 

 pencil of common light has suffered a 

 change at every successive reflexion, 

 which brings it, at the sixth reflexion, 

 into the state of polarised light. 

 Determination of refractive Powers 



by the Polarising Angle. 

 The law of the polarisation of light above 

 explained enables us to measure the refrac- 

 tive powers of bodies which are not trans- 

 parent, and which could not, therefore, 

 be submitted to the ordinary process, 

 and of small fragments of minerals and 

 other substances. If the substance has a 

 plane and polished surface, we have only 

 to place it on a goniometer, and measure 



POLARISATION OF LIGHT. 



the angle of maximum polarisation, and 

 the tangent of this angle will be the index 

 of refraction. If the substance is soft 

 or fusible by heat, we may impress upon 

 it a plane surface with a flat piece of 

 glass ; or if a surface cannot be obtained, 

 as in the case of animal or vegetable 

 membranes, we may press them with 

 great force between two prisms of glass, 

 and measure the polarising angle at the 

 separating surface of the membrane and 

 the glass. In the case of fluids, which 

 do not assume a level surface, or which 

 exist in too small quantities to be put 

 into a vessel, or to be exposed to evapo- 

 ration, we have only to place them on 

 the lower surface of a prism, and mea- 

 sure the polarising angle at the separat- 

 ing surface. The tangent of this angle 



will give ,, and m being known for 



glass, we shall have m' = r 



tang. A. 



Light refracted previous to its Re- 

 flexion, and Polarised by bodies at 

 an angle o/45. 



There is one important result of the 

 law of the tangents which Dr. Brew- 

 ster has deduced, namely, that the 

 force which produces refraction extends 

 beyond that which produces reflexion, 

 and therefore that light is polarised after 

 it has suffered refraction, and that the 

 real angle of polarisation in every body 

 is 45. Let M N, fig. 16, be the surface 



Fig. 16. 

 E 



of the body, O P the termination of the 

 attractive force which produces refraction, 

 and let us suppose that the reflecting 

 power is exerted at or very near 

 the surface M N, and after the at- 

 tractive force has produced one half of 

 the whole deviation due to it. Let a ray 

 R G be incident at G at the polarising 

 angle ; let G B be the refracted ray sub- 

 sequently reflected at B to A, and re- 

 fracted again at A S. Continue S A 

 to C, and F B to D. Then, since half of 

 the refraction is supposed to be performed 

 before the ray reaches B, and half of it 

 after it enters the body M N, we have 

 BAG equal to D B C, or to half the 

 of deviation, But ADB is, a 



