One most commonly thinks of refraction occurring when light strikes at an angle to an interface separating two regions with different refractive indices. However, a light ray traveling normal to such an interface will also be refracted, if the second region has a refractive index gradient parallel to the interface plane. If liquid–liquid interdiffusion produces such a gradient in the second region, then one can infer the diffusivity of solute particles by measuring the time-dependent refraction. We have performed such diffusion experiments with three different aqueous solutions and found reasonably good agreement with diffusivity values given in the literature. The experimental setup and data analysis are simple enough for an undergraduate student to complete in a few weeks, making this investigation ideal for inclusion in an advanced laboratory course.

1.
A. J.
Barnard
and
B.
Ahlborn
, “
Measurement of refractive index gradients by deflection of a laser beam
,”
Am. J. Phys.
43
(
7
),
573
574
(
1975
).
2.
F. A.
Bassi
,
G.
Arcovito
, and
G.
D’Abramo
, “
An improved optical method of obtaining the mutual diffusion coefficient from the refractive index gradient profile
,”
J. Phys. E
10
,
249
253
(
1977
).
3.
AIP Handbook, coordinating editor D. W. Gray (McGraw–Hill, New York, 1972), 3rd ed., pp. 2–221.
4.
W. Hauf and U. Brigull, “Optical Methods in Heat Transfer,” in Advances in Heat Transfer, edited by J. P. Hartnett and T. F. Irvine, Jr. (Academic, New York, 1970), Vol. 6, pp. 136–150.
5.
W. I.
Goldburg
, “
Dynamic light scattering
,”
Am. J. Phys.
67
(
12
),
1152
1169
(
1999
).
6.
R. T.
Schumacher
, “
Brownian motion of light scattering revisited
,”
Am. J. Phys.
54
(
2
),
137
141
(
1986
).
7.
C.
Booth
, “
Diffusion of salt in tap water
,”
Am. J. Phys.
46
(
5
),
525
527
(
1978
).
8.
H.
Fenichel
,
H.
Frankena
, and
F.
Groen
, “
Experiment on diffusion of liquids using holographic interferometry
,”
Am. J. Phys.
52
(
8
),
735
738
(
1984
).
9.
J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1975), pp. 11–27.
10.
See Ref. 9.
11.
See Ref. 9.
12.
R. K. Hobbie, Intermediate Physics for Medicine and Biology (AIP Press, New York, 1997), p. 89.
13.
H. J. V. Tyrrell and K. R. Harris, Diffusion in Liquids (Cambridge U.P., London, 1984), pp. 322–339.
14.
A. C.
English
and
M.
Dole
, “
Diffusion of Sucrose in Supersaturated Solutions
,”
J. Am. Chem. Soc.
72
,
3261
3267
(
1950
).
15.
Y.
Nishijima
and
G.
Oster
, “
Diffusion of Glycerol-Water Mixture
,”
Bull. Chem. Soc. Jpn.
33
,
1649
1651
(
1960
).
16.
J.
Gillis
and
O.
Kedem
, “
Free Diffusion with Coefficient Dependent on Concentration
,”
J. Polym. Sci.
11
,
545
557
(
1953
).
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