9. N. N. Vostroknutov et al., Izmer. Tekh., No. 8 (1975). I0. GOST 8.051-73, "State System for Ensuring Uniform Measurements (GSI). Allowable errors

in linear measurements from 1 to 500 mm," Ii. N. V. Smirnov and L. N. Bolsheev, Tables of Two-Dimensional Normal Distribution [in Rus-

sian], AN SSSR, Moscow (1962).

EFFECT OF LIGHT SCATTERING IN A CUVETTE ON THE ERROR

OF DIFFERENTIAL REFRACTOMETERS

M. A. Karabegov, Yu. I. Komrakov, and S. A. Khurshudyan

UDC 535,322.4.088.228

Refractometers in which different versions of differential cuvettes are employed have become widely used. The measured quantity in differential refractometers -- ~he difference between the refractive indices of a comparison and the measured liquid -- is converted into a displacement of a beam of light which leads to a redistribution of the light fluxes inci- dent on position-sensitive phototransducers. The transfer coefficients of a number of posl- tion-sensitive phototransducers depend on the light flux [I], which gives rise to an addi- tional error when measuring the light flux passing through the differential cuvette [2].

Below, using the example of a double-prism cuvette, it is shown that when a beam of light passes through a differential cuvette a change in the light flux occurs due to scat- tering of the light on the walls of the cuvette (see Fig. i).

The scattering of a beam of light when passing from the liquid into the glass is much less than the scattering of the beam at the "glass--liquid" and the "glass--air" boundaries. Neglecting terms corresponding to the scattering at the "liquid--glass" boundary, the depen- dence of the exit light flux ~ on the light flux at the entrance to the cuvette ~o can be found from the transformed Fresnel equation,

q S ~ ( h n ) = @ ~ I-- T s i n ~ ( ~ , + o ) + ~ o ) t g ~ ( ? , ---~ s i n ~ ( 0 - [ - [ ~ ) + tg ~ ( 0 - [ 3 ) ' (i)

where

? - : arcsin [-- sin cc ; o -= arcsin sin c~ ; 0 = arcsin e kNg

= arc sin (NgsinO), Ng, N, and n are the refractive indices of the glass of the differen- tial cuvette, the comparison liquid, and the measured liquid, respectively; and An = n--N is the measured difference in the refractive indices.

i i " 1 I I I / 1 1 1 1 1 1 / / ' ~ ' 7 / / , / I / 1 1 1 / ~ f I//--21 IN "" "" i / / I / / i / I / I / / / / I I I / 1 1 / , . I I i 0,2/I

/ . 4 " d / ] " " I i / i i i

, , I ~ , ,, ."/, , ' ~ ~'/,I , - / / / /.I

) / I N ~'~/,"/ ' / / I , , / i ~ . ~ / / //I / / / / / / / / / / / / / / / / . , , . / / " / / / / / / / ~ / /

, , , , / , / / / / / / , , / / / , , , , / ,, / , , / / , , , / , y / / ~ z/.. i

Fig. 1

Translated from Izmeritel'naya Tekhnika, No, 5, pp, 13-14, May, 1978.

0543-1972/78/2105-@611507.50 �9 1978 Plenum Publishing Corporation 611

TABLE i. Theoretical Values of 6(An) for Anma x = 0.001

An

2.10 -4

4.10 -4

6.10 _4

8.10 _4

r ~ 0,==60 ~ 0 ,=70 ~

N=I,4 N=I,4 N=I,33 N=1,33

TK7

O, 007 0,005 O, 003

0,002

N=1,33

TF5 TK7 TF5

0 , 0 0 9 0 , 0 0 9 0 , 013

0,007 0,007 0,009 0.004 0,004 0,006 0,009 0,002 0,003

TK7 TF5

0,024 0,033 0,018 0,024 0.011 0,016 0,006 0,009

TK7 TF 5

0,032 0,039 0,024 0,029 0,016 0,019 0,007 O,0IO

N=I,4

TK7

0,11 0,082 0,055 0,027

T F 5

0,134 0,100 0,066 0,032

TK7 TF5

0,133 0,130 0,100 0,012 0,066 0,074 0,033 0.037

TABLE 2. Theoretical Values of ~ (An) for TF6 Glass for Anma x = 0.1

J 2.10 - 3 0,491 0,201 1,531 0,7101 5,113 2,743 4 10-3 0,475 0 101 j1,,73 1 0,676j 4,+7+ l , , , .6 6.10 - a 0,460 0.,+3 11,+1710,6401 4,643t 2,42= +.1o-, o,446 o,1,, 1,36+ i o,o.o7 4,4. o I

10.10 - 3 I 0,430 0,166 1,311 0,576 4,216 t 2, i32 2.10 -2 I 0,359 0,124 11,067 I 0,433/ 3,293} 1,332 4.10 - 2 0,237 0,069 10,672 I 0,~231 1,9301 0,724 6.10 _2 0,134 0,029 0,374 0,090 / 1,016 0,:.:75 B.lO - 2 0,060 0,007 o,1563 o,o21 0,40:, o,0-~6

For the majority of photoelectric differential refractometers the calibration curves of which are constructed from two points, for example, for the initial and final points of the range of measurement An = Anmax, the nominal transformation function can be represented in the form

y = kcb4 (Anmax) An, ( 2 )

where y is the exit signal of the refractometer, k is a coefficient of proportionality, @~ (Anma x) is the light flux when An = Anmax, and the relative error of the refractometer is found from the expression

Ay ~.,. (Anmax) - - qb4 (An) 5 ( A n ) = �9 100 = �9 lo0. ( 3 )

Y r (Anmax)

Calculations using Eq. (3) carried out on the Nairi computer enabled us to determine how 6 (An) depends on various parameters. We used distilled water (N = 1.33) and a liquid with N = 1.4 as the comparison liquids, and the refracting angle of the cuvette was usually limited to the values ~ = 45 ~ , 60 ~ , and 70 ~ To determine ~(An) as a function of N_ we used the following grades of optical glasses: KF6 crown-flint (Ng = i,5), TK7 hard-crown~(Ng = 1.61) and TF5 hard-flint (Ng = 1.75).

The results obtained are shown in Tables 1 and 2. We can draw the following conclusions from the data obtained: The value of 6(An) increases as ~ and N~ increase, but decrease when N increases; the highest value of 6(An) is obtained at the beginning of the scale; 6(An)in- creases as the measurement range increases; when Anma x <__ 0.001 the effect of scattering of light in the cuvette on the error of the refractometer can be neglected; the effect of scat- tering must be taken into account when Anma x > 0.01.

l.

2.

LITERATURE CITED

The Present State and Future Prospects of the Use of Optoelectronic Methods in Measure- ment Technique (Review Information), TsNllTEIPriborostroeniya, Moscow (1974). Yu. I. Komrakov and S. A. Khurshudyan, Proceedings of the All-Unlon Conference on Ana- lytical Instrument Construction. Methods and Instruments for Analyzing Liquids, Vol. i, Part i, Tbilisi (1975).

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