14 



POLARISATION OF LIGHT. 



24 

 27 

 29 

 31 

 33 

 35 

 39 

 41 

 44 

 47 



Calculated Angles. 



, 61 0' 



56. 58 



54. 50 



53. 16 



51. 



50. 23 



, 46. 50 



, 45. 49 



, 44. 



42. 



Observed Angles 



fit wlikh they ];- 

 Ir.rKed tlic Light. 



60 8' 

 57. 10 

 55. 16 

 53. 28 

 51. 44 

 50. 5 

 47. 1 

 45. 35 

 43. 34 

 41. 41 



From a comparison of the numbers in the 

 second column, it will be found that the co- 

 tangents of the polarising angles are to one 

 another as the number of plates by which 

 the polarisation is effected. Hence if N, n 

 represent the number of plates in any 

 two parcels, and A, a the angles at which 

 the pencil is polarised, we have 



N : n = cotang. A ; cotang. a and 



N (tang. A) = n (tang, a) 

 that is, The number of plates in any 

 bundle, multiplied by the tangent of the 

 angle at which it polarises the trans- 

 mitted pencil is a constant quantity. 

 For crown glass, this constant quantity 

 is 41.84, when the light is that of a 

 good wax candle, placed at the dis- 

 tance of about 12 feet. Hence we have 



tang. A = 41 ' 84 : that is, divide the con- 



n 



stant quantity by any given number of 

 plates, and the quotient will be the natural 

 tangent of the angle at which light will be 

 polarised by that number of plates. The 

 constant quantity diminishes with the 

 refractive power of the plates. 



When light is transmitted through one 

 plate of glass, or through several, at an 

 angle of incidence less than that which 

 polarises the whole parcel, the trans- 

 mitted light will consist of two parts: 

 one P wholly polarised, and another p 

 which has suffered a physical change, 

 approaching, more or less, to that of 

 complete polarisation. According to the 

 preceding Table, 16 are required to po- 

 larise completely a pencil of light at an 

 angle; of incidence of 69 ; and 12 plates 

 will not polarise the whole pencil at 69, 

 but leave a portion p unpolarised. Now, 

 if the light p were wholly unpolarised 

 like common light, they would require to 

 pass through other 16 plates, at an an^le 

 of 69 ; but the fact is, that they require 

 only to pass through other 8 plates at 

 an angle of 69, in~ order to be com- 

 pletely polarised. They have, therefore, 

 been half polarised by the first 8 plates, 

 and the polarisation completed, by the 

 others. 



CHAPTER IV. 



of Light by Double Re- 

 fraction Malus's Formula; for the 

 Intensity of the Pencils. 



In treating of the double refraction of light 

 by Iceland spar, we alluded only to the sepa- 

 ration of the two images ; but when we^ex- 

 amine the light which forms the two pen- 

 cils e e', o o', fig. 2, we find that they are 

 both composed wholly of polarised light, 

 the light of the one being polarised in a 

 plane at right angles to that of the other, 

 in the same manner as the pencils A B', 

 EF, Jig. 16, reflected from, and trans- 

 mitted through, a bundle of glass plates. 

 The discovery of the opposite polarisa- 

 tion of the two pencils was made long 

 ago by Huygens, and the leading pheno- 

 mena accurately described in his " Trea- 

 tise on Double Refraction." Take two 

 rhombs of Iceland spar MN, fig. 19, 

 fig. 19. 



.^. ; __y 

 ? IK 



0<? 



which are not intersected by planes that 

 produce colour in a luminous body, and, 

 having fixed on the surface of one of 

 them a round aperture at B, not more 

 than one twentieth of the thickness B D 

 of the rhomb, place behind it, or close 

 to it, a similar rhomboid N, similarly 

 situated, with all the faces of the one 

 parallel to all the faces of the other, as 

 if they formed one piece. The single 

 rhomb M will separate the images "as 

 shown at A, fig. 20; but if the eye is 

 placed behind the two at F H, it will see 

 two distinct round apertures, separated 

 from one another and of equal brightness, 

 as shown at B, fig. 20. If we now turn 

 the rhomb N nearest the eye, from left 

 to right, two faint images will appear 

 as shown at C ; continuing to turn, 

 the four images will be all equally lumi- 

 nous as at D ; they will then become 

 as at E ; and when the crystal N has 

 turned round 90, there will be only 

 two images of equal brightness as at F. 

 Continuing to turn, other two faint 

 images wiB appear as at G j farther on 



