28
A.3 REFRACTOMETER DETECTOR
A.3.a Theory
The RI detector is a conventional dual cell, deflection design
Figure 8.
. Diffuse light
from the source is directed onto the mask behind the dual cell, passed through the mask, cell,
slit arrangement, and is then reflected by the adjustable concave mirror. The concave mirror
focuses and aims the beam back through the cell onto the mirrored prism. The prism splits the
beam into two component beams, each component hitting a separate photodiode detector. The
photodiodes generate an electric current proportional to the light received. These electric
currents are then subtracted from each other and the amplified difference forms the RI signal
output.
When both sides of the cell (sample and reference) contain liquid of identical refractive
indices, no deflection of the beam is observed. This would be the expected condition at
chromatographic baseline, for example. The concave mirror is then aligned so that near zero
signal is output. Now when the sample elutes into the sample side of the dual cell, the light
beam is refracted (deflected) according to Snell’s Law of Refraction:
[
]
sin
sin
=
n
n
1
-
A.3
s
r
r
s
θ
θ
where
q
is the angle of incidence with respect to the normal of the plane separating the
two
liquids,
and
r
and
s
refer to the reference and sample liquids, respectively.
The RI signal output can be shown to be proportional to the difference in refractive index of the
sample and reference liquids.
[
]
sin
-
45
sin
45
sin
)
-
sin(45
45
sin
=
n
n
2
-
A.3
r
s
θ
θ
≅
(For small angular deflections of
θ
.)
Here it is assumed that the RI cell is a 45
°
cell, which is the usual case. We then rearrange to:
[
]
θ
sin
1.414
=
n
n
-
n
3
-
A.3
s
r
s
However,
sin
d
L
and V
d = L sin .
output
θ
θ
≅
∝
Inserting and rearranging, we find
[
]
V
k
=
n
n
-
n
4
-
A.3
output
'
s
r
s
where
k
'
is an instrument constant.
In the usual application, the reference liquid is the solvent for the sample, so that we may
equally state that the signal is proportional to the sample concentration and the refractive index
increment (dn/dc) of the sample.
[
]
dc
dn
C
k
=
V
5
-
A.3
output