Using Snell's law to measure the refractive index of perspex

Marc Wierzbitzki 00-0815-XXX

Physics HL Experiment Portfolio

Hockerill Anglo Euopean College IB Session May 2012

Using Snell’s law to measure refractive index of Perspex Aim: In this experiment, we want to measure the refractive index of Perspex (n i) by using ( )   ( ()) )). After a value has been found, it will be compared to Snell’s law (  values which can be found on the Internet. Construction: To make the experiment easier to execute, we decided to draw our construction and our light rays on a piece of paper first to be able to read off the angles later. This can be seen here:

Execution: We will change the angle i and note down the change of angle r. Doing that it is very important that the ray of light is normal to the circle because otherwise it will be refracted once it enters the block of Perspex. This can be controlled by making sure that the ray meets the centre of the semi-circular block as shown on the lefthand side. In order to see the rays more clearly, we made the room as dark as possible. As we know that n r is approximately equal to 1, we can later find n i by calculating

() ( )

.

For each angle we will only do one reading, but after this reading has been taken, it will be checked whether the angle is still the same that has been noted down and if the ray goes through the centre of the semi-circle to ensure that there has been no refraction.

Results: i (°) ±1.500°

r (°) ±1.500°

40.00 20.00

65.00 29.00

27.00

43.00

18.00

28.00

01.50

02.50

42.50

79.00

() ±0.011 0.643 0.342 0.454 0.309 0.026 0.676

() ±0.011 0.906 0.485 0.682 0.469 0.044 0.982

ni ±0.021 1.409 1.418 1.502 1.518 1.692 1.453 1




Error analysis: Using a protractor did not give an accurate measurement of the angle. As the steps between the values on the scale was 1° and we still could make mistakes reading it off, I decided to take the error as ±1.5°. We also had some other errors, which I will discuss later on.

2




ni 1.2

1

0.8

) r ( n i s

0.6

0.4

0.2

0 0

0.1

y = 1.3631x + 0.0346

0.2

0.3

0.4

0.5

sin(i) y = 1.421x + 0.0144

0.6

0.7

0.8

y = 1.5287x - 0.0236

3




The above graph gives a mean value for n i=1.421. The minimum gradient is n i=1.363, whereas the maximum gradient is n i=1.529. This can be used to find the error in the mean, which will then be n i=1.421 ±0.108.

The graph above (Source1) shows the acrylic glass methyl methacrylate, also knows as Perspex.2 It can be seen that the refractive index found out in this experiment, n i=1.421 ±0.108, is not directly on the possible set of values, but considering the error, it is still within the range. The maximum gradient as shown on the graph is n i=1.529. From this, we can conclude that we did not find a very accurate result for the refractive index of Perspex. Nevertheless, the value that we found is still within the range of errors.

Possible ways to improve the experiment As I’ve said before, there are some things that influenced the accuracy of the experiment . First of all, something that can always be done is to try and take as many values as possible. We only did the experiment with 6 different angles. For the next time, we should include many more, maybe about 25 angles over a wide range from 0-45° (note that there is no angle bigger than 45° possible since the ray would then be reflected). Looking at the results and especially the graph, if the last data point – which was also used to calculate the minimum and maximum gradient – was wrong, all values would change. But as we were only able to plot six data points, it is not possible to say which values (if any) are significantly inaccurate and do not fit the overall picture. When redoing the experiment with the suggested 25 data points, this statement can be made and the mean, maximum and minimum values can be adjusted.

http://refractiveindex.info/?group=PLASTICS&material=PMMA , accessed September 11, 2011, 10:31 GMT 2 http://en.wikipedia.org/wiki/Poly(methyl_methacrylate http://en.wikipedia.org/wiki/Poly(methyl_methacrylate)) , accessed September 27, 2011, 18:57 GMT 1

4




Another mistake that we made was to take a very small angle. We tried to make i 1.5° and then r turned out to be 2.5°. But the angles were much too small to measure on our piece of paper. In addition to that we have to make sure that the incident ray of light hits the centre of the body because otherwise it will be refracted when it enters the block. This can be done by clearly marking the centre, which we tried to do, but it has to be clearly marked on the block of Perspex, and the person doing the experiment should check this every time after the angle has been changed. In addition to this, we also assumed that n r is approximately equal to 1, which is not accurate enough. Furthermore, we should try to get a narrower light light beam (by letting the ray pass through a very narrow slit first) as with some angles, the white light split into the rainbow colours and we could only estimate the middle of the ray to be able to find the angle. That looked similar to this: And lastly, it would be a good idea i dea to find a way to measure the angles more accurately. This could be done by utilizing a bigger protractor with smaller steps between the angles so that the error can be reduced from ±1.5° to maybe about ±0.5°. Conclusion We found the value of refractive index of Perspex (1.421 ±0.108) by taking Snell’s law into practice and afterwards found out that the mean value is not very accurate, but after including the error that has been calculated, we saw that the value is still within the possible range. Considering the suggestions stated above, the result could be improved and the error reduced in order o rder to draw an even better conclusion about this experiment.

5

Using Snell's law to measure the refractive index of perspex

Recommend Documents