J.-A. Deverin
and J.-J. Salzmann Cyanamid European Research Institute Cologny, Geneva Switzerland
Determination of the Index of Refraction TWO simple methods
Two simple methods for the determination of the refractive index of solutions are presented. Both require only a microscope and a spectroscopic cell. (1) Let A' be the real image of an object (e.g., grating) seen through a microscope (Fig. 1). If one inserts a medium of index n and of thickness d between the object and the objective, the microscope has to be refocused by the amount
where A is the new image of the object. AA'can he measured directly by means of a vernier. If the medium is a spectroscopic cell filled with the solution whose refractive index is to be measured, one has
where a is the thickness of the cell wall, n, is the refractive index of the cell material, d is the thickness of the solution, n, is the refractive index of the solution. The first term to the right of eqn. (2) is a constant of the cell. If A' and A refer to the real images as observed through the empty and filled cell, respectively, this constant is eliminated. If AA' is measured with an accuracy of 0.01 mm, the error of n, is of the order of (2) The second method is based on the equating of two optical paths, one going through the cell containing the solution of unknown index, the other passing a movable prism. The optical path 11 through the cell is given by
stant of the cell. Without changing the setting of the microscope the cell is removed and replaced by a prism (Fig. 2). This prism is then moved along the direction E-D until the image is sharp again. The corresponding optical path 1, through the prism is where n, is the index of refraction of the prism, cu the prism angle, and r the finite thickness of the prism edge. The angle a has to be small (e.g., lo0), siricc otherwise the image leaves the ficld of vision of thc microscope, Finally, equating 11 and l 2 one finds from eqns. (3) and (4) :
The length can be measured by a vernier. The error of n, is again of the order of lo-'. One can improve this mcthod by using two identical prisms gliding one above the other. I n this way a plane-pamllel plate of variablc thickness 1 is obtaincd and one finds
and the first term to the right of eqn. (3) is again a con-
The advantages of these methods lie in the simplicity of the equipment involved and in the use of a spectroscopic cell which allows mcasnrements of air-sensitive solutions. Moreover, the spectroscopic cell enables one to measure the spertrum of this same solut,ion without unnecessary manipulations. This is important since the index 71, should not be determined in an absorbing region. It should be pointed out that the first method gives an index relative to the air, whereas the second gives an index relative to the vacuum, provided n, and ?a, are relative to t,he vacuum, however this difference is much smallcr than t.he error on n,. The attention should be drawn to the following points. For a colored solution appropri,Ate monochromatic light has to be uscd and one must find a compromise between the concentration and the thiclmess in order to be able to focus exactly. One should not usc an objective having a magnification greatcr than 4x, for otherwise the distance between the object and the ob-
Figure 2. Microscope with cell replaced by prism.
the solution is strongly dcpcndent on temperature, a thermostated cell can be used.
11
=
2an.
Figure 1. The real image of an object seen through a microscope.
+ d n,
(3)
Volume 46, Number
I, January 1969
/ 51
