Diamonds And Luxury

The refraction of light, and the phenomena connected with it, have an important bearing on the study of precious stones.
We have already noticed that of the light which falls upon a transparent body, such as a precious stone, a portion is reflected at the surface, while another portion enters its substance and is propagated in straight lines through it. When the incident ray of light
strikes the bounding surface of the transparent body per¬pendicularly, the light which passes into the interior of the body is propagated in the same direction as that of the incident ray. If, however, the incident ray strikes the surface obliquely, the path taken by the light through the substance of the body will not coincide in direction with the incident ray, but will be in a new direction ; the ray may then be said to be bent or refracted.

In let MN be the surface of separation between the transparent body (precious stone), S, and the air, L. verragio diamond rings. 3 stone diamond ring. A single ray of light travelling in air in the direction AC, and striking the separating surface at C, will not be propagated in the stone in the same straight line, namely, along CK, but will be bent or refracted into the direction CB. CB is then the refracted ray corresponding to the incident ray AC. The directions AC and CB, and also BE, the normal to the surface at C, all lie in the same plane, which is perpendicular to MN, and in is the plane of the paper. This plane is known as the plane of incidence. Whenever light passes from air into a stone, the refracted ray CB is always nearer the normal DE than is the incident ray AC; that is, the light is bent towards the normal. This may be expressed otherwise by stating that the angle of incidence, A CD, is greater than the angle of refraction BCE.

When the angle of incidence is greater than ACD, the angle of refraction will be greater than BCE. In . 9, let AXC represent another ray of light in the same plane of incidence, such that the angle of incidence AXCD is greater than ACD, then the corresponding refracted ray is represented by CBV It will be seen from the ure that the angle of refraction BXCE is greater than BCE, which is the angle of refraction corresponding to the angle of incidence ACD. Similarly in every case the /ingle of refraction varies with the angle of incidence, and this variation is governed by a definite law, namely, the law of refraction.

In the plane of incidence and with C as centre , let a circle of any convenient radius be drawn. Let the circle cut the incident rays A C and AXC at the points A and Av and the refracted rays BC and BXC at the points B and Bv From these points drop perpendiculars, AG, AXGV BF, BXFX upon the normal DE. Then the ratio of the perpendicular AG to the corresponding perpendicular BF is the same as the ratio A1G1 to BXFV and will always be constant for the same substance whatever may be the angle of incidence.

In passing from air into any of these substances, the bending of the rays of light is greater the greater the refractive index of the substance, and conversely. The value of the refractive index is in many precious stones very high, but is far higher in diamond than in any other gem. The values for other stones will be given under the special description of each. In comparing two substances with different refractive indices, the one with the higher refractive index is known as the >' optically denser " substance, while the other would be described as the " optically rarer" ; thus precious stones are "optically denser" than water or air.
A ray of light in passing from air into a stone immersed in liquid will be twice bent; once at the surface of separation between the air and the liquid, and again at the surface of separation between the stone and the liquid. The amount of bending depends in each case upon the difference in the refractive indices of the two media through which the ray passes. Thus, if the refractive index of the liquid is much greater than that of air, the ray of light will be much bent in passing from air into the liquid. Similarly, if the refractive index of the stone is not much greater than that of the liquid, the ray will experience but little bending when entering the stone ; while if the index of refraction of the stone and that of the liquid are identical, there will be no bending of the ray of light, and it will travel through both in the same straight line.
The use of methylene iodide in determining specific gravities has already been described. Another of its convenient properties is a very high index of refraction, the value of which, moreover, can be diminished by diluting the liquid with benzene. If a stone be immersed in methylene iodide so diluted with benzene that the refractive index of the liquid is the same as that of the stone, there will be no bending of the rays of light, and they will pass in straight lines through the liquid and the stone. Provided that the liquid and the stone are of the same colour, the result will be that the latter becomes invisible and cannot be detected. If the index of refraction of the liquid be changed by the addition of benzene or of methylene iodide, the boundaries of the stone will become visible; its outlines will grow sharper and more distinct as the difference between its refractive index and that of the liquid is increased by the further addition of either one or other of the liquids.

The phenomenon just described is sometimes made use of for the purpose of discovering hidden cracks, enclosures, and other flaws in precious stones. The stone is immersed in a strongly refracting liquid such as methylene iodide ; its external boundaries will then become less distinct or, if the stone has the same refractive index as that of methylene iodide, invisible. Any flaws in the interior of the stone will thus be rendered prominent and can be easilv seen.

Light is refracted not only when passing from an optically rarer into an optically denser medium, as, for instance, from air into precious stone, but also in the reverse case, as, for example, when a ray of light in a stone passes out into the air. In the

passage of light from a denser to a rarer medium, the law of refraction still holds good. We shall see from, however, that the refracted ray is in this case bent away from the normal, or, in other words, the angle of incidence is less than the angle of refraction ; while in the previous case the refracted ray was bent toioards the normal, and consequently the angle of incidence was greater than the angle of refraction.

Let MN be the surface of separation between the stone S and the air L. It will be seen that the angle of incidence A CD of the ray A C in the stone is less than the angle of refraction BCE of the refracted ray; also that the refracted ray BC is bent away from the normal. In this case also, the bending of the ray is greater the greater the index of refraction of the stone, but the amount of bending is the same whether the light passes from stone to air or vice versa. In one case the light travels in the direction ACB, and in the other in the direction BCA.

In the case also of the passage of light from a denser to a rarer medium, the angle of refraction increases with the angle of incidence. In . 11, where MN is the surface of separation between the precious stone S and the air L, the ray AC, incident upon the surface MN at C is bent into the direction OB, AXC into the direction CBV and so on. As the angle of incidence ACD becomes greater and greater so the angle of refraction BCE also becomes greater and greater. When the angle of incidence reaches a certain value, represented by A2CD, the corresponding angle of refraction B2CE will be a right-angle ; the refracted ray will then emerge from the stone in a direction parallel to the bounding surface MN.

Obviously at 90° the angle of refraction has reached its maximum value and no further increase is possible. Should the angle of inci¬dence now be increased, even by a small amount, it will then be impossible for the ray of light to leave the stone, and it will be refracted no longer, but simply reflected by the bounding surface back into the stone. In . 11, the incident ray ASC is reflected from the surface MN, along the line CB3 inside the stone. This takes place according to the usual laws of reflection, the angle of incidence AZCD being equal to the angle of reflection B3CD. In the same way, every ray incident upon the surface MN at a greater angle than A2CD, will be unable to pass out of the stone, and will be reflected back again by the surface MN; A4CB4 for example, is the path of such a ray and its reflection.

When light, travelling in one medium, as, for example, air, strikes the surface of a denser medium, such as a precious stone, a portion of it enters the stone and is refracted as described above, while the remaining portion is reflected from the surface. This takes place invariably, whatever may be the angle at which the incident light strikes the surface of the denser medium. In the reverse case, when light travelling in one medium, for example a precious stone, strikes the surface of a rarer medium, for instance air, the same thing may happen, that is, the light may be partly reflected and partly refracted, but this does not happen invariably as in the former case.

It was seen from . 11, that when the angle of incidence exceeds a certain fixed value (A2CD) the light is not refracted at all, but is reflected from the bounding surface back into the stone. In all other cases, as has been shown, light incident upon the surface of separation of two media is divided into a refracted portion and a reflected portion. Since in this particular case the light is not so divided, but the whole of it is reflected, this kind of reflection is known as internal total reflection, or, briefly, as total reflection.

Total reflection takes place at the surface of separation of two media only when the light travelling in the denser medium strikes the surface at an angle exceeding a certain degree of obliquity. Total reflection never takes place when light passes from a rarer to a denser medium. In this case there will always be refraction, for when the incident angle reaches a maximum of 90°, since the refracted ray is bent towards the normal, the angle of refraction will be less than 90°, and the light will pass out of the rarer into the denser medium. It is always possible then for light to pass from air into a precious stone, but it cannot pass out again unless it strikes the surface of the stone at an angle not exceeding a certain degree of obliquity.

The limiting angle A2CD in . 11 is known as the critical angle or the angle of total reflection. Its value depends upon the refractive indices of the two substances at the boundary of which reflection and refraction takes place. The greater the difference in the refractive indices the smaller will be the angle of total reflection, A2CD. If the difference is very small the incident ray will make a large angle with the normal before total reflection takes place.

In diamond, which has a very high refractive index relative to air, the angle of total reflection is small, namely 24° 24', which is represented by the angle A1CD in . 12. A ray of light inclined to the normal at an angle slightly less than A1CD will be refracted and pass out into air in the direction CB1 while one inclined at a slightly greater angle will be totally reflected in the stone in the direction CB\. The ray A3C, making a still larger angle with the normal, will be totally reflected along CB3; while the ray A.2C will pass out of the stone along CB2, not undergoing total reflection.

If the optically denser body is, instead of diamond, glass, having, say, a refractive index of l-538, then the angle of total reflection will no longer be 24° 24' but 40° 30', the body, as before, being surrounded by air. In this case, only those rays which are incident at an angle greater than 40° 30' will be totally reflected.

Since the angle of total reflection increases when the difference between the refractive indices of the two media decreases, it follows that the angle of total reflection will be greater if the stone is surrounded by water instead of air. The angle of total reflection for a diamond placed in methylene iodide, the refractive index of which is 1-75, will be 46° 19', the angle A1CD in . 13. Some of the rays, the obliquity of which causes them to be totally reflected when the diamond is surrounded by air, will be refracted when the surrounding medium is methylene iodide ; thus fewer rays will in this case be totally reflected. The use made of this fact will be mentioned later.

Total reflection has a considerable influence on the path taken by the rays of light in a transparent cut stone. The beauty of transparent cut stones largely depends on the fact that the light which falls on the front of the stone is totally reflected from the facets at the back and passes out again from the front to the eye of the observer. If the light were allowed to pass out at the back of the stone, the latter would lose much of its brilliancy ; only when there is total reflection at the back of the stone does it appear, as it were, to be filled with light. The greater the proportion of light thus reflected from the back of a stone, the more brilliant will be its appearance. But to enable us to trace out the exact path of a ray of light in a cut stone, we must first consider some of the phenomena of refraction rather more closely.

Up to the present we have considered only the behaviour of a ray of light at the boundary of different bodies, namely, in passing from air into a liquid or into a precious stone, and vice versd, in passing from a precious stone into air or liquid. By combining these observations, the complete path of a ray of light passing through a precious stone is easily arrived at.
In . 14, let MN, PQ, be parallel sides of a transparent body, and let AB be a ray of light from a source, such as a small bright flame, falling obliquely upon MN. On passing into the plate, the ray is bent towards the normal, BE, and takes the path BC. This portion of the ray meets the second surface PQ at C, the angle of incidence, BCDV being equal to the angle of refraction, since the normals are parallel. On passing out into the air, the ray is again refracted, this time away from the normal, and takes the path CF.

From the geometry of . 14, it is easily seen that the second angle of refraction, FCEV is equal to the first angle of incidence, ABD; and that the paths of the ray outside the plate, namely AB and CF, are parallel. The direction of the ray on emerging from the plate is therefore the same as the original direction, but its path has been shifted a small distance, represented in . 14 by B'F. On observing a small object A through a transparent body with parallel sides, it will be seen in very nearly the position it really occupies ; this will not be the case however when the bounding surfaces, MN, NP (. 15), are not parallel.

In passing through a prism, the differently coloured constituents of white light are separated, and we have the phenomenon known as dispersion. The beautiful appearance of many precious stones, and specially of diamond, is due to their dispersion of light. The coloured constituents of white light, from a source such as the sun or a lamp, differ not only in colour but also in refrangibility or capacity for being refracted. Thus, the refrangibility of red light is the smallest, and that of violet light the greatest; yellow, green, and blue light occupy in this respect intermediate positions in the order in which they stand.
Dispersion of light.

It follows, then, that though we have hitherto spoken of a substance as having a single refractive index, this is only strictly true for monochromatic light, such as that given out by a Bunsen flame, or a spirit-lamp flame coloured by the vapour of either of the metals lithium, sodium, thallium, and indium. If white light be used, the refractive index of the substance will be different for each constituent of the light, that for red light being the least and that for violet light the greatest.
When white light passes through a prism, then, the red rays will be deviated or bent out of their course least, the violet rays most, and the other rays will fall in their proper order between the two extremes. In . 16 the ray of white light AB falls upon the surface MN of a refracting substance. Owing to the different refrangibilities of the constituents of the ray, these latter are separated and we get the original single ray of white light split up into red (R), yellow (G), green (Gr), blue (BV), and violet (V), rays, deviating from each other slightly in direction. Between the rays of the colours just mentioned lie rays of intermediate tints. The decomposition of white light into its coloured con¬stituents, or the dispersion of light, varies according to the dispersive power of the refracting substance. It is the more distinct the greater the angle between the extreme red ray and the extreme violet ray.
We have now to consider the dispersion of the light which passes through a precious stone. We will take first the case in which the stone has the form of a plate with parallel sides, as in . 17, and afterwards the case in which these bounding surfaces are inclined to each other and so form a prism.

The ray of white light, AB, falling obliquely on the surface MN of the precious stone, is split up into the differently coloured rays lettered BR, BG, BGr, BBl, BV. These rays pass out of the precious stone at the surface

PQ in the directions RR', VV, &c, all being parallel to the original white ray AB, as was explained before in connection with . 14. The eye placed at R'V will receive all these differently coloured rays at the same time and in the same direction ; the effect of this will be to produce in the eye the sensation of white light just as if the ray of light from A had not passed through the plate. With such a parallel-sided plate, then, a decomposition of white light into its coloured constituents takes place, but is not observable, since the effect produced by the first surface is neutralised by the parallelism im¬parted to the rays at the second surface.
.
The dispersion of light produced by a prism, on the other hand, is very noticeable, and is illustrated in . 18. A ray of white light, AB, falls upon the surface MN of the prism, and is separated into its variously coloured con¬stituents. Between the extreme red ray, BR, and the extreme violet ray, BV, lie the yellow, green, blue, and rays of intermediate colours. On passing again into air at the second surface, NP, of the prism, these rays are again refracted, and emerge still more widely separated.The angle between the extreme red ray RRX and the extreme violet VV1 is R1CV1; and, as before, this measures the amount of the dispersion, and varies with the substance of which the prism is made. An eye placed at R\VX will receive this bundle of coloured rays, diverging apparently from C, the various colours being perfectly distinct and brilliant. The ray of white light thus gives rise to an elongated band of colour which is known as a spectrum. The red end of the spectrum lies nearest to the refracting edge, N, of the prism, and the violet end furthest away from it; the other colours lying between these two, and following each other with no break or interruption in the same order as the colours of the rainbow, namely, red, orange, yellow, green, blue, indigo, violet. The spectrum may be conveniently shown to a number of persons at once by placing a white screen in the path of the coloured rays.
. 19 gives a perspective view of the path of rays of light from a candle-flame, A, through the prism MNPM'N'P'. The ray of light AB falls on the face MNMN' of the prism, and is resolved into the prismatic colours; the red ray travelling along BR, the violet ray along B V, and rays of other colours between. These rays inside the prism meet the face NPN'P', and on passing into the air are further refracted and separated, the red ray taking the path RR', the violet VV, and so on. Since rays of light emanate from every luminous part of the candle flame, a complete image of it will be seen at A' by an eye placed at R'V. In the direction V V the image will be coloured violet, that is, the side v of the image nearer the refracting edge NN' of the prism will be violet, while the margin r of the image lying on the line R'R will be coloured red. To an eye placed at R'V the image will be seen to the left of the actual position of the object, as is shown in . 19; the image is thus nearer the refracting edge of the prism than is the object.

Path of the rays of light through a prism. (Perspective view.)
The length of the spectrum formed by a prism depends upon a variety of conditions. It is longer the greater the angle between the rays RR} and VV1; this, in its turn, depends upon the dispersive power of the substance of the prism, for the spectra given under similar conditions by two similar prisms, but constructed of different substances, will differ in length. The amount of dispersion produced by a prism will obviously vary with the difference between the degree of refraction of the red rays and of the violet rays; the difference between the refractive indices of a substance for red light and for violet light is indeed frequently regarded as a measure of the dispersive power of the substance.

Amongst precious stones, and indeed the majority of known substances, diamond has by far the greatest dispersive power. The differences in the refractive indices of diamond and of window-glass for red and for violet light, that is the dispersive power of these substances, are given below : The dispersion produced by diamond is therefore more than double that produced by window-glass; as a result of this, the spectrum given by a prism of diamond will be more than twice the length of that given by a prism of glass having the same refracting angle. The prismatic colours are transmitted to the eye by diamond widely separated from each other, and the stone owes much of its beauty to this fact; in glass and other substances of less dispersive power, more or less overlapping of the prismatic colours takes place, and this renders them less perceptible to the eye as separate sensations.

The beautiful play of prismatic colours, shown by many precious stones, and especially by diamond, is quite independent of the colour of the stone itself, but is due to the decomposition of white light into its coloured cons tituents by refraction within the stone. The greater the dispersive power of a stone the more marked will be this play of prismatic colours ; on account of the specially high power of dispersion of diamond, the play of colours exhibited by this gem is far in advance of any other precious stone.
This play of prismatic colours is sometimes, especially by English jewellers, referred to as the " fire" of a stone. The same term, " fire," is, however, also used to denote the brilliancy of lustre of a stone ; it was used in this sense above when dealing with the quality of lustre.

Any two facets of a cut stone which are not parallel may constitute a prism and thus give rise to the decomposition of white light into its coloured constituents. The facets at the back and front of a cut stone should be so related as to give the maximum decomposition of white light. Further, the faces at the back of the stone must be steeply inclined, so that light, entering the stone from the front and being resolved into its component colours, will strike the back faces of the stone at such angles that it is totally reflected by them and passes out again at the front of the stone.

The more perfectly the form of cutting fulfils these conditions, namely, the greatest possible decomposition of white light into its coloured components, and the greatest possible internal reflection of this light from the back facets, the more beautiful will be the cut stone. The form of cutting most suitable for bringing out the beauty of the diamond is that known as the brilliant. This form is shown from different points of view in s. 29 and 52 among others, and in section in . 20.

The form of a brilliant will be discussed in detail later ; here it need only be mentioned that its numerous facets give it approximately the shape of a double four-sided pyramid, of which one apex is trunacted by a large plane, the table, and the other by a smaller plane. A brilliant is placed in its setting so that the table Im (. 20) is at the front towards the observer, while the small truncating plane hi is turned to the back away from the observer.

The path of a ray of light inside a stone cut as a brilliant is shown in . 20. Let us suppose a ray of light ab to fall on the oblique facet Tel, and to be refracted within the stone in the direction be. The refracted ray be falls very obliquely on the facet hi, and forms with the normal to this facet an angle greater than the critical angle of the substance; it will therefore be totally reflected in the direction cd, and cd and cb will be equally inclined to ki. In the same way the ray travelling along dc is again totally reflected from the surface hi in the direction de, "and is then reflected from the surface hn in the direction ef. The ray travelling along ef strikes <a href="http://www.eglusa.com/">egl</a> the facet Im at a high angle, that is, at an angle less than the critical angle of the substance ; it is therefore possible for it to pass out of the stone into air along the pa,th fg. This direction,fg will not, as a rule, coincide with the original direction of the ray ab, since in its journey through the stone it has undergone two refractions and three internal reflections. Moreover, as a consequence of the two refractions undergone by the original ray of white light, ab, it will be split up into iis component colours, and, on emerging from the stone, will present to the observer a beautiful play of prismatic colours. To avoid obscuring the diagram, the different paths of differently coloured rays are not shown in . 20, as they are in s. 17 and 18 ; the path, as shown in . 20, may be regarded as the mean path for the several colours, or, more correctly, as the path which would be taken by monochromatic light within the stone. Other rays of light entering the front and side facets of the stone will be refracted and totally reflected in the same manner, and will therefore follow a path very similar in direction to the one shown in . 20. The whole stone will therefore appear to be full of light, and will emit flashes of rainbow colours.

The many beauties of the diamond can be traced back to the optical characters of the stone; its high index of refraction causes a large proportion of the light which enters the front facets of a suitably cut stone to be totally reflected from the back faces, while from its high dispersive power results a wide separation of the rays of differently-coloured light, and, in consequence, a fine play of prismatic colours. These features of a cut diamond are specially noticeable when the stone is contrasted with another colourless stone, cut in the same manner, for example, rock-crystal. The latter appears in comparison dull and dead, owing to the fact that it possesses neither the high index of refraction nor the great dispersive power of the diamond. The highly refractive and dispersive glass called strass, when cut in the form of a brilliant, may, however, closely resemble a diamond in these characters.
From what has been said above, it is easy to see that the cutting of a stone is a very important factor in developing the potential beauty with which its optical characters endow it. A diamond cut in the form of a good brilliant, far exceeds in play of colour and general brilliance a similar stone cut in any other form, such, for instance, as a rosette (rose-cut), which does not fully utilise the optical characters of the stone.