64: REPORT ON PHYSICAL OPTICS. 



equal thread. When such a grating is placed before the object- 

 glass of a telescope, and a narrow slit, whose length is parallel 

 to the wires of the grating, viewed through it, the direct image of 

 the slit is bordered on either side by a succession of richly-coloured 

 diffracted images, which increase in breadth and diminish in bright- 

 ness as they recede from the centre. The first pair of spectra are 

 separated from the central image by a space absolutely black, and 

 a similar interval occurs between the first and second pair. Fraun- 

 hofer observed, under favourable circumstances, thirteen such spectra 

 on either side of the central image. He has measured with great 

 accuracy the angular deviations of the rays of each colour from the 

 axis ; and he has found that the experimental laws thus deduced 

 agree in the most complete manner with the results of the prin- 

 ciple of interference.* The results are the same, both by theory 

 and experiment, in the case of reflexion from ruled surfaces.f 



The optical phenomena of gratings are interesting in many 

 points of view. The appearance of lateral spectra, produced by 

 simply intercepting a part of the light, proves that the light actually 

 diverges in all directions from the front of the grand wave where 

 it meets the lens, and that it is to the interference of this light 

 with that intercepted by the grating that we are to ascribe its 

 want of sensible effect under ordinary circumstances.* Another 

 very remarkable circumstance of these phenomena is the purity of 

 the light of each simple colour, which is such that the fixed lines 



The angular deviation, 0,,, of any ray from the axis is expressed by the formula 



n\ 



sin 8 n = , 



in which n denotes the order of the spectrum, \ the length of an undulation, and 6 the 

 interval of the axes of the wires. The value of e is obtained with great precision, so 

 that the measurement of the angular deviations of the rays of each simple colour affords 

 the most exact data for the determination of the lengths of their waves. Fraunhofer 

 has in this manner computed the lengths of the waves, corresponding to the seven 

 principal fixed lines in the spectrum ; and the resulting values are perhaps the most 

 exact optical constants we possess. It is a remarkable consequence of the expression 

 above given, that when e is less than \, the angle 6 will be imaginary. In this cast', 

 then, there can be no coloured spectra ; and it follows that scratches or inequalities on. 

 any polished surface, whose interval is less than the length of a wave, do not disturb 

 the regularity of reflexion and refraction. 



t Fraunhofer's researches on diffraction are published in the Memoirs of the Bava- 

 rian Academy of Sciences, vol. viii. A very full analysis of them is given in the 

 Edinburgh Encyclopedia, art. OPTICS; and in Sir J. Herschel's "Essay on Li-ht " 

 Encyc. Metrop. 



J Airy's Math. Traett, p. 331. 



