Many fluids appear white because refractive index differences lead to multiple scattering. In this paper, we use safe, low-cost commercial index matching fluids to quantitatively study light transmission as a function of index mismatch, reduce multiple scattering to allow single scattering probes, and to precisely determine the index of refraction of suspended material. The transmission profile is compared with Rayleigh-Gans and Mie theory predictions. The procedure is accessible as a student laboratory project, while providing advantages over other standard methods of measuring the refractive index of an unknown nanoparticle, making it valuable to researchers.

1.
See, for example,
B. J.
Berne
and
R.
Pecora
,
Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics
(
Dover
,
Mineola, NY
,
2000
).
2.
C.
Houessou
,
P.
Guenoun
,
R.
Gastaud
,
F.
Perrot
, and
D.
Beysens
, “
Critical behavior of the binary fluids cyclohexane-methanol, deuterated cyclohexane-methanol and of their isodensity mixture: Application to microgravity simulations and wetting phenomena
,”
Phys. Rev. A
32
(
3
),
1818
1833
(
1985
).
3.
J. P.
McClymer
, “
The kinetics of crystallization of colloids and proteins: A light scattering study
,” in Research Reports-2001NASA/ASEE Summer Faculty Fellowship Program, edited by
G.
Karr
,
J.
Pruit
,
S.
Nash-Stevenson
,
L. M.
Freeman
, and
C. L.
Karr
, NASA/CR-2002-211840,
2001
, p.
XXXII
.
4.
Refractive index liquids from Cargille Labs, < http://www.cargille.com/>.
5.
See http://www.cargille.com/msds.shtml for material safety data sheets.
6.
S.
Wiederseiner
,
N.
Andreini
,
G.
Epely-Chauvin
, and
C.
Ancey
, “
Refractive-index and density matching in concentrated particle suspensions: A review
,”
Exp. Fluids
50
(
5
),
1183
1206
(
2011
).
7.
Series A optical liquids from Cargille Labs, <http://www.cargille.com/>.
8.
For example, Bangs Labs (http://www.bangslabs.com/) or microspheres-nanospheres (http://www.microspheres-nanospheres.com/). The polystyrene spheres appear to be the most economical.
9.

PMMA particles provided by Andrew Schofield, School of Physics and Astronomy, University of Edinburgh.

10.
Microparticles typically are assumed to have a Gaussian size distribution with some finite width. Polydispersity index is a relative measure of width of the Gaussian divided by its mean as determined by dynamic light scattering. Specifically, the width of the distribution is given by the second moment of a cumulant analysis. See, for example, Ref. 1, pp.
195
196
.
11.
Cauchy equation is an empirical equation for determining the index of refraction. See optical texts including as
F. A.
Jenkins
and
H. E.
White
,
Fundamentals of Optics
, 4th ed. (
McGraw-Hill
,
New York
, NY,
1981
).
12.

Micropipettes may not be common in many physics laboratories. They can be purchased at most chemical supply companies as well from Amazon.com. Users new to using a micropipette should be trained as accurate volume transfer is critical to the success of this method.

13.
See Reference 6, for example.
14.
D. F. J.
Arago
and
J. B.
Biot
,
Mem. Acad. Fr.
7
9
(
1806
).
15.
J. C. R.
Reis
,
I.
Lampreia
,
A. F.
Santos
,
M. L. C.
Moita
, and
G.
Douhéret
, “
Refractive index of liquid mixtures: Theory and experiment
,”
Chem. Phys. Chem.
11
(
17
),
3722
3733
(
2010
).
16.
K.
Lichtenecker
, “
Die Dielektrizitiitskonstante naturlicher und kiinstlicher Mis-chkorper
,”
Phys. Zeit.
27
(
4/5
),
115
158
(
1926
).
17.
A. V.
Goncharenko
,
V. Z.
Lozovski
, and
E. F.
Venger
, “
Lichtenecker's equation: Applicability and limitations
,”
Opt. Commun.
174
(
1
),
19
32
(
2000
).
18.
S. S.
Kurtz
and
A. L. J.
Ward
, “
The refractivity intercept and the specific refraction equation of Newton. I. Development of the refractivity intercept and comparison with specific refraction equations
,”
Franklin Inst.
222
,
563
592
(
1936
).
19.

Curve fits were implemented in Excel using “Goal Seek” to minimize the sum of squares of the residuals. Goal Seek does not provide an estimate of uncertainty in the fitting parameters.

20.
C. F.
Bohren
and
D. R.
Huffman
,
Absorption and Scattering of Light by Small Particles
(
Wiley
,
New York, NY
,
1983
).
21.
H. C.
Van De Hulst
,
Light Scattering by Small Particles
(
Dover
,
New York, NY
,
1981
).
22.
See, for example, Ref. 15.
23.
Oregon Medical LASER Center Mie scattering calculator, <http://omlc.org/calc/mie_calc.html>.
24.

A Mie calculation algorithm could be placed inside a non-linear least squares fitting routine so as to yield the best fit refractive index of the particle and particle diameter.

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.