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THE  POLARIMETER

Allan Mills


Retired from Dept. of Physics, University of Leicester, U.K.

allanmills1@hotmail.co.uk

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Abstract

Materials possessing asymmetry – either in their 3-D crystal architecture or molecular structure – rotate the plane of polarization of linearly polarized light passing through them.  The polarimeter measures the degree of rotation, and its precision was much improved by Laurent’s invention of the ‘half-wave plate’.  The instrument is still used (albeit in automated form) in the sugar industry to rapidly and specifically assess the concentration of sucrose in solutions.  A lecture demonstration apparatus is described.

Rotation is wavelength dependent, so it is usual to employ a sodium lamp as an intense source of illumination.  Attempts to repeat the so-called ‘barber’s pole’ demonstration of rotatory dispersion have not been impressive.

 

Materials that incorporate an asymmetric structure –one that is not superimposable upon its mirror image – rotate the plane of polarization of an incident beam of plane polarized light.  The asymmetric structure may be at the structural level, as in dextro or laevo-crystalline quartz, or at the molecular level.  Well known examples of the latter group are the sugars, such as glucose and sucrose.

The specific rotation  S  of an optically active substance in solution is given  in degrees per decimetre by the expression:

                    10 r

Sλt     =          ——–

                     l n

where   λ  is the wavelength of the light (commonly Na)

.             t   “    “   temperature   (commonly 20°C)

.             r  “     “    observed rotation (+ or  -)

.             l   “     “    path length  (cm)

.             n  “      “    concentration  (e.g. gm per 100 gm solution)

 

For sucrose dissolved in water, the specific rotation is +66.45°  for sodium light at 20°  C.

 

The polarimeter

Measurement of the degree of rotation induced by a given solution is carried out in a polarimeter.  Figure 1 shows a manual instrument of the type commonly used in the sugar industry in the 19th and early 20th centuries as a quick yet specific

Ca. 1890 Schmidt & Haensch polarimeter

Fig. 1  Classic Laurent-type polarimeter, such as that produced by Franz Schmidt & Haensch around 1890.

method of assessing sucrose concentration.  It was soon found to be difficult to set the analyzer exactly at the ‘crossed’ (null) position with respect to the polarizer. Laurent therefore developed a device made from optically active quartz that, when inserted between the polarizer and the cell, rotated one half of the field through several degrees (Ref. 1).  The analyzer could then be so adjusted that the intensity of the two fields matched across their boundary –  something the human eye can do with great sensitivity and precision, so that rotation could be measured to ±0.01°.

Demonstration

The phenomenon of optical rotation may readily be demonstrated in the lecture room with the projection apparatus diagrammed in Figure 2.

Fig. 2  Projection apparatus  demonstrating polarimeter principle of the polarimeter

Fig. 2   Projection apparatus to demonstrate the principle of the polarimeter, and the increase in sensitivity obtained by matching the intensity of adjacent fields.

Laurent’s half-shade refinement may be readily reproduced by two semicircles of Polaroid cut from sheet so that their polarizing axes are inclined at about 20°  to each other along a vertical diameter. Matching of the two fields may be accomplished to better than ±0.1°, but coloured fringes may be discerned at the border in the white light system. A yellow filter may be inserted.

 

Specific rotatory power

It was soon noted that specific rotations were strongly dependent on the wavelength of the light used to measure them.  This is illustrated for sucrose in Figure 3, where it may be seen that plane polarized light of short wavelength (i.e. blue)

Fig. Graph of sucrose solution rotation with wavelength

Fig. 3  Variation in specific rotation of sucrose solution with wavelength. Solution in water at 20° C.

 is more strongly rotated than that at the red end of the spectrum (Ref. 2).  For this reason, and to obtain a high intensity of nearly monochromatic radiation, it was (and still is) usual to employ a sodium lamp as the source of illumination in polarimetry.  Specific rotatory powers are therefore commonly quoted in terms of that radiation  (589 μ).

The ubiquitous (sometimes ‘built-in’) use of a sodium lamp meant that students were sometimes unaware of the variation in specific rotatory power with wavelength.  To remedy this, in the first half of the 20th century fortunate classes might be shown what came to be known as the ‘barber’s  pole’ experiment.  (This was when University Demonstrators really did set-up and demonstrate  phenomena relevant to the lecture classes!  Nowadays, merely the title of a junior academic post and a few textbooks commemorate  them.  That by Sutton (Ref. 3) is perhaps the best known.)

 

The ‘barber’s  pole’ demonstration

This consists of directing a collimated beam of white light from a high-intensity lamp upwards through a vertical column of concentrated sugar solution. A piece of Polaroid is inserted between the lamp and the lower end of the column, and a few drops of milk added to scatter some of the light sideways out of the tube.  According to Sutton (p.425) the varying rotation with wavelength will cause a separation of colours, generating a helix with the red end of the spectrum higher than the blue. He compares the effect with the medieval ‘barber’s pole’ sign, where red and white helices  symbolize the blood and bandages associated with these early surgeons.

I first tested the effect of placing 300 ml of water in a 25 inch glass tube of 1 inch nominal bore, with its lower end sealed with a thin glass plate. The light from a powerful lamp passed upwards without obstruction. The addition of 3 drops of milk then caused strong scattering of polarized light (the ‘blue sky’ effect). More milk resulted in too much attenuation of the beam along the tube.

The milky water was then replaced by strong sugar solution (300 g of sugar dissolved in 400 ml of hot water and allowed to cool) and 5 drops of milk added to promote optimal scattering.  The piece of Polaroid was replaced above the lamp.  Separation of the column of light into two faint reddish zones above two greenish areas was observed, and movement was noted when the Polaroid was rotated.  However, the result was disappointing – nothing like the traditional barber’s pole!  I would consider it unsuitable as a demonstration.  This is surprising, since Sutton claims his entries have all been tested, and most are indeed worthy of repetition.  Perhaps someone else will have greater success?

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References

  1.   Frederick Bray,  Light  (London: Edward Arnold, 1938).
  2.   R.C. Weast (edit.)  Handbook of Chemistry and Physics  (Cleveland, OH: Chemical Rubber Company, 1965).  Page E-167.
  3.   R.M. Sutton, Demonstration Experiments in Physics (New York: McGraw-Hill, 1938).