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5th ring: Pale blueish green, white, pink.
After the seventh order the colours become too faint to be distinguished. The rings decrease in breadth, and the colours become more crowded together, as they recede from the centre. When the light is homogeneous, the rings are broadest in the red, and decrease in breadth with every successive colour of the spectrum to the violet.
NOTE 200, p. 172. The absolute thickness of the film of air between the glasses is found as follows:-Let AFBC, fig. 59, be the section of a
lens lying on a plane surface or plate of Fig. 59.
glass P P', seen edgewise, and let E C be the diameter of the sphere of which the lens is a segment. If A B be the diameter of any one of Newton's rings, and BD parallel to CE, then B D or CF is the thickness the air producing it. E C is a known quantity ; and when A B, the diameter, is measured with compasses, BD or FC can be computed. Newton found that the length of B D, corresponding to the darkest part of the first ring, is the 98,000th part of an inch when the
rays fall perpendicularly on the lens,
and from this hé deduced the thickness corresponding to each colour in the system of rings. By passing each colour of the solar spectrum in succession over the lenses, Newton also determined the thickness of the film of air corresponding to each colour, from the breadth of the rings, which are always of the same colour with the homogeneous light.
NOTE 201, p. 174. The focal length or distance of a lens is the distance from its centre to the point F, fig. 60, in which the refracted
Let L L' be a lens of very short focal distance fixed in the window-shutter of a dark room. A sunbeam SL L' passing through the lens will be brought to a focus in F, whence it will diverge in lines FC, FD, and will form a circular image of light on the opposite wall. Suppose a sheet of lead, having a small pin-hole pierced through it, to be placed in this beam; when the pin-hole is viewed from behind with a lens at E, it is surrounded with a series of coloured rings, which vary in appearance with the relative positions of the pin-hole and eye with regard to the point F. When the hole is the 30th of an inch in diameter and at the distance of 61 feet from F, when viewed at the distance of 24 inches, there are seven rings of the following colours :
1st order: White, pale yellow, yellow, orange, dull red.
2nd order: Violet, blue, whitish, greenish yellow, fine yellow, orange red.
* 3rd order: Purple, indigo blue, greenish blue, brilliant green, yellow
4th order: Blueish green, blueish white, red.
6th order: Very faint green, very faint red. 7th order: A trace of green and red.
NOTE 202, p. 175. Let L L', fig. 61, be the section of a lens placed in a window-shutter, through which a very small beam of light SLL' passes into a dark room, and comes to a focus in F. If the edge of a knife KN be held in the beam, the rays bend away from it in hyperbolic curves Kr, K r', &c., instead of coming directly to the screen in the straight line KE, which is the boundary of the shadow. As these bending rays arrive at the screen in different states of undulation, they interfere, and form a series of coloured fringes, rr', &c., along the edge of the shadow K ESN of the knife. The fringes vary in breadth with the relative distances of the knife-edge and screen from F.
NOTE 203, p. 177. Fig. 43 represents the phenomena in question, where SS is the surface, and I the centre of incident waves. The reflected waves are the dark lines returning towards I, which are the same as if they had originated in C on the other side of the surface.
NOTE 204, p. 180. Fig. 62 represents a prismatic crystal of tourmaline, whose axis is. A X. The slices that are used for polarising light are cut parallel to A X.
NOTE 205, p. 181. Double refraction. If a pencil of light Rr, fig. 63, falls upon a rhombohedron of Iceland spar A B XC, it is separated into two equal pencils of light at r, which are refracted in the directions r0, rE: when these arrive at O and E they are again refracted, and pass into the air in the directions 0 0, E o, parallel to one another and to the
incident ray Rr. The ray r0 is refracted according to the ordinary law, which is, that the sines of the angles of incidence and refraction bear a
constant ratio to one another Fig. 63.
(see Note 184), and the rays R Rr, r0, 00, are all in the
same plane. The pencil r E, B
on the contrary, is bent aside out of that plane, and its refraction does not follow the constant ratio of the sines; - E is therefore called the extraordinary ray, and rO the ordinary ray.
consequence of M
this bisection of the light, a spot of ink at O is seen double at O and E, when viewed from the reflected ray rs is then polarised, and may be viewed through a piece of tourmaline in s, or it may be received on another plate of glass, B,
rI; and when the crystal is turned round, the image E revolves about 0, which remains stationary.
NOTE 206, p. 182. Both of the parallel rays Oo and E o, fig. 63, are polarised on leaving the doubly refracting crystal, and in both the particles of light make their vibrations at right angles to the lines 00, E o. In the one, however, these vibrations lie, for example, in the plane of the horizon, while the vibrations of the other lie in the vertical plane perpendicular to the horizon.
NOTE 207, p. 183. If light be made to fall in various directions on the natural faces of a crystal of Iceland spar, or on faces cut and polished artificially, one direction A X, fig. 63, will be found, along which the light passes without being separated into two pencils. A X is the optic axis. In some substances there are two optic axes forming an angle with each other. The optic axis is not a fixed line, it only has a fixed direction; for if a crystal of Iceland spar be divided into smaller crystals, each will have its optic axis; but if all these pieces be put together again, their optic axes will be parallel to A X. Every line, therefore, within the crystal parallel to A X is an optic axis; but as these lines have all the same direction, the crystal is still said to have but one optic axis.
NOTE 208, p. 184. If IC, fig. 48, be the incident and CS the reflected rays, then the particles of polarised light make their vibrations at right angles to the plane of the paper.
NOTE 209, p. 184. Let A A, fig. 48, be the surface of the reflector, IC the incident and C S the reflected rays; then, when the angle SC B is 57°, and consequently the angle PC S equal to 33°, the black spot will be seen at C by an eye at S.
NOTE 210, p. 185. Let A B, fig. 48, be a reflecting surface, IC the incident and CS the reflected rays; then, if the surface be plate-glass, the angle SCB must be 57°, in order that CS may be polarised. If the surface be crown-glass or water, the angle SCB must be 56° 55' for the first, and 53° 11' for the second, in order to give a polarised ray.
NOTE 211, p. 186. A polarising apparatus is represented in fig. 64, where Rr is a ray of light falling on a piece of glass r at an angle of 570:
whose surface is at right angles to the surface of r. The ray rs is again reflected in s, and comes to the eye in the direction s E. The plate of mica, MI, or of any substance that is to be examined, is placed between the points r and s.
NOTE 212, p. 187. In order to see these figures, the polarised ray rs, fig. 64, must pass through the optic axis of the crystal, which must be held as near as possible to s on one side, and the eye placed as near as possible to s on the other. Fig. 65 shows the image formed by a crystal of Iceland spar which has one optic axis. The colours in the rings are exactly the same with those of Newton's rings given in Note 199, and the cross is black. If the spar be turned round its axis, the rings suffer no change; but if the tourmaline through which it is viewed, or the plate of glass, B, be turned round, this figure will be seen at the angles 0°, 900, 108°, and 270° of its revolution. But in the intermediate points, that is, at the angles 45°, 1350, 225°, and 315o, another system will appear, such as represented in fig. 66, where all the colours of the rings are complementary to those of fig. 65, and the cross is white. The two systems of rings, if superposed, would produce white light.
NOTE 213, p. 188. Saltpetre, or nitre, crystallises in six-sided prisms having two optic axes inclined to one another at an angle of 50. A slice of this substance about the 6th or 8th of an inch thick, cut perpendicularly to the axis of the prism, and placed very near to s, fig. 64, so that the polarised ray rs may pass through it, exhibits the system of rings represented in fig. 67, where the points C and C mark the position of the Fig. 67.
optic axes. When the plate B, fig. 64, is turned round, the image changes successively to those given in figs. 68, 69, and 70. The colours of the Fig. 69. Fig. 70.
rings are the same with those of thin plates, but they vary with the thickness of the nitre. Their breadth enlarges or diminishes also with the colour, when homogeneous light is used.
NOTE 214, p. 189. Fig. 71 represents the appearance produced by