Jan. 15, 1874J 



NATURE 



205 



a lialf wave-length ; so that with plates of moderate thick- 

 ness a single colour only may in general terms be con- 

 sidered to be suppressed. This being so, the beam 

 emergent from the analyser will be deprived of that 

 colour, and will in fact consist of an assemblage of all 

 others ; or in other words will be of a tint complementary 

 to that which has been extinguished. 



Next, as regards the colours of the tw-o images, that is, 

 the two which are formed either simultaneously by a 

 double-image prism or successively by a Nicol in two 

 positions at right angles to one another. In the first 

 place it is to be remembered that the two sets of vibra- 

 tions into which the selenite has divided the polarised 

 ray are at right angles to one another ; secondly, that 

 one set is retarded behind the other through a certain 

 absolute distance, which is the same for every ray, and 

 consequently through a distance which is a different 

 fraction of the wave-length for each colour ; thirdly, that 

 these two are re-combined or "resolved" in a single 

 direction in each image by the analyser. 



This being so, bend two wires in the following form : — 



and place them at right angles to one another about their 

 middle line M N M' N' . ., so that the points M of the 

 two wires coincide, and likewise N, and so on. This will 

 represent the condition of the vibrations as they emerge 

 from the selenite, when the plate is of such a thickness as 

 to cause a retardation equal to one or to any whole num- 

 ber of wave-lengths. Turn the wires about their middle 

 line M N M' N' until they meet half way, i.e. in a 

 position inclined at 45° to their original directions ; this 

 will represent the vibrations as resolved by the analyser 

 in one image. Turn the Avires about their middle line as 

 before, but in reversed directions, until they meet in a 

 position at right angles to the former ; this will represent 

 the vibrations as resolved by the analyser in the other 

 image. On looking at the -wires when so brought to- 

 gether, it will be found that in one case the crests fall 

 upon the crests and the hollows upon the hollows, so that 

 the vibrations combine to increase the intensity of the 

 light. In the other case the crests fall upon the hollows 

 and the hollows upon the crests, so that the vibrations 

 interfere and completely neutralise one another. 



The same principle would obtain if we shifted one wire 

 along the middle line so that the points M of the two 

 wires no longer exactly coincide. This would represent 

 the condition of the vibrations as they emerge from the 

 selenite when the plate is of such a thickness as to cause 

 a retardation of a fraction of a wave-length equal to the 

 amount of shift. And on turning the wires as before, we 

 should find that in one im.age the waves partially com- 

 bine, and that in the other they partially interfere. The 

 shifting of the wires would represent either the effect of 

 plates of different thickness upon waves of the same 

 length, i.e. rays of the same colour ; or that of a single 

 plate on waves of different lengths, i.e. on rays of diffe- 

 rent colours. From these considerations we may conclude 

 that the rays which are brightest m one image are least 

 bright in the other ; or, in other words, that the colours of 

 the two images are complementary. 



It has been remarked that the colour produced by a 

 plate of selenite depends upon the thickness of the plate. 

 In fact, the retardation increases with the thickness, and 

 consequently, if, for a given thickness, it amounts to a 

 half wave-length of the shortest (say violet) waves, for a 

 greater thickness it will amount to a half of a longer (say 

 green) wave, and so on. And if, instead of a series of 

 plates of different thicknesses, we use a wedge-shaped 



plate, the entire series of phenomena due to gradually in- 

 creasing retardation will be produced. This is easily seen 

 to consist of a series of tints due to the successive extinc- 

 tion of each of the rays, commencing with the violet and 

 ending with the red. And the tints will consequently 

 have for prevailing hues the colours of the spectrum in 

 the reverse order. This series of colours will be followed 

 by an almost colourless interval, for which the retardation 

 is intermediate between a half red-wave length and three 

 half violet-wave lengths. Beyond this again the series of 

 colours will recur ; and the same succession is repeated 

 as the wedge increases in thickness. It will, however, be 

 observed that the colours appear fainter each time that 

 they recur, so that when the thickness reaches a certain 

 amount (dependent upon the nature and retarding power 

 of the crystal) all trace of colour is lost. 



It is not difficult to account for this gradual diminution 

 in the intensity of the colours if, by means of a diagram, 

 we examine the mode in which the waves of various 

 lengths interfere with one another ; but spectrum analysis 

 furnishes an explanation which is perhaps more easy of 

 general apprehension. If the light emerging from the 

 analyser be examined by a spectroscope, it will be found, 

 in the case of a plate giving the most vivid colour, that 

 the spectrum presents a dark band indicating the colour 

 which has been extinguished. On using thicker and 

 thicker plates the band will be found to occupy positions 

 nearer and nearer to the red end of the spectrum, until 

 the band finally disappears in the darkness beyond the 

 least refrangible rays that are visible to the eye. If the 

 analyser be turned round the band will gradually lose its 

 characteristic darkness, until, when the angle of rotation 

 has reached 45°, the band will have disappeared alto- 

 gether. The spectrum is then continuous, and when re- 

 compounded will give white light. This corresponds to 

 the fact noticed before, that when the analyser is turned 

 round, the colour given by a selenite plate fades and 

 finally disappears when the angle of rotation amounts to 

 45* If the rotation be continued a band reappears, not, 

 however, in its original position, but in the part of the 

 spectrum complementary to the former. 



If the thickness of the plate be further increased, two 

 bands will be seen instead of one ; with a still greater 

 thickness there will be three bands, and so on indefinitely. 

 The total light then of which the spectrum is deprived by 

 the thicker plates is taken from a greater number of its 

 parts ; or in other words, the light which still remains is 

 distributed more and more evenly over the spectrum, and 

 consequently at each recurrence of the tints the sum total 

 of it approaches more and more nearly to white light. 



The following experiment will be found very instructive. 

 Take two wedges of selenite or other crystal, and having 

 crossed the polariser and analyser, place the two wedges 

 side by side in the field of vie a" so as to compare the tints 

 produced by the two. Then place one over the other, 

 first with the thick end of the one over that of the other ; 

 next with the thick end of the one over the thin end of the 

 other. If the two plates are exactly similar, the combi- 

 nation in the first instance will be equivalent to a single 

 wedge whose refracting angle is double that of a single 

 wedge ; and the number of bands produced will con- 

 sequently be doubled. In the second combination the 

 angles of the wedges will compensate one another, and the 

 result will be equivalent to a uniform plate whose thick- 

 ness is equal to the sum of the mean thicknesses of the 

 wedges. The field will then be coloured with a uniform 

 tint, viz., that due to a plate of the thickness in question. 



By making use of the principle that the colour produced 

 depends upon the thickness of the plate, selenites have 

 been cut of suitable shapes and thicknesses, so as to pro- 

 duce coloured images of stars, flowers, butterflies, and 

 other objects. 



W. Spottiswoode 



{To be continued.) 



