DE2406008A1 - Transparent jewellry stone of natural or synthetic material - material refractive index and facette angles define light exit angle within given relationship - Google Patents

Abstract

Transparent jewellry stone of a natural or synthetic material with refractive index n = 2.2 in a diamond grind, a parallel table and top and bottom part facettes where the refractive index of the stone material, the back facette angle and an uneven diamond division give a defined light exit angle for light falling vertically onto the tablet. The definition inter-relates the light exit angle, the refractive index, the limiting angle of the total reflection, and the inner angle. The diamond division is chosen according to the refractive index with a reducing number of corners on reducing refractive index.

Description

Transparent gemstone The SrfindunS concerns a transparent one Gemstone made from a natural or synthetic material with a refractive index n # 2.2 for a brilliant cut with a round ink, a table parallel to it and top and bottom facets. A colored, transparent material is also used included that occurs naturally or is artificially produced.

The diamond brilliant with a conventional brilliant division shows a brilliance that makes the stone appear bright, but with the desired one Spectral colors are measured. It has already been suggested for a diamond-cut diamond to improve this effect in relation to the spectral colors by for the diamond-brilliant-cut diamonds an odd division with a number of corners greater than 9 is used for the angle of inclination of the lower and upper facets in relation to the girdle plane are chosen so that the reflected by the lower facets and exiting through the upper facets Light at an opening angle of the spectrum (farthing angle) »between 1 ° 20 'and 12 ° 57' with respect to the upper facets. If nan such If conditions are transferred to other materials, then they result geometrically a Diamonds Similar gemstones, but which when using such a piece not have the brilliance.

It is also known to have an angle between the brilliant cuts The girdle plane and the rear facets should be between 37 and 450.

In the German patent specification 2 014 966 it was proposed under To use a back facet angle smaller than 350 for certain considerations. This German patent specification is also based on the knowledge that the so-called Auffiederungswinkel P, which should be rough for the price of the stone, by the Angle is determined, which are formed by the ii game standing facets, if they are sides of an odd pyramid. It was also assumed that that the exit angle of a light beam from an optically denser material can be at most equal to the flaring limit angle, because the exit angle of the light from an optically dense material, in turn, defines the flaring angle certainly. For a diamond, a light emission angle of a maximum of 23 ° is 56 'and thus a feathering limit angle of 12057 is given.

In general, it follows from the German patent specification that optional the number of corners for a gemstone to be worked the angle of inclination of the front and back facets must be chosen in order to achieve a strong dispersion of the exiting To get Lichtatstrahles, so that the gem has as much fire as possible. This also resulted in a version with 7 corners that the sum of the angles of the front and rear facets to the girdle plane is, for example, 28.40. These However, the condition does not apply in general, but at most for a diamond, its fire with such a number of corners is significantly reduced for other reasons is.

From British patent specification 221 960 are gemstones with a Division that leads to 9 corners is known. If for these gemstones in particular with regard to diamonds, a rear facet angle. in the specified range of 38 ~ 410 is used, then this leads to a completely unusable gemstone. For the purposes of the invention, a useful result would only be with; a refractive index reached between 2.28 and 2.13. But no material is known for this The division 9 = 3 x 3 is only for ornamental reasons. This well-known version is neither suitable for the material diamond nor for any other known material Material to arrive at a gemstone that can be used in the context of the invention.

Materials occur naturally or are produced synthetically and further developed, which are now processed with a finish that is below ornamental point of view is imitated the brilliant cut, but the light reflected in a humble way so that the fire is limited. With stones like that it is desirable, for example, a basic color, e.g. of tanzanite, in blue or to make purple as rich as possible.

The invention is based on the object, including such gemstones except for diamond, which either has excellent optical properties or one for permanent use have required hardness to perform 80 that for the A cut is applied to the respective material in a form that is as individual as possible creates optimal brilliance with lively fire and changes depending on the material. The specification with a refractive index n <2.2 is based on the fact that with n @ 2.2 a Adaptation of the treated materials is inexpedient because they (such as Pabulit, Rutile) have a large playing moment (dispersion of the material).

According to the invention, this object is achieved in that the refractive index of the stone, the rear facet angle and an odd diamond division Light emission angle of 1. 160 (arc tg 1 <# '' '0 RUr perpendicular to the board falling light. Here # "'means the light exit angle, n the refractive index and # @ critical angle of total reflection.

The values t each denote the inner angle, i.e. the angle in the material of the stone at the reflection plane or

the exit plane in relation to the normal to this plane.

From this point of view, it is also advantageous in itself known rear facet angle in the range preferably between 24 ° and 51.5 ° to the Rondist plane the facet division or each odd-numbered brilliant division in Dependence on the refractive index with decreasing number of corners with decreasing To choose the refractive index, whereby the light exit angle £ is greater than 160. The preferred rear facet angle is for reasons of optimal behavior has been chosen. It is taken into account that it can also be undercut. To go out is based on the fact that in the case of transparent gemstones with n s 2.2 the height of Pyramid at the back is not essential.

It is preferred that the front racette angle is # <330.

What is essential, however, is the knowledge that with one essentially constant area of the rear facet angle the number of corners can be changed must, depending on the refractive index. This can be done for certain materials it is provided that with a refractive index n = approximately 1.56 a number of corners 7, n n about 1.83 a corner number 9, n - about 1.9 to 2 a corner number 9 is selected.

In these examples particularly suitable materials are mentioned, namely in the order of the indications glass, YAG, zircon.

As is well known, light vibrates (an electromagnetic Wave) into two vectors, the electric vector parallel to the plane of incidence and the perpendicular magnetic vector. At tg # "" '= 1 / n the parallel vector goes undamped out of the denser material and with tg # "" '= n undamped in the denser material into it. This law leads in the application to the brilliant ship an attractive gem, since the electrical component is the more essential is. At the same time, the angle of the feathering is also true for such materials as YAG (with a small dispersion of the material) became so large that the gemstone shows many individual spectral colors.

With a Ritck facet angle of the order of 28.50 for a material with a refractive index n <1.7 (glass) a smaller odd one Number of corners can be selected if the back of the 8tone is mirrored.

A teaching of the invention is based on the inclusion of the above conditions in that the rear facet angle 9 is chosen so that the angle of the light beam with the perpendicular to the rear facet is always greater than the total reflection angle for the material in question and that the number of corners is chosen so that the light exit angle (EW ') of the parallel light vector through the refractive index of the transparent material essentially with tg (# "" ') = 1 / n the approach angle # ""' as the most favorable angle is determined. This leaves the possibility of changing the rear facet angle open, but there is always a dependency on the refractive index and again the corners depending on the refractive index.

number is changed. Under these conditions there is also a cut in glass to make it resemble the diamond brilliant.

As a characteristic example, the YAG (Yttriu @ Aluminum Garnet) With a refractive index n "1.8334 and a dispersion - 0.028 at one Mohs hardness of 8 1/2.

Ii conventional cut, the YAG diamond does not show any spectral colors, in a new cut, on the other hand, it has a lively fire. Due to its high hardness of 8 1/2 it is also suitable in practical use It is also noted that the back facet angles of the cut are therefore critical for all materials, because through the double reflection on them the light ui four times the angular amount the tolerance of the rear facet angle reaches the panel or the front facets and there, if there are deviations from the conditions of the invention, either one so small Exit angle receives that it only appears bright and not colored, or over the The angle of total reflection increases and thus remains in the stone. Such a stone looks boring.

It should be noted that up to total reflection one of the sharpest Limits in optics. Si. is to be observed under all circumstances when a cut should have the desired success of a strong fire, and in twofold Respect, i.e. the relevant angle should once be sur reflection on the rear facets larger and the other time too light emission on the board and front facets smaller be than the total reflection angle.

The invention is explained below on the basis of exemplary embodiments, which are shown in the drawing.

These show: FIG. 1: a diagram for the cuts of gemstones in a coordinate system whose abscissa is the number of corners and whose ordinate is the Light exit angle has denser material in air, with certain materials with their refractive indices and back facet angles are indicated; Fig. 2: on off 1 derived diagram in a coordinate system, the abscissa of which is the refractive index and whose ordinate indicates the exit angle £; Fig. 3: a side view of a Gemstone; FIG. 4s a plan view of the gemstone according to FIG. 3; FIG. Fig. 5: a diagram for the intensity of the light vectors shown for the substance YAG as an example.

Figures 3 and 4 are only used to explain dimensions. The gemstone has the girdle level 1, a table 2, so-called front facets 4 and back facets 5. The back facet angle 6 is with # and the front facet angle 7 denoted by #. It can be seen that the anterior and posterior facets are relative to one another are offset. Fig. 4 shows that there are seven front facets so that one heptagonal division is created.

From Fig. 3 it can be seen where the angles # ', # "and #"' according to the above Definition, always inside the material and measured to the normal on the assigned Level, to be assumed. d and # 1 denote the outer angles, based on the Normal of the plane.

Fig. 1 is derived from the formula (1) sin (180 ° / m) # sin (#) = ½ arc tg 1 / n where m = number of corners, a whole odd number (#) = rear facet angle n = refractive index If this equation is based on the back facet angle or the number of corners j resolved, the sizes for the most favorable light exit angle result (2) tg # "" '= 1 / n because sin also applies. (# "'/ 2) = ½ arc tg 1 / n where #"' = light exit angle denser material / air.

Also included is (3) sin #o "'= 1 / n where - (# o"') = Critical angle of total reflection (# "" ') = most favorable light exit angle.

In Fig. 1, the abscissa 8 is the corner number m and aut is the ordinate 9 the light exit angle plotted. With reference to the above formulas are then as parameters the lines 10, 11, 12 for rear facet angles of 55 °, 45 °, 37 ° drawn. For example, glass is specified as materials in area 13 with the refractive index 1.56; in the range 14 YAO with the refractive index of 1.8334 and in the area 15 zircon with the refractive index 1.93 .... 1.99. One each.

for each area there is an upper value 16, 17, 18 for the Light exit angle, where. it is the critical angle for the total reflection acts.

It is also noted that the critical angle of total reflection is obtained when (3) is satisfied.

If now for a certain feature in the area of the selected back angle the most favorable number of corners is to be determined, the point of intersection between the Angular curve determined with a division corresponding to the number of corners and the Intersection point selected according to (3). This results in certain rear facet angles on the one hand and certain corner numbers on the other hand, which lead to the desired result to do.

For a "diamond-brilliant-like" removal of a cut a transparent material is the back facet angle next to the odd pitch decisive. This angle is determined by the formula (3) and is by no means To exceed.

To get a cut from others: transparent material than the diamond Similar to diamond-cut diamonds, it is necessary to make it permanent in use close. Glass with a Mohs hardness between 4.5 .... 7.0, especially in the soft types, differs greatly from diamonds, so that it seems inevitable, to protect the cut stones.

Such protection can be achieved by a layer of a substance which is much harder to wear than the base body. Such layers can be applied in a high vacuum.

In FIG. 2, the refractive index is on the abscissa 19 in a coordinate system and on the ordinate 20 the inner light exit angle # is indicated.

In FIG. 2, d: Le upper curve 26 denotes the angle # o "', the critical angle the total reflection, which in the various areas in Fig. 1 by the lines 16, 17, 18, and the lower curve 27 the angle # "" ', i.e. the most favorable Light exit angle, which in Fig. 1 in each case by the lines 31, 3; 2, 33 for the different areas 13, 14, 15 is indicated.

From Fig. 1, the relationship with the number of corners also results with reference to a selected rear facet angle, so that FIG. 1 One area can be read in each case, in which particularly favorable conditions are achieved will. It can be seen that the ratio between the rear facet angle and the angle of total reflection of the material in question becomes smaller, The smaller the refractive index of the material in question.

Otherwise the rear facets have to be mirrored, as is the case with glass is common. Glass has a ratio of 1: 1.025.

If glass is mirrored on the back, the ratio is true the said angle is infinite. There will be incident light from all directions reflected over the girdle level.

Nevertheless, according to the above information, the rear facet angle determines the light exit angle; for example, glass cuts with 7 corners and 400 at 22 in FIG. 1 or with 5 corners and 28.5 ° at 21 in Fig. 1 the same exit angle of -32.60.

The following materials are specified, for example: material refractive index Total reflection angle zircon 1.93 - 1.99 30 ° 39 'YAG (yttrium aluminum garnet) 1.833 33 ° 3 '(synthetic) Monticellite 1.79 - 1.84 33 ° 30' Corundum 1.76 - 1.77 34 ° 30 ' Feldspar 1.52 - 1.53 40 ° 54 'Tansantt glass 1.50 41 ° 48' Glass 1.90 31 ° 45 'In Fig. 1 For glass, the rear facet angle of 28.5 ° is at position 21 and the rear facet angle of 40 ° at the point 22 on the line 31, which delimits the area 13 downwards.

The best light exit angle is then on line 31 Ordinate 9 can be read off.

The corresponding line for region 14, YAG, is designated by 32 and intersects the ordinate 9 at the light exit angle # "'by 28.6 ° At the point 23 there is a rear facet angle of 46.5 °. The point 24 denotes in the area 15, zirconium, the rear facet angle 42.8 °, with the chosen Number of corners of the exit angle # "'at the intersection @ point of the line 33 with the ordinate 9 can be read.

In Pig. 5 the special conditions for the material YAG now specifically explained. Fig. 5 contains practically two diagrams, which of one The abscissa 34 represents an inner angle of incidence corresponding to the division on the line 35 # from 0 to 900 is applied. Ordinary section 36 contains from the abscissa 34 upwards from 0 to 100 the percent of the reflectance r at the air / material interface, i.e. in the present case YAG, and the section 37 from top to bottom from 100 to 0 «are the values of the permeability d at the interface Air / material, i.e. TAG and at the material / air interface with the abscissa 38; because the light exit angle # "'is indicated on the abscissa) 8.

The values for the reflectance r and transmittance d are respectively so designated, however, the decomposition of components is also given by ru and that the for entry or

The exit plane represent parallel components of the vectors r and d, while the curves r, and d, the components of the vectors perpendicular to the planes indicate.

The diagram represents the reflectance r and the transmittance d over the angle of incidence £ according to FRESNEL's Formulas for that Material YAG (Yttrium Aluminum Garnet).

The index of refraction of TAG is: n = 1.8334 at the angle of incidence # = 0 ° applies: n - 1 r = # # 2 = 8.65% n + 1 4 n d = # # 2 = 91.35%.

n + 1 The critical angle of total reflection is: #o "'= arcain (1 / n) = 33.05 ° This corresponds to point 29 in Fig. 2. The same results for others Materials the points 28 for zircon and 30 for glass.

The other values in the diagram were based on FRESNEL's formulas calculates r = tg2 (# - #) / tg2 (# + #) r = sin2 (# - #) / sin2 (# + #) r @ + r @ = r 2 d = sin2 (#) sin2 (#) / sin2 (# + #) cos2 (# - #) d = sin2 (#) sin2 (#) / sin2 (# + #).

It can be seen from FIG. 3 that # is the outer perpendicular angle of incidence is.

For the material YAG, FIG. 5 shows that the angle of incidence at the point # = arctg n = 61.39 ° the parallel component of light unhindered enters the material, where the reflectance is 0 and the transmittance is 100 % is. As can be seen on line 38, this corresponds to the light exit angle # "'= 28.61 °. This corresponds to the area 14 in FIG. 1 for the material YAG Intersection of line 32 with ordinate 9, so that it can be seen from FIG. 1, as depending on the number of corners and the rear facet angle an advantageous one Cut can be chosen. Such a cut can be read off for the number of corners 9 for example at position 23.

The breakdown of components shown in FIG. 5 allows the most favorable working point due to the contact of the curves r ″ and d ″ with the abscissa 34 for the respective Na.

determine the material, the values being determined using the formulas given will. At the inner, exit angle of 28.610, according to FIG. 3, the result is outer the lines 31, 32, 33 in FIG. 1 each show the position of the maximum working point, with others to maintain the working point Values such as rear facet angle and number of corners can be changed depending on one another are.

Fig. 5 explains the relationships for a material, namely for YAG. Corresponding curves can be set up for other materials. the Components rlj and d "are particularly essential to that also shown in FIG. 3 Auffiederungswinkel ß.

Claims (5)

Claims 1. Transparent gem stone made of a natural or synthetic Material with refractive index n C 2.2 in a brilliant cut with a girdle, a table parallel to it and upper and lower part facets, characterized in that that the refractive index of the stone material, the back facet angle and an odd one Brillanttdlung a light exit angle of # "'= 16 ° <arc tg 1 / n <for result in light falling perpendicularly onto the board, where # "'is the light emission angle, n is the refractive index and #o "'is the critical angle of total internal reflection, where E denotes called inner angle. 2. Gem according to claim 1, characterized in that the diamond graduation depending on the refractive index with decreasing number of corners with decreasing Refractive index is chosen. 3. Gem according to claim 1, characterized in that at one Refractive index n = about 1.56 a corner number 7, n = about 1.83 a corner number 9, n . about 1.9 to 2 a corner number 9 is chosen. 4. Gemstone according to one of claims 1 to 3, characterized in that that at a back facet angle on the order of 28.50 for one material with a refractive index below 1.7 (glass) a smaller, odd number of corners was chosen and the back of the stone is mirrored. 5. Gemstone according to one of claims 1 to 4, characterized in that that the rear facet angle (#) is chosen so that the angle of the light beam with the perpendicular to the rear facet is always greater than the total reflection angle for the material in question and that the number of corners is chosen so that the light exit angle (# "') of the parallel light vector through the refractive index of the transparent material is essentially determined with tg (fl) = 1 / n.