Wavelength vs Refractive Index

How does the Wavelength affect the Refractive Index? The aim of this experiment is to investigate the relationship between the refractive index and the wavelength. We will be testing 5 different wavelengths: 630nm (red), 570nm (yellow), 532nm (green), 445nm (blue) and 405nm (violet). Figure 1
Figure 1

What is the refractive index? The refractive index is the measurement of how hard it is for light to pass through a certain substance, thus affecting the speed of light. By knowing the refractive index of a substance you can also know the speed of light in that substance. For example, a glass has a refractive index of about 1.5 this means that light travels at 300,000,000 (speed of light in a vacuum) divided by 1.5 (the refractive index) this gives 200,000,000m/s. My variables are the wavelength, the glass rectangle, lasers, angle of incidence and angle of refraction, protractor and the distance between the laser and the glass rectangle (beam divergence). My independent variable is the wavelength which I am going to control. My dependent variable is the angle of refraction and angle of incidence. My controlled variable is, the glass rectangle, the protractor and the lasers, also the distance between the laser and the glass rectangle (because of the beam divergence). My independent variable, the wavelength, is going to be changed 5 times, using 5 different lasers of different wavelengths from 630nm to 405nm. My dependent variable, the angle of incidence and angle of refraction, depends on the wavelength, so for each wavelength I will take 3 different readings, with the same protractor. This is so that the results are more accurate and any wrong reading can be discarded. Throughout the experiment I will use the same glass rectangle, protractor, and the same lasers to ensure a fair experiment and to reduce the error. I will also keep each laser 10cm from the glass rectangle so that the beam divergence can also be controlled, and not affect the experiment. I believe that the wavelength will be proportional to the refractive index. With this I predict that as the wavelength increases so will the refractive index. Design The experiment could have been done with a light box and color filters, but it would have been less accurate. So I thought it would be best if lasers were used instead of light boxes, as the results would be more accurate. As the lab did not have any lasers, lasers from students home were brought to do the experiments, most of which were very high quality. We tried to get as many lasers as possible to have a wide range of results. The rest of the equipment we used was from the laboratory. Here is the list: * Lasers: -> Green laser, (532nm ± 10nm) -> Yellow laser, (570nm ± 10nm) -> Red laser, (655nm ± 25nm) -> Blue laser, (445nm) -> Violet laser, (405nm ± 10nm) * Glass rectangle * Protractor, 180° ±0.5° * Ruler, (just to make straight lines, no measurements needed) * Paper and pencil

A4 paper
A4 paper
Method
Point plotted
Point plotted
Figure 2
Figure 2
Ray
Ray
Glass rectangle
Glass rectangle
Red laser
Red laser

1. Set up the experiment as shown in figure 2. 2. Trace the glass rectangle and the rays with a pencil. To trace the rays plot an “X” where the laser meets the paper and where the laser meets the glass box. Then plot another “X” where the laser leaves the glass box and another one 10cm after. Be careful not to move the block during the experiment. 3. Change the position of the laser and point it to the glass rectangle and repeat step 2. 4. Repeat step 3. You should now have 3 rays drawn. 5. Calculate with your protractor the angle of incidence and the angle of refraction of the three lines drawn. 6. Use the formula “refractive index= sin I/sin R” to calculate the refractive index. 7. Repeat steps 1-6 using the yellow laser, the violet laser, the blue laser and the green laser. 8. After having all of the results, right down all of your results in a table in your book. 9. Analyze and compare the data.

Some of the lasers that were used were very powerful, so due to this, the experiment had to be done in an isolated place. The experiment took place in a little ventilated room, with little light so the lasers would be more visible. Everybody in the room wore appropriate glasses to block the laser radiation from the retina. The laser was handled carefully at all times. We also had adult supervision whenever the laser was turned on.

Raw data

| Violet | Blue | Green | Yellow | Red | Angle of incidence (A) (°) | 32 | 40 | 28 | 32 | 36 | Angle of refraction (A) (°) | 20 | 26 | 19 | 22 | 23 | Angle of incidence (B) (°) | 61 | 51 | 45 | 19 | 41 | Angle of refraction (B) (°) | 36 | 31 | 27 | 13 | 30 | Angle of incidence (C) (°) | 34 | 61 | 16 | 58 | 27 | Angle of refraction (C) (°) | 19 | 34 | 12 | 35 | 16 | The protractor used to measure the angles had an error of 0.5°. We know this because the smallest number in the protractor was 1°, so ½ = 0.5°. There is also the error in the beam divergence and in the beam diameter. The ruler is also not perfectly straight so there is also an error in that, as we will have to draw straight lines with it. These three errors are very difficult to measure but I estimate that all of them together should give roughly an error of 0.5°. The lasers itself also have a manufacturer error in its wavelength. Error in lasers Wavelength | Violet | Blue | Green | Yellow | Red | Wavelength (nm) | 405±10 | 445±5 | 532±10 | 570±10 | 655±25 | Uncertainty (%) | 2.47 | 1.12 | 1.88 | 1.75 | 3.82 | Calculations: You can calculate the uncertainty in percentage by dividing the uncertainty in “nm” by the wavelength, times 100. Example: (green laser) (10/532) x 100= 1.879699248% ≈1.88% Processed Data | Violet 405±10nm | Blue 445±5nm | Green 532±10nm | Yellow 580±10nm | Red 655±25nm | Refractive Index (A) | 1.63 | 1.58 | 1.52 | 1.47 | 1.44 | Refractive Index (B) | 1.64 | 1.60 | 1.51 | 1.45 | 1.35 | Refractive Index (C) | 1.62 | 1.56 | 1.53 | 1.47 | 1.40 | Average Refractive Index | 1.63 | 1.58 | 1.52 | 1.47 | 1.40 | To calculate the refractive index, you have to follow Snell’s law, Example: (Refractive index A of Green)
(n= refractive index)
Sin(28) / Sin(18)= 1.519241891 ≈1.52
Example: (Refractive index A of Green)
(n= refractive index)
Sin(28) / Sin(18)= 1.519241891 ≈1.52

To calculate the average refractive index you have to add all 3 refractive index and divide by three. For example: (green) I decided to use two decimal places so that it would be easier to distinguish the difference between each one of them, and also so that it could be more accurate.

I decided to use two decimal places so that it would be easier to distinguish the difference between each one of them, and also so that it could be more accurate.

(1.52 + 1.51 + 1.53) / 3 = 1.52 Total Uncertainty | Violet 405±10nm | Blue 445±5nm | Green 532±10nm | Yellow 570±10nm | Red 655±25nm | Total Uncertainty in refractive index (±%) | 20.6 | 16.7 | 30.2 | 25.5 | 21.8 | Uncertainty in laser wavelength (nm) | 10.0 | 5.0 | 10.0 | 10.0 | 25.0 | Calculations: To calculate the uncertainty in the refractive index you have to calculate the error in the angle of incidence and in the angle of refraction, and then add them both together. Example: (green) 1) Angle of incidence= 30° ((0.5+0.5) / 28) x 100 = 3.571428571…% ≈3.6% Angle of refraction= 20° ((0.5+0.5) / 18) x 100 = 5.55555….% ≈5.6% 3.6 + 5.6 = 9.2% 2) Angle of incidence= 44° ((0.5+0.5) / 45) x 100 = 2.22222222…% ≈2.2% Angle of refraction= 26° ((0.5+0.5) / 28) x 100 = 3.84615385% ≈3.8% 2.2 + 3.8 = 6.0% 3) Angle of incidence= 15° ((0.5+0.5) / 17) x 100 = 5.882352941… % ≈5.9% Angle of refraction= 11° ((0.5+0.5) / 11) x 100 = 9.09090909…% ≈9.1% 5.9 + 9.1 = 15.0% Total => 8.3 + 6.1 + 15.8 = 30.2%

Line of best fit (Ax^B)

This line of best fit graphs shows that there is a correlation between the points. However it is difficult to draw any reasonable and accurate conclusion because the error bars are way too big. It is very clear looking at the graph that the error bars are humongous. And also the gradient does not change much, it almost looks like a straight line graph, but actually it has a very slight small curve. The best fit line has a negative gradient.

Maximum and Minimum line

As expected the minimum and maximum lines were very different from the original line. This is because of the huge errors present in the experiment. The minimum best fit line has a negative gradient while the maximum best fit line has a positive gradient. The errors are just too big, and because of that they give unreal maximum and minimum best fit lines.

Conclusion In conclusion we can see from the graph that there is a correlation between the refractive index and the wavelength. So it could be assumed that the refractive index is inversely proportional to the wavelength. The graph is very difficult to interpret as the error bars are very large and very disproportional to the graph. The laser which had the biggest refractive index, 1.63, was the violet laser, the one with the shortest wavelength 405±10nm. The laser with the smallest wavelength was red laser 655±25nm with 1.39 as the refractive index. It is very clear that as the wavelength increases the refractive index decreases. So in theory radio waves should have a very low refractive index (almost 1). Due to the limited equipment and time that we had, it would be very difficult to improve this experiment. But if we had access to a spectrometer, then I am sure we would have better quality and more accurate data, as it wouldn’t have the errors present in this experiment. It is very difficult for us to compare our data with what our data should have been with 0 error because to do this we would need to know exactly what the glass rectangle was made out of, as different substances have different densities which lead to different refractive index. However the graph obtained in this experiment does follow the same type of trend as the other graphs in books and internet do.

Bibliography http://www.rpi.edu/dept/phys/Dept2/APPhys1/optics/optics/node7.html http://issphysics.wikispaces.com/file/view/Lab+Report+Template.pdf http://www.visualopticslab.com/OPTI515L/Background/OpticalMaterials1.pdf http://uk.answers.yahoo.com/question/index?qid=20100107041138AAKhiJn http://homepages.rpi.edu/~schubert/Educational-resources/Materials-Refractive-index-and-extinction-coefficient.pdf http://refractiveindex.info/?group=GASES&material=Air http://www.philiplaven.com/p20.html http://www.nist.gov/data/PDFfiles/jpcrd282.pdf http://wiki.answers.com/Q/How_does_refractive_index_vary_with_wavelength

Bibliography: http://www.rpi.edu/dept/phys/Dept2/APPhys1/optics/optics/node7.html http://issphysics.wikispaces.com/file/view/Lab+Report+Template.pdf http://www.visualopticslab.com/OPTI515L/Background/OpticalMaterials1.pdf http://uk.answers.yahoo.com/question/index?qid=20100107041138AAKhiJn http://homepages.rpi.edu/~schubert/Educational-resources/Materials-Refractive-index-and-extinction-coefficient.pdf http://refractiveindex.info/?group=GASES&material=Air http://www.philiplaven.com/p20.html http://www.nist.gov/data/PDFfiles/jpcrd282.pdf http://wiki.answers.com/Q/How_does_refractive_index_vary_with_wavelength