A NEW EQUATION RELATING INDEX OF REFRACTION
AND SPECIFIC GRAVITY*
Survey,Claremont,Cal'if.
Roennr D. Arr-nn, Ll. S. Geol,ogical,
ABSTRACT
A new equation relating index of refraction and specific gravity is proposed: aBy/d:k'
The terms a|l and fr are referred to as refractive capacity and specific refractive capacity,
respectively. The new equation is compared with 3 classical equations by means of 12
groups of polymorphous compounds. Specific refractive capacities are in closer agreement
Ior AlzOa, SiOz, CaCOa, AlrSiO5, and NaAISiOT than are the classical constants. AII equations yield satisfactory agreement between modifications of MgSiO3, CaSiOr, ZnS, and
NarSOr. Specific refractive capacities for the respective polymorphs of TiOz, As2O3' and
SbsOa show gross discrepancies, considerably greater than those found with the older
equations. Such discrepancies demonstrate that refraction of light is a constitutive as weli
as an additive property and are thought to result from variations in manner of aggregation.
Specific refractive capacities for the common oxides are tabulated. Average index of
refraction is calculated for 26 compositions by means oI (l)ah /d: k ail (2) (n- I) /tI: k;
in the majority of these examples, the former expression yields indices closer to those experimentally measured.
INrnooucuoN
During the past century, three principai equations relating index of
reJraction to specific gravity have been proposed. The existing formulas
(Larsenand Berman, 1934)are listed in Table 1. The Lorentz and Lorenz
Tasln
1. EQunrroNs Ror-errnc Imlnx
Author(s)
Gladstone and Dale
Lorentz and Lorenz
Lichtenecker
ol Rnlrucrron
Equation
n-l
alll
Spncu'rc Gruvrrv
Designation of Constant
Specific refractivitY
d
nz-l
7
n'12
d
Specific refraction
Iog n
d
equation is based on the eiectromagnetic theory of light, whereas the
others are of empirical origin.
Although numerous articles dealing with relationships among chemical
* Publication authorized by the Director, U. S. Geoiogical Survey.
24s
ROBERT D. ALLEN
composition, index of refraction, and density in glass have recently
appeared, at present only approximate generalized formulas for wide
ranges and accurate expressionsfor limited ranges of composition are
possible(Sun, Safiord, and Silverman, 1940).
The postulate upon which these relationships are based may be stated
as follows: for a definite chemical composition there exists a constant fr,
which may be calculated from the index of refraction and density of any
one of the composition's physical modifications (solid, liquid, gas;
polymorphs). In other words, it is assumedthat refraction of light is an
additive property dependent solely on concentration and composition.
Despite the limited validity of the postulate, this type of equation is
useful for computations within restricted rangeswhere index of refraction
is an additive property. Conversely, definite discrepanciesmay supply
usefulinformation about the nature of bonding.
B.q.srslon Pnoposrn EeuarroN
The concept of the indicatrix has been fundamental in redefining refractivity, the capacity of a substance to refract light. The indicatrix
(Fletcher, 1892), a geometrical abstraction utilized in optical mineralogy
to depict the behavior of light in crystals, may be defined as a threedimensional geometric figure so constructed that the three principal
indices of refraction of light waves in their directions of vibration are
equal to its three mutually perpendicular semiaxes.Thus, in isotropic
substances,which have but one index of refraction, the indicatrix is a
sphere. In uniaxial crystals, which have two indices of refraction, the
indicatrix is either a prolate or oblate spheroid of revolution depending
on whether the substanceis optically positive or negative, respectively.
For biaxial crystals, with three indices, the indicatrix takes the general
form of a triaxial ellipsoid. fn essence,then, the indicatrix is a vectorial
representation of the refraction of light in three dimensions.
The refractivity of a substance is here considered to be proportional
to the volume of its indicatrix. The formulas expressingvolume for the
three classesof optical indicatrix are as follows:
Sphere
Spheroid of revolution
friaxial ellipsoid
4f3rn3
4f3roze
4/3ra!t
In the general case,therefore, refractivity is proportional to the product
aBy. The product of the three indices of refraction of a substance-aBy
for biaxial crystals, a2eIor uniaxial crystals, andns ior isotropic substances
-may be defined as refractive capacity. A new synthetic constant, ft,
may be obtained from the formula aBy/d: i, where d is the specificgravity. This value ft may be termed the specificrefractive capacity.
INDEX OF REFRACTION AND SPECIFIC GRAVITY
247
T,tsur.ertoN oF CoNSTANTsol SolrB ColruoN
Puvsrcel 1VIorrlrcarroNs
The four equations are compared by computation of their respective
constants for 12 groups of polymorphous or dimorphous compounds.
Data for water-ice and for the isomers of chlorotoluene are also given.
Tridymite is omitted from the table because of uncertainty in optical
data. For uniaxial and biaxial crystals the mean index of refraction, n,
equals {a'e ot {"Al; this quantity must be determined for solution of
the classicalequations. Specific gravities are calculated (Schlecht, 1944)
for crystal modif.cations of SiOz and CaCOs as well as for compounds
which show gross lack of agreement between values of ft when experimental specific gravities are employed. Sourcesof experimental data are
indicated by numbers in parentheseswhich refer to the bibliography.
It should be pointed out that impurities in minerals may afiect the
calculations in some cases.For instance, minor amounts of iron, titanium,
or chromium may be present in corundum. Columbium, tantalum, and
iron have been reported in rutile; iron is usually present in anatase and
brookite. It is considered likely, however, that the optical and specific
gravity data cited would be essentially correct for the corresponding
ideally pure compounds.
Dlscussrow
Specific refractive capacities are in closer agreement than are the constants calculated by means of the classical equations for polymorphs of
the following compositions: Al2O3,SiOz, CaCOa,AlzSiOr, and NaAlSiOa.
Each of thesegroups is characterizedby appreciable differencesin specific
gravity and indices of refraction. In contrast, for those groups of substanceswhose polymorphs do not have widely different physical properties, such as, MgSiO3, CaSiO3,ZnS, and Na2SO4,all four equations yield
comparable results.
The specific refractive capacities for TiOz, AsrOa, SbzOr, and H2O
show gross discrepanciesbetween the respective modifications of each
composition. The differencesare considerably greater than those arrived
at through use of the older formulas. The immediate explanation lies in
the mathematical nature of the various equations. In a series of polymorphous compounds whose indices of relraction are dependent upon
variables other than chemical composition and specific gravity, the ratio
ofu/d would be subject to greater variations than the corresponding ratios of the previously introduced equations.
It is clear that index of refraction is a constitutive property as well as
an additive property, that is, the manner of aggregation of chemical
elements is a determining factor besidesthe kinds and concentrations of
ROBERI' D, ALLEN
248
Tltrl-a 2, ConsraNrs or SoMECouuoN Prvsrc,l;- MoorrtcArtoNs
Formula
Physical
modification;
crystal system
a, 1 768
e, 1 76O
"Third phase";
isometric
3.47
1. 6 9 6
I
JJJ
0 104
log n
d
0.0620
0.0661
o 0712
0.0711
0.206
0.205
0.0738
0 073s
o,2 612
e, 2.899
0 403
0.400
0.160
0.15s
0 102
0.101
414
4.12
(calc )
e,2 583
E, 2.584
'y,2 7OO
0 392
0 394
0 160
0 161
0.101
0 102
390
444
(calc )
a, 2.561
c, 2.488
0 394
0 380
0.165
0 159
0.104
0.100
387
3.88
(calc )
1. 7 5 5
0 195
0 195
0. 106
0.106
0.0631
0.0630
0.198
0.196
0.0960
0.0950
0.0581
0.0575
a,218
p,2 3s
.y,235
0 224
0 1017
0.0625
Rutile;
tetragonal
4.23
426
(calc.)
Brookite;
orthorhombic
Senarmontite;
pseudoisometric
€,
0 192
!
d,
0.123
0 123
2.33
2.342
(calc.)
Claudetite;
monoclinic
a, 1.544
,r2+2
0.209
0 208
Low cristobalite;
tetragonal
AsrO,
(6)
1 486
(mean,
4.26
(calc )
p, 1.92
a,2 0l
5.50
5.56
(calc )
2 087
o 225
o 219
Valentini te
5.76
(exp and
calc.)
Calcite;
hexagonal
2 710
2.743
(calc.)
o, I 6585
e, 1 4865
0 22r
0 218
0 126
0 125
0 0752
0 0743
2.95
2.944
(calc )
c, I 530
p, r.681
7, 1 685
o 21+
0 214
O 12r
0.121
0.0721
0.0720
2.645
(calc )
o, 1 550
e, 1 645
0.220
0 126
0.0752
a, 1.650
B, 1.6s3
.y, 1 658
0.206
Vateri te;
hexagonal
MgSiOr
(1 1 )
2.66
2.664
(calc.)
d-l.
Indices of
refraction
398
(calc )
Low quartz;
( 5 , 1 2 , 1 3 ) hexagonal
(7)
gravlty
Corundum;
hexagonal
(synthetic)
sio,
CaCOs
Specific
Enstatite;
orthorhombic
INDEX OF REF'RACTION AND SPECIFIC GRAVITY
249
Tanrn 2 (eontinued.)
Formula
CaSiO,
(10
Al,sios
(U
Physical
modification;
crystal system
Specific
gravity
CICoH.CHT
(3)
log n
d
a, 1.651
8, 1.6s4
t, 1.660
0 205
0.115
0.0686
Wollastonite;
monoclinic
2.915
4,1.O1O
0.215
0.121
0 0724
1.47
B, 1.629
t,1.631
Pseudowollastonite;
monoclinic
a, 1.61O
p, r.610
1.654
",
0 215
0.122
0.0725
Kyanite;
tri clinic
a, 1 712
8, 1.72O
1,1 728
0 200
0.110
0 0654
Sillinanite;
orthorhombic
a, 1.659
8,1.660
r,1.680
0 206
a, 1.634
p, 1.639
t, 1,.643
o.203
a,1.509
p, | 514
1,1 514
o 204
a, t -537
e, 1 533
0.205
2.369
0 343
@,2356
e, 2.378
0.343
2.619
Sphalerite;
isometric
Wurtzite;
hexagonal
H,O
(3, 6)
1
"'_1 .
n2+2 d
319
Nephelite;
hexagonal
Na,SOo
(7, I 1)
refraction
Clinoenstatite;
monoclinic
NaAlSiO,
(11)
ZnS
(6)
Indices of
Thenardite;
orthorhombic
2.664
NarSO+-III;
orthorhombic
2 696
Ice; hexagonal
0 917
o 921
(calc )
Water
a, 1.471
p, 1.477
a, 1.484
0.0687
0 120
0 0716
332
0. 0938
0 106
3.32
0 0636
0.0634
1.4825
(mean)
o, I .309
e, 1.310
0 337
0.336
0 209
0.208
o.128
o.127
1. 0 0
1. 3 3 5
0.335
0 207
0.125
2.38
O-Chlorotoluene
1 0817
1. 5 2 3 8
0 484
0 283
0.169
3.27
M-Chlorotoluene
1.0722
1 5214
0.486
0 284
0.170
3.28
P-Chlorotoluene
1.0697
1.5199
0.486
0.284
0 170
3.28
250
ROBERT D. ALLEN
elements. No formula, therefore, which involves only index of refraction
and density as variables can be expected to produce a constant for all
phasesand polymorphs of a given chemical composition.
The gross differences in specific refractive capacities of TiOr, AszOs,
and SbzOsmay be a reflection of variation in bond type from one polymorph to another. Pauling (1948) has pointed out differencesin bonding
between the respectivepolymorphs of AszOrand SbzOs.Arsenolite (AsrOr,
isometric) and senarmontite (Sb2O3,pseudo-isometric), whose specific
refractive capacities are relatively low, consist of small moleculesof the
type AaXo.On the other hand, claudetite (AszOa,monoclinic) and valentinite (Sb2OB,
orthorhombic), whose specific refractive capacities are relatively high, have infi.nite molecules. A somewhat parallel situation is
presented by water with discrete molecules (specific refractive capacity
:2.38) and ice with infinite molecules (specific refractive capacity
:2.44).It
may be noted that anomalous values of molar refraction*
(Glasstone, 1946,p.528) have been useful in the determination of bond
type in organic compounds. Variations in bond mechanism could account for anomalous values of fr encountered in the modifications of
TiOz.
It might also be significant that Ti, As, and Sb are all elementscapable
of existing in more than one state of positive valence.
Spncrrrc RernacrrvB CapacrrrBs oF TrrE OxrpBs
Specific refractive capacities of the oxides have been calculated (1)
from the oxides themselvesor (2) from compounds containing the oxides.
The specificrefractive capacity, ft, of a compound of the type mAX 'nBX,
where m is the weight percentage of AX and n is the weight percentage
of BX, is given by the equation
mktx t
nkax
100
: Ktx.nx.
If Ktx.ex and either ktx or ksx are known, the equation may be solved
for the unknown ft value. Many of the specificrefractive capacities tabuIated below have been calculated in this manner. Of course, this computation presupposesadditivity of fr values.
Referencesin Table 3 are indicated in parentheses.
CercularroN or AvERAGEINDEX or RBlnecuoN loR MrNonars,
Anrrlrcral ColrpouNos, ano Glassns
Average index of refraction may be calculated for a compound whose
specific refractive capacity and specific gravity are known. (Conversely,
* Molar refraction is defined as (nz-l)
/(n2*2)
'M
/il,where M is the molecular weight.
INDEX OF REFRACTION AND SPECIFIC GRAVITY
251
density may be calculated if average index of refraction and specific
refractive capacity are known.) Specificrefractive capacity is given by the
earlier described equation
mktx I
--100--
nkax
: rrAX'BX'
Calculated average indices of refraction for minerals, artificial compounds, and glasses,obtained from (1)aB7/d:k and (2)("-l)/d:k,
are tabulated in Table 4. Experimental indices and data used in the calcuIations are included. Values of & for the Gladstoneand Dale equation were
taken from Larsen and Berman (1934). Chemical analysesare recalculated to 100 per cent. As before, referencesare indicated in parentheses.
In 15 of 26 compositions the average indices calculated by means of
the new equation are substantially nearer to the experimental values than
are those obtained from the Gladstone and Dale equation. In nine
compositions the two equations yield calculated indices which differ
from the experimental by similar increments. In two compositions indices calculated by the Gladstone and Dale equation are significantly
nearer to the experimental. It must be pointed out that certain oxides,
such as HzO, COz, Fe2O3,TiOz, are not characterizedby constant specific
refractive capacities for all compounds (see Table 3), and calculations
involving these oxides should be carried out with caution.
Suulranv
A new equation relating index of refraction and specific gravity is
proposed: aBy/d:ft. The term aBy is referred to as refractive capacity
and is proportional to the volume of the indicatrix; ft is designated as
specific refractive capacity.
The new equation is compared with three earlier equations by computation of their respective constants tor 12 groups of polymorphous compounds. Specific refractive capacities for the respective polymorphs of
AIrOs, SiOz, CaCO3, AlzSiOs, and NaAISiOa are in closer agreement
than the classical constants; each of these groups is characterized by
appreciable difierences in specific gravity and indices of refraction. In
contrast, every equation yields satisfactory agreementbetween modifications of MgSiOs, CaSiO3,ZnS, and Na2SO4;each of these groups is characterized by small difierencesin specificgravity and indices of refraction.
The specificrefractive capacitiesfor TiO2, AszOs,SbzOa,and HzO show
Iarge discrepancies,greater than the constants calculated from the older
formulas, between the respective modifications of each composition.
These anomalies are attributed to variations in the manner of aggregation of atoms.
Specific refractive capacities for the common oxides are tabulated.
ROBERT D. ALLEN
Tesrn 3. Spncrlrc Rnln.lcrrvB C.lpacrrrns or rrm CouuoN OxTDES
Oxide
Specific refractive
capacity
Source of data
Agro
1.O7
AgNOr
(11)
Al203
138
Alzor
(11)
AszO:
1.40
|.74
Arsenolite
Claudetite
(6)
(6)'
BzOa
1.60
1. 6 5
1.70
CaBzOa
MgaBzOs
B2O3glass
(11)
(11)
(3)
BaO
0.909
Celsian
BeO
t.7r
Beo
BizOr
0.820
Bi2o3
(3)
COr
1. 3 1
1.40
Calcite-aragonite
Dolomite
(7)
(7)
CaO
1. 6 3
Anorthite
(5)
CrOr
2.36
KzCrOr
(11)
Cr:Oa
2.09
3. 0 1
FeCrzOr
CrsOa
G2)
(11)
CsrO
0.834
CszSOr
(11)
CuzO
J.JI
CusO
(11)
CuO
t.7s
CuSO+
(11)
FeO
r.42
1.54
FeAbOr
Fayalite
(2)
(5)
FezOe
2.49
5.80
Andradite
Hematite
(5)
(6)
HrO
2.2s
2.38
2.M
Gypsum
Water
Ice
(7)
(3)
(6)
Heo
t.41
Heo
(3)
(5)
(11)
INDEX OF REFRACTION AND SPECIFIC GRAVITV
253
Trw-n 3-(continued.)
Oxide
Specific refractive
capacity
Source of data
(s)
KrO
I.JJ
Orthoclase
Ltzo
2.20
Liro
(11)
Mgo
146
Mgo
( 11 )
MnO
r.44
Tephroite
NrOu
1.60
BaNzOo
NurO
1.28
AIbite
PzOs
1.03
1.26
NarPgOz
KHzPOT
(3)
(11)
Pbo
1.08
Pb(NOt,
(3)
Rbro
0.885
RbzSOr
( 11 )
SOa
r.t4
Anhydrite
(7)
SbzOa
1. 6 5
209
Senarmontite
Valentinite
(6)
(6)
SiOz
139
Quartz
(s)
SnOz
1.20
Cassiterite
(3)
SrO
1.04
1.11
Celestite
SrAlzSizOe
(7)
(11)
ThOz
1.03
ThOz
(3)
TiOz
4.18
4.35
4.68
Anatase
Brookite
Rutile
(6)
(6)
(6)
WOe
r .u.')
CaWOr
( 11 )
ZnO
1.16
r.45
ZnAlzOn
Zincite
(11)
(6)
l.
Zircon
ZrOz
/J
(s)
( 11 )
(s)
(s)
ROBERT D. ALLEN
254
Teslr 4. C.lrcurerno Avenncn Iworcns or Rrrnectrow ron Mnvrnals,
Axrrlrcter Coueoumos,eNl Gr-assns
E values employed
Substance
Composition
oh
/d
(n-1)
I
Specific
gavity
/d
A""rug" itd"* oI refraction
Calculated
otu/d
Tridymite
(n-r)/d'
t.473
1.476
2.144
2.146
(s)
Baddeleyite
0.201
5.71
0.200
0.193
0.1950
360
(s)
Spinel
(s)
MgO'Al,Or
28.3470
MsO
71.6670
Alzor
Ks
3A1,Or'2SiOr
71.8070
Al'Or
28 2o7o
sio,
Ky
Grossularite
(s)
Anorthite
(s)
MnO'SiO'
MnO
54.1570
45.8sTo
sio,
Ka
1.44
1.39
L 4t7
0.191
0.207
0.1983
3MgO' Al'Or' 3SiOr
30.017a
MgO
25.29Ta
AlrOr
44.7070
sio"
Kp
1.46
1. 3 8
|.39
1.409
0.200
0.193
0.207
0.2013
t.70+
r.707
3CaO' AlzOa'3SiOr
37.3570
CaO
22.64170
Al,Or
4O.OlTo
SiOz
Ke
1.63
1. 3 8
t.39
1.477
0.225
0.193
0.207
0.2106
1.73L
1.743
1.63
1.38
r.39
1.435
0.225
0 2r4
0.207
0.2065
2.765
1.54
0.909
1.39
1.255
0.187
0.127
0.207
0.1776
3.33
43 6470
56.3670
0 181
o.t77
0 -1 7 8 8
2.69
27.r87o
0.310
o .t 7 7
0.2132
2.23
CaO' Al,O''
CaO
Al,or
sio,
K,T
2SiOr
20.1670
36.657a
43.re7a
Iron barium
silicate
(11)
FeO'BaO'4SiOz
FeO
I5.447o
32.957a
BaO
SiOz
51.6170
K
Thenardite
NazSOr
NazO
SOs
(s)
Kr
Li,so,
Li"o
SOr
72 827a
INDEX OF REFRACTION AND SPECIFIC GRAVITY
255
Trr;;n 4-(continuetl)
& values employed
Substance
Composition
ofu/d
(n-1)/tl
Arcanite
(7)
KISO'
K"O
SOr
K,t
54.0570
45.9570
Sodium nitrate
NaNOr
NazO
NrOr
K
36.4670
63.5470
1.28
1.60
1.483
0.181
0.240
0.2185
Cesium nitrate
( 11 )
CsNOr
CsrO
NrOc
K
72,29To
27.7170
0.834
1.60
1.046
0.t24
0.240
0.1561
Rubidium uitrate
( 11 )
RbNOr
Rb'O
NzOe
63.3870
36.627a
0.885
1.60
1.147
0.129
0.240
0.1697
SiOr
B,Or
NarO
AlzOr
12To
12To
llTo
5To
L.39
1.70
t.28
1.38
1.415
0.207
0.220
0.181
0.193
0.2050
Ordinary crown
glass, Wright's
no.1
(11)
SiOr
AsrOr
MnuOr
CaO
KrO
NazO
K
74.670
o.37o
O.l7o
5.o7o
l1.oYa
9.OT
1.39
1.57
1.44
L.63
1.33
r.28
1.386
0.207
0.214
0.300
0.225
0.189
0.181
0.2040
Sodium potassium
calcium glass
(11)
SiOr
61.O27a
Na,O
6.3rTa
K,o
9.s97a
CaO
22.787a
AtOr
O.3OYa
(plus FerOr)
1.39
t.28
1.33
1.63
1.38
0.207
0.181
0.189
0.225
0.193
A
Borosilicate crown
glass, Wright's
no. 12
( 11 )
^
siot
BOr
Al,ot
AsrOr
BaO
K
31.O7o
12.0To
8.0%
l.O7o
48.070
MnO' SiOr glass
( 11 )
MnO
SiOr
K
54.1570
45.8570
Expaimental
1.495
0.2077
Barium crown
glass, Wright's
no. 45
( 11 )
Average index of refraction
Specific
gravity
1.39
r.70
1.38
1,57
0.91
1.198
0.207
0.220
0.193
0.214
0.127
0. 1691
0 .1 9 1
0.207
0 .1 9 8 3
Calculated
dtu /d. (n-t) /d
1.497
1.499
1.510
256
ROBERT D, ALLEN
Ttrl-a 4-(conti.nued)
& values employed
Substance
Composition
otu /d
(n-1) /d
Average
Specific
gravi ty
sio,
Pbo
K,O
Na'O
AsgOr
K
59.3To
27.570
8.07o
5.O7o
o.2To
1.39
1.08
1.33
1 28
1.57
| 295
0.207
0.137
0.189
0.181
0.214
0.1850
Beryllium glass,
Lai and Silverman's no. Br
(11)
sio,
Na,O
BeO
R
73.4070
18-9670
7.6470
t39
1.28
t.71
1.393
0207
0.181
0 238
0.2044
245
Gahnite Analysis
FeO
MnO
ZnO
Al,o,
FerOr
SiOr
Ke
1. 7 1 7 a
0 SOVo
41.317a
53 28%o
2.51Ta
O.69Ta
1.42
1.44
1.16
138
2.49
1 39
1 318
0.187
0.191
0 153
0193
0.308
0.207
0.1793
4.57
Ferroan gahnite
analysis no. 14
(6)
MgO
FeO
MnO
ZnO
AlrOr
CrrOr
Ke
2-3870
8.52To
O.10Ta
31 3270
57.597a
O.O97o
l.+6
1.42
1.44
r.t6
1. 3 8
2.09
r.317
0.200
0.187
0.191
0.1s3
0.193
0.270
0 1802
438
Augite analysis
no.13
(4)
SiOr
AlzOa
Fe:Os
FeO
MgO
CaO
Na'O
K,O
H,O(+)
Tioz
MnO
Rt
s0.glVa
2.68Yo
1 867a
IO OSVI
l2.397o
20 5570
0 4770
0.0270
o 1e7o
o.4o7o
O 4870
1.39
1.38
2.49
1.42
1 46
1.63
1 28
1 33
225
4.18
1.44
1.483
0.207
0.193
0 308
0 187
0.200
0.225
0.181
1.189
0340
0.397
0 191
0.2100
3.394
Hedenbergite
amlysis no. 18
(4)
siol
AlrOr
FerOr
FeO
MgO
CaO
Na,O
KrO
H,O(+)
Tio,
MnO
48.4270
0 30Va
l.sl/a
22.977a
l.O6Va
21.33Ta
o.147a
0.03Va
0.467a
o.o8To
3.7170
1 39
1 38
2.49
1.42
1.46
t.63
1.28
1.33
2.25
4.18
1. 4 4
1.473
0207
0. 193
0.308
0.187
0.200
0.225
0.181
0 189
0.340
0.397
0.191
0.2078
3.535
Wright's no. 53
(11)
Ks
Experinental
1.5193
L.734
index of refraction
Calculated
afu/d
INDEX OF REFRACTIONAND SPECIFICGRAVITY
257
The constants are calculated (1) from the oxides themselvesor (2) from
compounds containing the oxides.
Indices of refraction are calculated for 26 compositions (minerals'
artificial compounds,and glasses)by means of (l) aBy/d:h and (2)(n
-l)/d:ft.
In the majority of these examples, the former expression
yields indices closer to those experimentally obtained.
In some respectsthe new equation is more convenient than the others.
It is not necessaryto compute an average index of refraction when an
anisotropic substanceis involved. Furthermore, if two indices are known,
the third can be calculated readily, provided that k and d ate known.
AcrNowr-BoGMENTS
Criticisms and suggestionsby H. W. Jafie, of the U. S. Geological
Survey, enabled the writer to expand and improve the preliminary manuscript. Contributions were also made by F. M. Byers, G. J. Neuerburg,
and G. I. Smith, all of the Survey. Assistance was rendered by George
Tunell, of the University of California at Los Angeles.
RelcreNcns
1. Fr.rrcnnn,L.(1892),TheOpticalIndicatrixandtheTransmissionofLightinCrystals,
London.
2. Gr.essrown, S. (1946), Textbook of Physical Chemistry, 2d ed., p. 528-534' D. Van
Nostrand Co., New York.
3. Handbook of Chemistry and Physics (1951), 33d ed., Chemical Rubber Publishing Co.,
Cleveland.
4. Hrss, H. H. (1949), Chemical composition and optical properties of common ciinopyroxenes, P art I : A rn. M iner a1,.,34, 621-666.
5. Lntser, E. S., euo Brnuax, H. (1934), The microscopic determination of ihe nonopaque minerals: [/. S. Geol.Suraey, Bu]L848.
6. Par.ecnr, C., Bonuan, H., aNo Fnoltonr., C. (1944), Dana's System of Mineralogy,
7th ed., v. 1, John Wiley & Sons, New York.
7. Palacnr:, C., Bonuax, H., eNn FnoNnnr-, C. (1951), Dana's System of Mineralogy,
7th ed., v. 2, John Wiley & Sons,New York.
8. Peur,rxc, L. (1948), The Nature of the Chemical Bond, 2d ed', pp. 247-250, CorneII
Univ. Press, Ithaca.
9. Scnr,ncrrr, W. G. (1944), Calculation of density from r-ray data,: Am. Mineral.,29,
108-110.
10. Sur, K.-H., Sarrono, H. W., alto Srr.vrnu,lN, A. (1940), Review of the relation of
density and refractive index to the composition of glass, II: Am. Ceramic Soc. Jour.,
23,343-354.
11. WrxcHor.r,,A. N. (1931),MicroscopicCharactersof Artificial Minerals, 2d ed., John
Wiley & Sons,New York.
12. WrNcnnr.r,,A. N. (1951), Elements of Optical Mineralogy, Part II. Descriptionsof
Minerals,4thed.,JohnWiley & Sons,New York.
13. Wvcrolr', R. W. G. (1948),Crystal Structures,Sec I, IntersciencePublishers,New
York.
Manuscript receiteilMarch 25, 1955.