Measuring a Gemstone RI above 1.81

by Raul Berenguel, PhD

The determination of a refractive index (RI) above 1.81 can be a problem for several reasons. While you could use an electronic refractometer to measure a gemstone RI, it would be expensive because the low-cost models do not detect the highest and the lowest RI values found in gemstones. This also means that you will not be able to find the birefringence value.

The good news is if you are dealing with singly refractive stones you could use a micrometric scale and your  microscope. This comes in handy for separating diamonds from YAG, cubic zirconia, GGG, or even glass.

This addition can be of great value to you, although for the moment maybe you are thinking that this upgrade will be of no use. This technique was used by F.S.H. Tisdall and also by B.W. Anderson (BSC, FGA, FKC) to measure refraction indices above 1.81 (without limits). But, to be precise, remember that its main application is for uniaxial gems or SR type. For the latter, under good conditions and if the gem is not too small, an RI accuracy better than 0.02 could be obtained in the RI determination. It can also be used for other important measuring issues, like determining the deepness of an inclusion.

In 1980 the technique was to apply a small ruler and a Vernier to the microscope. Now, we can use digital callipers, and instead of taking measurements down to 0.1 mm (0.004 inch) with the Vernier (see the historical note at the end of this article), you can reach 0.01 mm (0.0004 inch) with an accuracy even better than ±0.02. You also have the advantage of zeroing the calliper in any position.

Let’s apply these concepts. For this upgrade you will need a digital calliper, two screws, a few bolts and an L-shaped piece of metal. Remember that this is only a guideline because each microscope has its own shape, dimensions, etc., and some parts could interfere with the displacement of the digital reader or its position. For this upgrade you will spend about US $20 (you will not need an expensive calliper).

The general aspect of the adaptation is the one shown in Figure 1.

Figure 1
Figure 1: Shows the general adaptation required to measure an RI higher than 1.81

First, it is imperative that you carefully study the way of adapting the calliper to your microscope. Keep in mind that what you want the calliper to move with the displacement of the objectives when you are focusing. Be sure to consider several plans carefully and do not attempt to apply the first idea. Be sure that your adaptation will be done in such a way that the calliper will be absolutely vertical and horizontal in relation to the planes of the microscope. In our case, we had to do two trials before getting it right. Normally, you will find that the best way is to work with the calliper in an upside-down position. This will give you negative numbers, but this is not relevant, since you will take them as positive values.

After the assembly, you will have to cut some parts of the calliper. If you have a mini-drill with cutting discs, you can use that. If you do not have a drill of your own, take the parts you want to cut to a metalwork store to do it. Never cut the metal without taking off the reader, which the electronic part of your calliper. The heat required to cut the metal will ruin the electronics. To disassemble the calliper, another few words of advice: do it step by step, understanding where each piece belongs. For instance, in the interior of any calliper is a small copper curved strip that acts as a tension spring. It is connected to a retention pin. Look at Figure 2, you can see which parts needed to be cut off in our case.

Figure 2
Figure 2: The parts marked with an X indicate the parts that we needed to cut off for our calliper.

The final result can be seen in Figure 3.

Figure 3
Figure 3: This photo shows our disassembled calliper.

Note the hole that we made. It is about 3.5 mm (0.138 inch). That will serve as passage for a 3 mm (0.118 inch) screw. The top of the calliper remains untouched because it will serve to perfectly align the horizontal and vertical axis (See Figure 4).

Figure 4 - Measuring a Gemstone  RI above 1.81
Figure 4: This photo shows how the calliper aligns with the base of the microscope.

Of course, after very carefully positioning, we must mark the point where we will drill a threaded insertion for the screw. You will most likely have to add some spacing nuts between the calliper and the microscope body in order to keep some free space between the digital reader and the body of the microscope. See Figures 5 and 6.

Figure 5
Figure 5: This photo shows the addition of the spacing nuts.
Figure 6
Figure 6: This photo shows the spacing that you need between the calliper and the microscope body.

If the bottom screw fails to be perfectly aligned, you will have to insert another screw to slightly bend the calliper. It happened to us, and we used it as an opportunity to align the vertical position.

In this mounting, you must (of course) remove the metal stripe used to measure deepness. When you dismount the calliper, just pull it out and it will break. You will have no use for this part.

Now, attach the digital reader to the upper platform of the microscope. We used an L-shaped piece of metal that we secured by drilling a threaded insertion for a small screw. But before doing that, you must attach the L-shaped piece of metal to the digital reader. To do this, use the Patex NURAL 21 glue to do the cold welding between the two. After 24 hours, mark the exact position, then drill and thread the hole for the screw. To see this, see Figure 7. If the metals you are working do not stick well with NURAL, you could use the Patex EXTREME glue (do not only some inner gluing, but carefully build a “cover” that embraces the “L” shaped piece).

Figure 7
Figure 7: In this photo you can see the L-shaped bracket and the screw that holds it in place.

You can paint this rear part of the digital reader so your device looks better if you would like. To do this, cover all the microscope parts completely with a painting adhesive roll. Next, cover the reader and other parts you do not want painted. Using matte black will give a professional look to the upgrade. Do not forget to protect the metal slide rule, as you just want to paint the back of the reader.

Important note: If your microscope is a binocular one, always use only one ocular, preferably the fixed one (normally this is the right one) and not the one that allows you to regulate the diopter (usuallythe left one). If the focusing is done by looking through the two oculars, mistakes can occur.

Now let’s do some testing. We have an old cubic zirconia that a friend purchased in Brazil several years ago. It is in bad shape, but by using only the microscope, let’s see if it is a cubic zirconia or not.

The gem must be examined with the table in a horizontal position. This can be difficult to arrange, so take your time. We choose to mount a dark field plate and close the iris at the point that the gem rests in a very good position.

Note: Choose a moderate magnification, such as 20X. If you go above this magnification, errors can occur, due the increased difficulty in perfectly focusing.

First, we carefully focused the table of the gem. To do this, you need a point on the gem on which to focus. This can be dust that is present on the gem’s surface, any marks the gem may have, or it could even be a small ink mark you make with a fine-point, non-permanent marker. Next, we pinpointed the culet too. When we thought that the table was perfectly focused, we zeroed the calliper. Next, we focused the microscope to the culet. In most cases, the pinpoint mark is very useful. When we determined it was perfectly focused, we stopped and read the calliper: 2.15 mm (0.085 inch). This is the apparent depth of the stone.

Using a gem digital calliper (Leveridge type), we know that the real depth of the gem is 3.90 mm (0.154 inch). Well, if we divide the real depth by the apparent depth, we get the RI of the gem — 3.90 / 2.15 = 1.814.

Looking at an RI table (we have one organized in decreasing RI order and another in gemstone alphabetical order), we find a value of 2.15 for the RI of cubic zirconia. Consulting another table, we found what we already knew at the first look through the microscope: it is glass. Not ordinary glass, but an extra dense flint glass. We do the confirmations using a density determination and a spectroscopic view, just to be sure.

Another thing you can do with this tool is to estimate how deep an inclusion is. Position the gem so that the inclusion you wish to measure is visible and take a depth reading. Multiply that apparent depth by the gemstone RI, and the result will be the real depth from the surface you chose to the inclusion.

These calculations are possible because of the Law of Refraction, also known as Snell’s Law (Willebrod Snell, 1591-1626). It was deducted from the old corpuscular theory of light from René Descartes (1596-1650), so, in France it is known as Descartes Law. Looking at Figure 8, we can state that the sine of angle A divided by the sine of angle B is equal to the index of refraction.

Figure 8
Figure 8: This diagram shows us that sin A/sin B = RI. This is Snell’s Law.

Historical note: The Portuguese mathematician Pedro Nunes (1502-1578) was the real inventor of the mathematical and practical use of what is known as Vernier. In fact, Pierre Vernier (1580-1637) applied the concepts of Nunes to a linear metrical device, as Nunes had described the mathematical foundations of it and applied those concepts to measuring angles within minutes of error during the Portuguese Discovery Era, many years before Vernier. The name Vernier, however, was adopted all over the world, except in Portugal and Brazil, where this device is called Nónio. First, by the proximity of the name Nunes, and secondly because the concept is based in the 1/9 division of any 10 parts scale (or any other relation).