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Refractrometry. Aim: Using a model Pulfrich refractometer determine the refractive index of a range of sugar solutions and hence determine the refractive index of some sugar solutions with an unknown concentration.

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Physics Coursework: Refractometry


When light crosses the boundary between two materials, it changes its speed and normally its direction, this is refraction. The refractive index (  ) for a pair of materials is a ratio of the wave velocities.


The incident and refractive angles are measured from the normal (perpendicular to the object).

Aim: Using a model Pulfrich refractometer determine the refractive index of a range of sugar solutions and hence determine the refractive index of some sugar solutions with an unknown concentration.

The following equations show how we can combine different equations for refractive index to come up with one that is useful for  my experiment

The refraction from liquid to glass:

The refraction index from air to glass:

And if:


And if:


Using these we can calculate the refractive index from air to liquid is:

We also know that C = 90° - r (because we will use a right-angled block) so sin C = cos r

In conclusion we can come up with a final equation for the refractive index for air to liquid is:

I will then plot the refractive index against the concentration of the sugar solution and draw a line of best fit. From the line of best fit and the refractive index of my unknown concentrations I should then be able to draw a line down from the line to determine the concentration.

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Whenever using glass wear care should be taken to minimise the chance of breakage, e.g. keep it well on the bench.


My input variable will be the concentration of the sugar solution. I will use a fairly broad and evenly spaced range of concentrations to ensure my graph is accurately drawn and leaves little space to miss important changes in correlation.

This should give me an output variable of refractive index which I will calculate using the equation I have stated previously.

There will be a few control variables that I will have to ensure are kept constant to maintain the credibility of my experiment:

  • The same Perspex block should be used so that the refractive index that I am measuring is the same throughout the experiment.
  • I will use the same equipment for the whole experiment to reduce variation in accuracy and sensitivity, for example different types of black paper may alter the accuracy of my experiment.
  • An especially important part of apparatus to keep constant is the measuring equipment (ruler and protractor), as they may have variations in the accuracy of their scale. The scale at which I am able to read the protractor will affect the sensitivity of my investigation.
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Concentration of A ~ 11.0%

Concentration of B ~ 26.5%

 Looking at my graph I could say that there were no anomalies in this set of results as I have decided to use the first and last concentration in my line of best fit, however they could be excluded as they are not quite as in line with the others.

As I could not use my results because of their inaccuracy, there must have been considerable accuracy/sensitivity problems in my experiment. I think that probably the most considerable error was human error in distinguishing with our eyes the disappearance of the black paper. If I did this experiment again I would take a range of readings with the pins; one when the black paper first starts to disappear and one when the paper has completely disappeared. I would then take a mid-point of this range as my value.

I also think that the sensitivity in my protractor was limited as I could only read it accurately to ±0.5º, and as the angles were so close it would have been better to have used a more accurate measuring tool.

In conclusion, I am disappointed that my results did not work as I controlled all independent variables etc to ensure the reliability of the experiment. This shows that the sensitivity and accuracy of this experiment is poor, however with a good set of results I feel I came to a good conclusion of concentrations

Annie Rankin        Physics Coursework        May 2006

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