1 68 



NATURE 



\yan. 1, 1874 



parallel to the line joining the blunt angles, is not 

 divided. In fact, the image either of the aperture of the 

 lantern projected on a screen, or of an object seen by the 

 eye in the direction in question, appears single, as if 

 passed through a block of glass. The direction in 

 question (viz., the line a b itself, and all lines passing 

 through any part of the crystal parallel to a b), is 

 called the optic axis of the crystal. If, however, the 

 crystal be tilted out of this position in any direction, 

 it will be seen by the appearance of two images instead 

 of one, that the rays are divided into two. The angular 

 divergence of the two sets of rays, or what comes to the 

 same thing, the separation of the two images, depends 

 upon the angle through which the crystal has been turned ; 

 or, as it may also be expressed, upon the angle between 

 the directions of the incident ray and the optic axis of the 

 crystal. When this angle amounts to a right angle, the 

 separation is at its greatest ; and if the crystal be still 

 further turned, the images begin to come together again 

 until, when it has turned through another right angle, they 

 coincide. 



This process of separation, or doubling the rays, is called 

 double refraction. And the following experiment will 

 show that one set of rays follows the ordinary law of re- 

 fraction, while the other follows a different law. The 

 image produced by the first set of rays is, in consequence, 

 called the ordinary, and that produced by the second the 

 extraordinary image. Let us now take a sphere of Iceland 

 spar, which will act upon the rays issuing from the lamp 

 as a powerful lens. In every position in which it is placed 

 it produces two images on the screen ; but in that in 

 which I now place it the two images are concentric, differ- 

 ing only in this, that one is larger than the other. The 

 direction in which the light is now passing is that of tlie 

 optic axis ; and it is to be observed that, although there 

 is a difference in the magnifying of the two images, there 

 is still no divergence of rays, or separation of images in 

 the sense used before. In fact, if we suppose the curva- 

 ture of the lens to be gradually diminished, we should 

 find the difference of the sizes of the two images, as well 

 as the absolute size of both, diminish ; until when the 

 surfaces of the lens became flat, the difference would 

 vanish, and the two images would absolutely coincide. 



This difference in the size of the images shows, more- 

 over, a very iinportant property of double refracting crys- 

 tals. The amount of refraction produced by a transparent 

 medium standing in air depends, as is well known, upon 

 the velocity with which, a ray of light traverses the medmm 

 compared with that with which it traverses air. The smaller 

 the velocity in the medium, the greater the refi action. 

 The greater the refraction, the greater the magnifying 

 power of a lens constructed of that medium. Hence in 

 the two concentric images we can at once point to the 

 system of rays which has traversed the crystaJ at a lower 

 velocity than the other. 



Let us now turn the crystal round into some other 

 position, so that the direction of the optic axis shall no 

 longer coincide with that of the rays from the lamp or 

 frotn the object. During this process one of the images, 

 the larger, remains stationary, as would be the case with 

 the single image, if we had used a sphere of glass. This, 

 therefore, is the ordinary image. The other shifts about, 

 separating itself from tlie first, until the crystal has been 

 turned through half a right angle, and then drawing back 

 again untd the crystal has swept round through a com- 

 plete right angle. This is, consequently, the extraordinary 

 image. 



It will be noticed that when the sphere has been turned 

 through a right angle, the extraordinaiy image is no 

 longer circular, but elliptical, and that the major axis of 

 the ellipse lies in the direction in which the motion has 

 taken place, that is, perpendicular to the axis about 

 which the sphere has been turned. This is due 

 to the fact, shown above, that the nearer the direc- 



tion of the incident rays to that of the optic axis, 

 the less the divergence between the ordinary and 

 the extraordinary rays. The distortion of the image 

 when the sphere has turned through half a right angle is 

 due to the difference of angles between the optic axis and 

 the rays which enter the crystal on one side and on the 

 other of the central ray of the beam coming from the 

 lamp. 



That the rays forming each of the images are polarised, 

 and that the direction of their polarisation is different, is 

 easily shown by interposing a plate of tourmahn or other 

 polarising instrument between the lamp and the sphere of 

 spar. But inasmuch as the polausation m many positions 

 of the sphere is far from uniform, the phenomenon be- 

 comes rather complicated ; and the character of the 

 polarisation of the two images is better studied by using 

 flat instead of curved surfaces for separating the rays. 



For the purpose in question there is, perhaps, no better 

 instrument than the double-image prism. This consists 

 of a combination of two prisms, one of Iceland spar, so 

 cut that the optic axis is parallel to the refracting edge ; 

 the other of glass, and usually having a refracting angle 

 equal to that of the spar. The rays passing through the 

 crystal prism being perpendicular to the optic axis, under- 

 go the greatest separation possible. And the chromatic 

 dispersion caused by that prism is corrected or neutralised 

 entirely in the case of the extraordinary, and nearly so in 

 that of the ordinary ray, by the glass prism which is 

 placed in a reversed position. In this arrangement the 

 extraordinary image occupies the centre of the held, and 

 remains fixed while the double-image prism is made to 

 revolve in a plane perpendicular to the incident rays ; 

 while the ordinary image is diverted to a distance from 

 the centre, and revolves in a circle about that centre, 

 when the prism revolves. 



If the nature of the light in the two images thus formed 

 be examined by any polarising instrument, it will be found 

 to be polarised in both cases ; but that the vibrations in 

 the one image are always perpendicular to those in the 

 other. And m particular the vibrations in the extraor- 

 dinary image are parallel, and those in the ordinary are 

 perpendicular to the optic axis. 



On these principles polarising and analysing instru- 

 ments have been constructed by various combinations of 

 wedges or prisms of Iceland spar, the details of which it 

 is not necessary to describe in full. But the general pro- 

 blem, and object proposed, in all of them has been to cause 

 such a separation of ordinary and extraordinary rays, 

 that one set of rays may, by reflexion or other methods, 

 be further diverted and afterwards thrown altogether out 

 of the field of view. This done, we have a single beam of 

 completely polarised light and a single image produced 

 from it. 



One such instrument, however, the Nicol's prism, on 

 account of its great utility and its very extensive use, de- 

 serves description. A rhombohedron of Iceland spar 

 double of its natural length is taken (see Fig. 10) ; and one 

 of its terminal faces P, which naturally makes an angle of 

 71° with the blunt edges K, is cut off obliquely so as to 

 give the new face, say P' (not given in the figure), an in- 

 clination of 6S" to the edges K. The whole block is then 

 dividtd into two by a cut through tlie angle E in a direc- 

 tion at right angles to the new face P' ; the faces of this 

 cut are then carefully polished, and cemented together 

 again in their original position with Canada balsam. 

 !• ig. II represents a section of such a prism made by a 

 plane passing through the edges K (Fig. 10). A ray en- 

 tering as a b is divided into two, viz., Id c the ordinary, and 

 bd the extraordinary. But the refractive index oi the 

 Canada balsam is r54, i.e. intermediate between that of 

 the spar for the ordinary (i '65) and the extraordinary (1*48) 

 rays respectively ; and in virtue of this the ordinary ray 

 undergoes total reflexion at the surface of the balsam, 

 while the extraordinary passes through and emerges ulti- 



