American Mineralogist
Vol. 57, pp. 237-236(7972)
DIFFERENTIAL DISPERSION MEASUREMENT OF
REFRACTION INDEX
JonN McAwDREw,
Diuision ol MineralogA,Cffno'
Uniu ersitg oI M elbourne, Parlt uille, Awstral;ia,3052
Assrnect
by using the difierential dispersion line in place of the dispers'ionline can be kept
to 0.0001,which is insignificant relative to other errors common to both methods.
INrnonucrroN
Microscopicimmersionmeasurementof refractive index at ambient
temperature using wavelength dispersionis notably rapid, convenient,
much wider utilization, particularly
and accurate.The methoddeserves
as recentdevelopmentsin high intensity electricalglobes,and of continuously variable interferencefilters, simplify wavelengthvariation
illumination.
of microscope
It does however require measurementof the refractive index of
liquids at the particular wavelengthsof matching' or determination
of their individual dispersioncurves. The present note shows that
when using liquids of similar dispersion,such as in a seriesmixed
from two components,it is only necessaryto know their refractive
index n;l at the standard sodium D wavelengthof 589.3nm to determine that of the solid at this wavelength.This further simplifies
the dispersionmethod of refractive index measurement,while not
requiring liquids at exactly 0.005spacingof refractive index as does
the chart of Watkin (1958). The procedurecan also be appliedto immade at different temperatureswith the same
mersionmeasurements
liquid.
Mnrrror
is to plot
The normal procedureused for dispersionmeasurements
the refractive index, on a linear scale,against the wavelengthtr nm
of matching,on a scaleinverselyproportionalto (r, - 200) (Fig. 1).
Hartmann dispersiongraph paper eonstructedto these scalesis convenientto use.
231
232
JOHN MIANDREW
X
o
z
F
o
UI
WAVELENGTH
Frc. l. Dispersionline and difierential dispersionline of xenotime o.
A different procedureis to plot on Hartmann paper np of the
liquids against,the actual wavelength at which the solid matches
them. The line through these points representsthe differential dispersionof the solid and liquids and intersectsthe standardD wavelength aL np of.the solid, as of coursedoesthe dispersioncurve (Fig.
1). The differential dispersioncurve is sufficientlycloseto a straight
line to determinenp to within 0.001by linear interpolationor extrapolation from two suitably locatedpoints on it. Only nn of.!,heliquids
needbe measuredto determinethis differentialdispersioncurve,avoiding the refractometryof the liquids at varying wavelengthswhich is
normally used in locating the dispersioncurve of the solid.
A straight differential dispersionline is obtained when the dispersionof the solid and each liquid corresponds
to a straight line on
Hartmann paper,and the liquids have the samedispersion(nr - nd.
This follows from tr'igure2, whieh complieswith these conditions.A,
and B' are points on the dispersionline of the solid, A and B the
DIF FEREN TI AL DISPE RSION
233
equivalent points on the differential dispersion line plotted by the
new procedure.For liquids with the same dispersion, and hence
parallel dispersionlines, the dotted triangles are similar. The shaded
right angle triangles, geometrically dependent on these, are also
similar, with equal anglesat their commonapex C. ACB is therefore
a straight line, and linear interpolation between A and B locates
C and no.
The physical significanceof ACB, as the dispersionof the solid
minus the dispersionof the liquid, relative lo np of.the solid, is apparent from Figure 2. Dispersionof the liquids normally exceedsthat
of the solid, so the slope of the differential dispersionline is reYerse
to that of the dispersionlines of the solid and liquids.
Drscussron
This methodrequiresliquids of neighbouringrefractive index which
do not differ greatly in dispersion(tu - nd.It is thus applicableto
using the one liquid (Emmons,1928;
double variation measurements
plotting
wavelength
1943),
the
of matching against rzp of the liquid
at the temperatureof matching.Suitableliquids for single,dispersion
variation are mixtures of end components,with adjacent liquids
differing in refractive index by i to t of the dispersion(no - nd.
The differential disnersionline obtained from measurementsat
X
o
z
F
O
E
;
WAVELENGTH, NM
Frc. 2. Geometrical basis of the differential dispersion line.
2M
JoHN MyANDREW
ambient slide temperature (determinedto 0.1oC with a thermistor
probe) has been found to determinena of minerals to within 0.001
of measurements
by the dispersionline. This error accordswith the
precisionwith which matching of the refractive index of the solid
and liquid can be normally observedby the Becke line. The two
methodsare howevertheoretically equivalent only if the liquids of
differentz2 used in a determinationhave the samedispersion,a condition which can be only approximatelymet in practice.
EnnonINrnonucnosy LrNren Pr,orrrNc
As the error introducedby using the differential dispersionline in
place of the dispersionline to determinerefractive index is lessthan
0.001,it has beenindirectly ascertained,
usingrefractiveindicesknown
to 0.0001or better at monochromaticwavelengthsemitted by mercury,
sodium and hydrogen lamps for axinite (Miiller, lg58), spodumene
(Bottcher,1956),calcite (Gifford, 1902; 1910),and chrysolite (Ernst,
1925). The dispersioncurvesof thesemineralswere plotted on Hartmann paper,togetherwith thosefor selectedliquids in the monochlornaphthalene-diiodomethane
seriesdiffering in refractive index by approximately half their dispersion (no - ns). Liquids of adjacent
refractive index differed by 3 percentto 4 percentin dispersion.The
scale of plotting was sufficientto clearly read refractive index to
0.0001,and wavelengthto lessthan the variation producinga 0.0001
changein refractiveindex.The Hartmann dispersionpaperused,Selector No. 397$ of Schleicherand Schull, varied from a scaleof l/(x 200.0)at 450 nm In l/ Q\ - 196.4)at 650 nm, relative to the location
of the 400nm and 700nm wavelengths.
The intersectionof the dispersioncurve of eachmineral with those
of the liquids determinespoints on the differential dispersionline of
the minerals to within 0.0001in refractive index. rla aa,flthen be
determinedby linear interpolation or extrapolationto the D wavelength from pairs of thesepoints. The error in np introducedby using
this differential dispersionplotting procedureis listed in Table l. It
doesnot exceed0.0001when two fairly widely spacedpoints on the
differentialdispersionline are used,suchpoints being between420 nm
and 665 nm, either straddling 58g.3nm or with one point near 58g.8.
Interpolation from more widely spaced points gives greater error.
Extreme extrapolationfrom wavelengthswell away from D, and outside that used in dispersionmeasurements,gives errors of up to
0.0007when the differential dispersioncurve is taken to be linear.
The differential dispersionplotting procedurewhen appropriately
usedwithin the wavelengthrangeof ca.48Onm to 650nm, on minerals
235
N
OI N'FERE N TI AL DI SPERSIO
TABLE 1.
ERRORIN z,
ARISING FROMLINEAR INTERPOLATIONOR
E X T R A P O L A T I OONF D I F F E R E N T I A LD I S P E R S I O N .
Wdvelengths of matching
Mine::a1
Norma]
Trnao
"-.-.
.i r. - n, . D
wavelength
wor:king range
axinite,
E
cnnulrrmcna
R
(D
caLcite,
479.8
580.9
0.0001
52L7
653
0.0001
474.0
600
0.0001
nhnr<n1
i+a
5t7 .0
665
0.0001
nhrrrcnl
i+o
4 4 8 .3
665
0.0002
4I8 ,4
479.8
0 ,0007
4 4 5. 0
52L.7
0.00045
448,3
517.0
0.0004
Xxtreme extrapolation
axinite,
B
<nnirrmano
al'ntenl
r'+a
ru
without a strong absorptionband in this region and hencewith dispersioncloseto linear on the Hartmann scale,can thus be expectedto,
of itself, introducean error of not greaterthan about 0.0001.This is
the error when using liquids differing in dispersion (ns - nd by not
more than 3 percent per 0.010 differencein refractive index.
Such an error is less than the standard deviation of. ca. 0.0002
found in visual dispersionrefractive index measurementsunder exceptionally favorable circumstances(Morse, 1968). It is appreciably
smaller than the experimental error normally obtained with this
method, and also less than the error in measurementof refractive
indicesof the comparisonliquids on an Abbe type refractometer,unlessparticular care is taken (Fisher, 1958; Fujii and Bloss, 1962).
Differential dispersionmeasuremenL
of nn is thus normally limited
in accuracyby the error in matchingthe refractive index of the solid
and liquids, and in determiningthe refractive index of the liquids.
zrc
JOHN McANDRETV
The procedureis more than adequatein accuracy for immersron
refractive index determinationas well as being well suited for such
measurements,
particularly using fixed grain mounts (Olcott, 1960)
or a spindlestage(Wilcox, 1959;Jones,1968).
RnnnnnNcns
Borrcnun, G. (1956) Zur kenntnis des kunzits und hiddenits. I Teil: Optik u-nd
chemismus. Hamburger Beitr. Angew. Mineral. Kristallplrys. Petrogen. 7,
9-56.
EuuoNs, R. C. (1943) The universal stage. Geol. Soc.Amer. Mern.8,55-102.
EnNst, E. (1925) Uber olivin von Onundarfjord, NW-IsIand, und ein beitrag zur
kenntnis der olivingruppe. Neues Jahrb. Mineral. Petrogr.52A, 113-156.
Frsnnn, D. J. (1958) Refractometer perils.Amer. M'ineral. 4,777-780.
Fu.ru, T., eNo Br,oss, F. D. (1962) Some properties of a-monochloranaphthalenediiodomethane immersion media. Amer. Mineral. 47, %7-290.
Grrronr, J. W. (1902) The refractive indices of fluorite, quartz and calcite. Proc.
Roy. Soc. Lond. 70, g2g-440.
(1910) Addition refractive indices of quartz, vitreous silica, calcite, and
fluorite. Proc. Roy. Soc.Lond,.,Ser.A, 84, 193.
Jowos, F. T. (1968) Spindle stage with easily changed liquid and improved crystal
holder. Amer. M,inerar.$. 1399-1403.
Mdr,r.nn,G. (1958) Zur optik des axinits von Boung d'Oisa.ns.Neu,esJahrb. Mineral. Abh.90, 28b-801.
Monsn, S. A. (1968) Revised dispersionmethod for low plagioclase.Amer. Mineral. s3,105-115.
Or,cort, G. W. (1960) Preparation and use of a gelatin mount medium for repeated oil immersion of minerals. Amer. Mineral. 45, 1099-1101.
Werrrws, J. S. (1959) Graphs for the elimination of the Hartmann Net in determination of refractive indices in high dispersion media. Amer. M'ineral.
44.314-32t.
Wncox, R. E. (1959) Use of the spindle stage for determination of principal refractive indices of refraction of crvstal frrlsments. Amer. Mineral. 44, 12731293.
Manuscript receiued,June 1,1971; acceptedtor publication, August 18,1971.