60 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



" It is very remarkable that, under a certain angle of incidence, a part of a spectrum 

 arising from reflection consists of perfectly polarized light. This angle of incidence is very 

 different for the different spectra, and even very sensibly different for the different colours of 

 one and the same spectrum. With the glass-grating e = 0.0001223 there is polarized : (£t) (+i) , 

 that is, the green part of this first spectrum, when a = 49° ; (£t) ,+ ii) , or the green part in the 

 second spectrum lying on the same side of the axis, when cr = 40°; lastly, (£t) (_I) , or the 

 green part of the first spectrum lying on the opposite side of the axis, when a = 69 . 

 When (Et) i + " is polarized perfectly, the remaining colours of this spectrum are still but 

 imperfectly polarized. This is less the case with (Et) (+U) , and a can be sensibly changed 

 while this colour still remains polarized. (-Ex)'" 1 ' is under no angle of incidence so com- 

 pletely polarized (so ganz vollstandig polarisirt) as (£t) (+I) . With a grating in which e 

 is greater than in that here spoken of, the angle of incidence would have to be quite different 

 in order that the above-mentioned spectra should be polarized*." 



If we suppose <r„ a function of v such that ir_, = 69, a +l = 49, cr +2 = 40, we get by inter- 

 polation <r = 58.33 ; so that if we suppose the central colourless image, which arises from light 

 reflected according to the regular law, to have been polarized at the polarizing angle for light 

 reflected at a surface free from grooves, we get n = tan 58 n 40' = 1.64, from which it appears 

 that the grating was made of flint glass. The inclination of E in the spectrum of the order 



v to the plane of the grating may be calculated from the formula cos t = sin a H , given 



e 



by Fraunhofer, and obtained from the theory of interference ; and 9 = 90° — r — a, where 9 

 is the angle of diffraction. We thus get for green light polarized by reflection and the ac- 

 companying diffraction, 



order of spectrum a 9 a + 9 



- 1 69° - 18°13' 50°47' 



58°40' 58°40' 



+ 1 49° + 17°l' 66°l' 



+ 2 40° + 33°52' 73°52'. 



If we suppose the formula (49) to hold good in this case, m becomes infinite for the angles 

 of incidence cr and the corresponding angles of reflection cr + 9 contained in the preceding 

 table. 



Another observation of Fraunhofer' s described in the same paper deserves to be mentioned 

 in connexion with the present investigation, because at first sight it might seem to invalidate 

 the conclusions which have been built on the results of the experiments. On examining the 

 spectra produced by refraction in another glass-grating on which the light was incident perpen- 

 dicularly, Fraunhofer found that the spectra on one side of the axis were more than twice as 

 bright as those on the other §. To account for this phenomenon, he supposed that in ruling the 

 grating the diamond had had such a position with respect to the plate that one side of each 

 groove was sharp, the other less defined. This view was confirmed by finding that a glass plate 

 covered with a thin coat of grease, and purposely ruled in such a manner, gave similar results. 



* Gilbert's Annalen der Physik, B. xiv. (1823) S. 364. 



■f In Fraunhofer's notation the wave length is denoted by w. § Ibid. p. 353. 



