604 



POLARIZATION OF LIGHT. 



That polarization will only take place at these 

 angles may be proven by a very simple modifica- 

 tion of the experiment detailed in describing the 

 apparatus, fig. 2, a modification first pointed out 

 by Sir D. Brewster. Let the apparatus, fig. 2, be 

 in the position represented in the engraving, that is, 

 with the mirror C placed at the polarizing angle 

 for glass, i. e. 56, as stated before, the image will 

 not be seen when the plane of the ray C E is per- 

 pendicular to the horizon, and consequently no 

 image will be seen by the eye at E. Let us now 

 breathe gently upon the glass C, so as to cover it 

 with a thin film of water; the image of the luminous 

 object R will now be seen at E, for the ray A C is 

 now no longer reflected from the glass C, but from 

 the surface of the film of water upon it, and the 

 polarizing angle of water in 53 14' ; but from the 

 position of the glass C it is at 56, and, therefore, 

 the light will not be polarized, but turn it round, so 

 that C with its film of water stand at an angle of 

 53 14' to the glass A, and the light will be invis- 

 ible to the eye at E. 



It is a curious and beautiful law discovered by 

 Sir D . Brewster that the index of refraction for any 

 transparent body is the tangent of its angle of pol- 

 arization ; so that the index of refraction being 

 given, the angle of polarization may easily be found 

 by turning up the index of refraction in a table of 

 natural tangents, the corresponding angle will be 

 the angle of polarization. From this law several 

 important deductions may be drawn, as, the com- 

 plement of the polarizing angle (i. e. what it wants 

 of 90) is equal to the angle of refraction at the 

 polarizing angle the sum of the angles of incidence 

 and refraction is a right angle : and when a ray is 

 polarized by reflection, the reflected ray forms a 

 right angle with the refracted ray. The converse 

 of the same law is extremely useful in determining 

 the refractive powers of bodies which are not trans- 

 parent, for we have only to find the angle of com- 

 plete polarization, and, taking its tangent we have 

 the index of refraction. From this law the atten- 

 tive reader will easily perceive that another impor- 

 tant deduction may be drawn, which is, that since 

 differently coloured rays have different angles of re- 

 fraction, they must also have different angles of 

 polarization ; hence when the blue light becomes 

 polarized, the red light still appears. In oil of cassia 

 the phenomena illustrative of this are very con- 

 spicuous, and the following statement of the polariz- 

 ing angles for the mean and extreme rays of the 

 spectrum in that substance, as also in glass and 

 water, will show the truth of the inference we have 

 drawn from the general law. 



OIL OF CASSIA. 

 Polarizing anirl.' 



Red, 59 57 



Violet, 59 39' 



Mean, 58 39' 



PLATE GLASS. 



Red, 56 36' 



Violet, 57 35' 



Mean, 57 43' 



WATER. 



Red, 53 4' 



Violet, 53 19' 



Mean, 53 B U' 



Thus in oil of cassia the difference of the polarizing 

 angles for the extreme rays of the spectrum is 1 

 24', for plate glass 19', and for water 15'. From 

 what has been said above it is to be inferred 

 that in any body there is only one angle at which 

 incident light becomes polarized by reflection, yet 

 by successive reflections light may be polarized at 



any angle of incidence. Thus Sir T). Brewster in ex- 

 pt'rimcnting with glass, whose refractive index was 

 1.525, gives the following results, among others. 



No. of Reflections. 

 1 

 5 

 10 

 100 

 1000 



Angle of Polarization. 

 56 45' 

 69 1' 

 73 4' 

 81 57' 

 86 15' 



when the angle of incidence is greater than 56 

 45' ; and 



1 56 45' 



5 41 43' 



10 35 18' 



100 18 11' 



1000 8 U 46' 



where the incident angle is less than 56 45'. A 

 similar law holds with the separating surfaces of 

 water and glass, nor is it necessary that the succes- 

 sive reflections be all made at the same angle. 



Sir D. Brewster discovered that the force which 

 produces refraction extends beyond that which pro- 

 duces reflection, and that after refraction light is 

 polarized in every body at an angle of 45, and 

 when a ray of light is incident at the polarizing 

 angle, upon any transparent body, the whole of the 

 reflected ray is polarized, and a nearly equal portion 

 of the transmitted ray is polarized in a plane at 

 right angles to the polarization of the reflected ray. 



In experimenting on polarization, there are two 

 different kinds of apparatus employed the one for 

 procuring and the other for analyzing polarized 

 light. Polarized light may be obtained by reflec- 

 tion from a single plate of glass or other material, 

 but the substance should have a low dispersive 

 power ; if glass be chosen, annealed crown plate 

 glass will answer best. When a great deal of light 

 is required, six, twelve, or more plates of annealed 

 crown glass must be placed together, and cemented 

 at the edge, and having been previously well clean- 

 ed, the light reflected from, or transmitted through 

 these plates may be used, but if these plates cannot 

 be obtained, thin films of blown glass may be em- 

 ployed, placed in a trough between two plates of 

 the thinnest glass. One of the most powerful means 

 that can be employed of obtaining polarized light, is 

 by taking a piece of clear mica, and cutting it into 

 the form of a right-angled parallelogram, whose 

 sides are parallel and perpendicular to the plane of 

 the resultant axis. (See Refraction, Double). Take 

 now the mica, and put it in a vice, and with a very 

 thin-bladed knife separate ten, twelve, or more of 

 the laminae, when the edges must be cemented, so 

 that the laminae may not alter their positions. 

 Polarized light may also be obtained from doubly re- 

 fracting crystals of great thickness, from prisms of 

 Iceland spar doubly refracting, and also from single 

 image prisms of the same substance, agate and tour- 

 maline. 



Some of the most singular and beautiful pheno- 

 mena in the whole of the physical sciences, are ex- 

 hibited in the colours arising from the action of crys- 

 tals on polarized light. This, which by a judge has 

 been pronounced to be at once " one of the most im- 

 portant, as well as one of the most complete, 

 branches of optical knowledge," derived its origin 

 from the independent researches of M. Arago and 

 Sir D. Brewster researches which have been suc- 

 cessfully followed up by M. Biot, Dr Young, M. 

 Mitscherlich, M. Fresnel, and Sir J. E. Herschel. 

 One of the simplest methods of observing the 

 phenomena to which we now allude is as follows. 



Let there be two plates A C, fig. 3, placed in thr 

 same relative position, both to themselves and the in- 



