Download Chapter 4 - Refractometry - Index of Refraction

CHAPTER 4 - REFRACTOMETRY – Index of Refraction Measurements
The Critical Angle Gem Refractometer:
For gem identification, the most useful information is the indices of refraction, since they
provide quantitative numerical values and optic sign. Faceted gems and polished surfaces are
best examined with a standard, critical angle, gem refractometer which is relatively inexpensive
and readily available (Figure 4-1). In addition to the refractometer, one needs a light source, with
monochromatic sodium filter, and a bottle of high index immersion oil.
The key element of the refractometer is a transparent glass prism of very high refractive
index usually in the form of a hemisphere or hemicylinder with a flat, polished upper surface.
The index of refraction of the prism (n ≈ 1.90) must be greater than that of the gem and precludes
use of the refractometer for gems of higher refractive index like diamond and zircon*. A polished
facet of the gem is placed in contact with the polished surface of the glass prism, with a film of
oil between the polished surfaces. The standard contact oil, which must also have a refractive
index greater than the gem is methylene iodide with dissolved sulfur (n = 1.81). This becomes
the limiting feature of the refractometer, which cannot be used for gems of refractive index
greater than 1.81. A small bottle of contact oil is normally purchased with the standard
refractometer and may last for years, as only a tiny amount is used for each measurement.
Anyone using liquids of high refractive index should be aware that they may contain very toxic
elements and should avoid all oral, eye and skin contact. Such liquids are also highly corrosive
to the soft lead glass of the refractometer prism, which should be wiped clean with acetone after
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every use.
Light, coming through the hemicircular prism from below, encounters the prism-gem
interface where it passes from the higher index of the glass into the lower index of the gem and is
totally reflected, at incident angles exceeding the critical angle, and transmitted, at incident
angles less than the critical angle (Figure 4-2). The field visible through the eyepiece is part dark
and part light, separated by a “shadow edge”. The refractometer measures the critical angle for
the gem mineral which is inversely proportional to the sin of the critical angle (n = 1/sin CA) and a
visible scale is calibrated to read directly as index of refraction at the shadow edge. If the light
source is white light, the shadow edge is a color spectrum, usually appearing as a narrow bluegreen band, which may be more easily recognized than a sharp, but faint, shadow edge. A sharp
edge is read with much greater accuracy, however, and requires a monochromatic light source,
usually provided by a sodium vapor filter.
*Since several important gem minerals, including diamond, have indices of refraction above 1.81, a refractometer
with prism and contact oil of higher refractive index would appear to be an obvious solution, and numerous attempts
have been made to construct such an instrument. The most successful has a cubic zirconia prism which allows a
refraction index range from 1.44 to 2.06. Cubic zirconia has great hardness (8½) and is chemically inert, so the prism
surface is resistant to scratching and corrosion by high index liquids. The high index, contact liquid usable with a CZ
prism, however, must have an index of refraction greater than the refraction indices to be measured, and all such
liquids are extremely viscous, highly toxic, and very corrosive. Also, the measurement scale in the CZ refractometer
must be greatly condensed, making the index of refraction readings much less accurate than those obtainable with the
standard refractometer.
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With a faceted gem lying at the center of the glass prism in optical contact with the glass,
a standard procedure is to rotate the gem 360° about an axis normal to the prism surface,
recording observed refractive indices for every 45° of rotation (Figure 4-3 and Figure 4-4). These
data may be plotted as a graph, or one may gain the needed information by merely observing
changes in the position of shadow lines as the gem is rotated†.
†The gem refractometer commonly has a polarizing cap which fits over the eyepiece. Since the two waves passing
through the gem are always polarized at right angles to one another, rotating the polar cap causes one shadow edge to
become visible with the exclusion of the other, with every 90° of rotation.
Every transparent mineral must be either isotropic or anisotropic. If isotropic, the mineral
has only one refractive index and shows a single shadow edge which does not change as the gem
is rotated on the refractometer prism.
Anisotropic minerals must be either uniaxial or biaxial and must show dual shadow
edges, as the gem is rotated.
If uniaxial, the mineral has two principal indices of refraction (nω and nε). Rotation of the
gem will show that one refraction index never changes (nω) while the other changes with
rotation from the fixed index nω to a maximum or minimum value (nε). If the variable index is
larger than the unchanging index (nε > nω), the mineral is optically positive. If smaller (nε < nω),
the mineral is optically negative.
If biaxial, the mineral has three principle indices of refraction (nα, nβ, nγ) but shows only
two shadow edges. Rotation of the gem will normally show that both shadow edges (i.e.
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refraction indices) change with rotation. One refraction index can range from a maximum (nγ) to
an intermediate value (nβ) and the second refraction index can range from the intermediate (nβ)
to a minimum value (nα). Note that light passing through a biaxial crystal in any direction, other
than an optic axis, is divided into two polarized waves, one having an index of refraction
somewhere between nγ and nβ, and the other having an index of refraction somewhere between nβ
and nα. The greatest refractive index, or the high point on the upper curve, is never greater than
nγ, which must be at least that large. The smallest refractive index, or the low point on the lower
curve, is never less than nα, which must be at least that small. The intermediate refractive index
nβ is somewhere between the lowest value of the upper curve and the highest value of the lower
curve, which may be the same value, i.e., nβ, Our plot has provided a small range of values for nβ,
a minimum value for nγ, and a maximum value for nα.
When an optical direction X, Y or Z is the rotation axis normal to the prism surface, one
index of refraction will remain constant and a biaxial gem may appear uniaxial. Measurements
on a second facet should resolve the question.
Unfortunately, no procedure is ever as simple in practice, as described, in theory. Small
birefringence means that the principle indices of refraction of a mineral, uniaxial or biaxial, are
very near one another, and shadow edges we see may separate only slightly with gem rotation. If
the separation is too small to yield definitive results, one should record the approximate index of
refraction for the mineral and try for an interference figure as described in the following chapter.
Interference figures are expected to yield optical character and sign and are best when
birefringence is small. Many common gem minerals (e.g., quartz, corundum, beryl, feldspar,
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topaz, chrysoberyl) show very small birefringence (<0.01).
Spot Method - Measuring the refractive index of a rounded, polished cabochon surface
with the gem refractometer is a more challenging exercise and may yield only an approximate
value. By removing the entire eye lens assembly from the refractometer, one can see the index
scale and a spot which is the oil contact of the rounded mineral surface on the flat prism surface.
By nodding up and down, one sees the spot move up and down on the scale, and at some point on
the scale, the spot changes from light to dark, which marks the refractive index of the cabochon
gem. The smaller the spot of oil contact the better the index reading. One can repeatedly remove
the gem cabochon, wipe the oil from the rounded surface, and return it to the prism surface to
reduce the size of the oil contact spot.
Relief:
A simple method of judging index of refraction is to compare the cut gem or mineral
fragment to that of its surrounding medium. A colorless transparent object in a colorless
transparent liquid is visible only because light rays are refracted or reflected at the interface
between the object and the medium surrounding it. If the object and the liquid have exactly the
same index of refraction (and dispersion) the object is invisible, since light rays pass from one
medium to the other without deviation. This, of course, suggests the possibility of determining
the refractive index of a gem by immersing it in liquids of know refractive index until one is
found where the gem is invisible. True invisibility is unlikely because any anisotropic crystal will
show two indices of refraction, one for the fast wave and another for the slow wave, and also the
crystal is very unlikely to have the same dispersion as the liquid in which it is immersed.
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The degree of visibility of a transparent object in an immersion medium is said to be its
relief (Figure 4-5). The invisible object is said to have zero relief, and an object whose refractive
index is considerably different from its immersion liquid is said to have high relief. Relief may
be expressed as a quantitative value, which is the numerical difference between the index of
refraction of the object and the index of refraction of its immersion liquid. A gem or mineral
fragment is said to have positive relief if its index of refraction is greater than that of the liquid
which surrounds it, and negative relief if its index is less. Gem minerals in air, water or most
common liquids show relief so large that one cannot begin to estimate the refractive index of the
gem, however, we commonly immerse a gem in some high index liquid like methylene iodide (n
= 1.74) to reduce its relief and expose internal features like inclusions or color zoning. Grossular
garnet and chrysoberyl are almost invisible in methylene iodide and spinel and corundum show
low relief.
Numerical values for index of refraction can be achieved using the concept of relief, and
the key to the procedure is to know whether one is seeing positive or negative relief, i.e. is the
index of the crystal fragment greater or less than the index of the immersion medium?* Two
procedures will be described, both of which are destructive procedures requiring tiny fragments
of the gem material to be sacrificed for the information gained, and both of which require use of
a microscope. The procedures are not useful for cut gems, but are useful for a piece of rough
which has no polished surface and from which a few tiny fragments can be broken. The mineral
fragments should be the size of table salt grains, or smaller, on a glass microscope slide,
immersed in a drop of oil of known index of refraction and covered with a thin coverglass. If the
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immersion oil proves to be of higher refractive index than the fragments, one selects an oil of
lower refractive index, until one is found below the refractive index of the fragments. We now
have an upper and lower limit for the index of the fragments and we may converge the limits, by
mixing oils, until the fragments have “zero” relief. We must prepare a new slide mount with new
fragments for each change of immersion oil.
*Graduated sets of immersion liquids are commercially available (R.P. Cargille Laboratories, Inc., 55 Commerce
Rd., Cedar Grove, NJ 07009, [email protected]). Many oils in common use can also be used.
The Central Illumination or Becke Line:
This method is standard procedure for mineralogists and petrographers and is designed
for use with a petrographic microscope (Figure 4-6)*. A Becke line is a thin bright line at the
interface between a transparent fragment and its immersion liquid when the relief is low (Figure
4-7). If relief is too high, the Becke line is hard to see and may appear as a bright shadow and, if
the relief is almost zero, the Becke line may appear as colored dispersion fringes. We can
eliminate color fringes and negate the effects of dispersion by using a monochromatic light
source, usually sodium vapor light. Essentially all indices of refraction cited in articles and
tables are values for the sodium wavelength (λ = 5890 Ǻ). Random fragments are almost always
thicker in the middle than on their edges and act as crude converging or diverging lenses, so that,
by raising the focus of the microscope, the Becke line moves toward the medium of higher
refraction index. The bright Becke line moves into the mineral grain, if the refractive index of the
fragment is greater than the refractive index of its immersion oil, and the Becke line moves away
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from the fragment if its index is less (Figure 4-7). The Becke line is most visible with high
magnification and low light intensity.
*For standard procedures using a petrographic microscope for the measurement of refractive indices, the reader is
referred to any book on optical crystallography e.g., Phillips, Mineral Optics, W.H. Freeman (1971).
If the fragments are isotropic (i.e. amorphous or isometric), they have only a single index
of refraction to be measured, and orientation of the fragments is not important. If the fragments
are anisotropic, however, each fragment passes two mutually perpendicular waves having
different indices of refraction, each of which can be measured. Between the crossed polars of a
petrographic microscope, the fragments are bright with interference colors against the black
background and become dark with every 90° of stage rotation, as the polarization directions of
the two waves rotate parallel to the N-S and E-W polarization directions of the upper and lower
polars of the microscope. If a particular fragment is rotated to its position of maximum darkness
(“extinction”), the vibration directions of its two waves are N-S and E-W. If we remove the
upper polar of the microscope, we now see the fragment in white light and only that wave which
is vibrating parallel to the polarization direction of the lower polar. Raising the focus of the
microscope, the Becke line moves either into or out of the mineral fragment, telling us whether
the index of refraction of that wave is greater or less than the refractive index of the immersion
oil. Rotating the microscope stage 90° brings the other wave into the polarization plane of the
lower polar and we can determine index of refraction of that wave in relation to the immersion
oil. By preparing new slides with new fragments and new immersion oils, we can bracket, one
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index at a time, the refractive indices of the two waves to whatever degree of accuracy is useful
for us. It is seldom worth our effort, however, to measure the index of refraction of a gem
mineral to accuracy beyond the second decimal place (i.e. ± 0.01), because mineral impurities
and less-than-ideal composition allow a small range for the refractive indices of any given
mineral species. Dispersion, birefringence and other optical limitations also discourage the quest
for great accuracy.
If we try consistently to select fragments of maximum birefringence (i.e., maximum
interference colors) and remove the upper polar, we can measure the greatest and smallest
refractive indices for that particular gem mineral by the procedure cited above. If the mineral is
uniaxial, we are measuring nω and nε and, if the mineral is biaxial, we are measuring nα and nγ. If
we select fragments of minimum birefringence (i.e., almost dark between crossed polars), we are
looking almost parallel to an optic axis, and we are seeing nω (uniaxial) or nβ (biaxial). We can,
of course select a fragment of maximum birefringence and another of minimum birefringence in
the same slide mount. If nε is greater than nω, or if nβ is nearer to nα than to nγ, the mineral is
optically positive.
Unfortunately, jeweler’s microscopes are not manufactured with polars which can be
easily inserted and removed or with a rotating stage, or even with a flat stage ready to receive a
microscope glass slide. The Becke line method is possible with a jeweler’s microscope; however,
it requires major alteration of the microscope and considerable experience.
The Oblique Illumination:
This procedure is more practical for use with a jeweler’s (gemological) microscope. The
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stage of a jeweler’s microscope is open and will require a plate of glass on the microscope stage
to support microscope slides of small mineral fragments immersed in an oil of known refraction
index and covered with a thin cover glass.
When the relief of the fragments is low and light is restricted over one-half of the visible
field, bright fringes form on one side of the mineral fragments and dark fringes on the opposite
side (Figure 4-8). If the index of refraction of the mineral fragments is greater than that of the
immersion oil, the bright fringes are on the side toward the dark half of the visible field and dark
fringes on the bright side of the field (Figure 4-8A). If the refraction index of the mineral
fragments is lower than that of the immersion oil, the dark fringes are on the dark side of the
visible field and the bright fringes are on the illuminated side of the field (Figure 4-8B). By
preparing new fragment mounts and changing the immersion media, one can arrive at near zero
relief, and one can bracket a refractive index with successive oil mounts.
One may restrict the light over one-half of the visible field by simply inserting a card
below the microscope stage or, with a gemological microscope, one may partially insert the disk
which swings over the light source to change from direct to dark-field illumination.
The Hodgkinson Method:
This method is an interesting method and a unique approach to the determination of
indices of refraction. It has the huge advantage of requiring no special equipment at all, beyond a
human eye. It does require a darkened room, a small bare filament light source and much
practice. By merely looking through a faceted gemstone at a tiny light source, one can learn to
estimate index of refraction by displacement of the image he sees, birefringence by image
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separation and dispersion by spectral color fringes on the image. This may well prove a useful
skill for one who travels much or operates without standard gemological equipment. Hanneman,
W. (1980) Educating the eyeball – the Hodgkinson Method, Lapidary Journal, 34, 1498-1519.
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