Deviation of Light by a Prism.

Nigel Evans

Physics Coursework – “Deviation of Light by a Prism”

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Deviation of Light by a Prism

Aim

The aim of this investigation is to test using a prism how the angle of deviation (how far the light ray is deviated from its original position) is affected by varying the angle of incidence (where the light ray goes into the prism), and whether this has any relation to the angle of emergence (where the light actually comes out of the prism).

Planning

I firstly need to conduct theoretical work and a preliminary investigation to test what is going on and to get a clearer view of the aspects of the investigation. In my theoretical work I will have to use the geometry of triangles and Snells Law. For Snells law to work, I will need to know the refractive index of the glass that I am using. To do this I will use a glass block of the same glass as the prism, and then use sighting pins (and light) to pinpoint the incident ray and the emergence ray and then find the angle of refraction. A more detailed description of how this experiment is going to work can be seen below.

To find the refractive index of the glass that I will be using in the actual experiment, I set up a glass block that was of the same type of glass as the prism, and lined up sighting pins through it. This enables me to draw the angle of incidence (measured from the Normal (dotted line below), a line at 90° to where the incident ray strikes the glass block) and this also enables me to draw the angle of emergence (where the light exits the prism). I then would connect both the lines up and draw the path, which the ray actually takes through the prism (the refracted ray). After this I would measure the refracted ray, again the is measured from the same normal, and then I would use Snells Law to calculate the refractive index of the prism. I will be measuring all angles using a 360° protractor.

Snells Law =

(Where “i” is the angle of incidence and “r” is the angle of refraction, and “n” is the refractive index of the material in question) This is also assuming that light is travelling form a vacuum into the glass, even though it will actually be travelling from air into glass. I have considered this fact to be negligible because the refractive index of air is roughly equal to 1 (about 1.003) and substituting this value into the formula gives the same refractive index as it would for a vacuum.

This will enable me to find the refractive index of the borosilicate crown glass. I will repeat this experiment using both light and sighting pins. This experiment will be repeated in order to obtain an accurate average thus ensuring an accurate figure for the refractive index of the glass. I will also compare my averaged answer to the one in a data book and average the two together to obtain an accurate refractive index of the glass that I will be using. Below is a table of values that I collected for both the light method and the sighting pin method. The actual drawings of these results can be seen on the next few pages.

The Data Book (“Table of physical and chemical constants – 14th addition” – By “G.W.C. Kaye and T.H.Laby”) that I consulted to check if this value was correct gave an answer of 1.509. I have averaged the one obtained above and the one given by the data book to obtain a refractive index value for the glass I am using of 1.51.

Another Preliminary investigation which I under took was to see actually which path the ray of light took through the prism, so I could make my diagrams more accurate and get a clearer view of exactly what the investigation would entail.

Prediction

Until I actually commence with my calculations to see how the angles vary compared to one another, I can offer no prediction based on initial knowledge, as my knowledge what happens to light in a prism, and how the angles change with respect to one another is limited.

Hypothesis

Above is a diagram for the actual path that a ray of light takes through a prism.

The letter “I” represents the angle of incidence.

R1 represents the first angle of refraction.

The second angle of refraction is represented by “R2”.

The letter “E” represents the angle of emergence.

The Greek letter delta, “δ” represents the angle of deviation.

On the next page is a larger diagram of the above prism, the advantage of this being that the letters and angles that I will be referring to throughout my experiment can be seen here in clearer detail.

Example Calculation of Deviance 1:

Firstly I need to specify an angle of incidence, for this example calculation I will be using 40°. This will be measured from the normal (line at 90° to point where incident ray strikes). As the light enters the prism it is refracted so I need to use Snells Law to work out the angle of refraction:

Therefore sin r = sin 40 / 1.51

= 0.42569

Sin-1 0.42569 = 25.2° This is the first angle of refraction, R1.

I know that the angle of refraction is at 90° to the prism, and so I can work out the angle that R1 makes with it using 90 – R1.This gives:

90° – 25.2° = 64.8° (call this angle “a”)

I also know the angle at the top of the prism because this is always 60° for the type of prisms that we are using, so I can use a rule from the geometry of ...

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Therefore sin r = sin 40 / 1.51

= 0.42569

Sin-1 0.42569 = 25.2° This is the first angle of refraction, R1.

I know that the angle of refraction is at 90° to the prism, and so I can work out the angle that R1 makes with it using 90 – R1.This gives:

90° – 25.2° = 64.8° (call this angle “a”)

I also know the angle at the top of the prism because this is always 60° for the type of prisms that we are using, so I can use a rule from the geometry of the triangles which tells me that the angles in a triangle always add up to 9°and so I can use this to find the angle that R2 makes with the inside of the prism:

180 – (60 + a) = b (call the answer to this angle “b”)

180 – (60 + 64.8) = 55.2°

Now to work out the second angle of refraction I will use the fact that it is at 90° to the inside of the prism, which means that:

90 – b = R2

90° – 55.2° = 34.8°

This is angle R2, which is the second refracted ray. Now to calculate the angle of emergence we need to use Snells law again, which if we apply it to the angles used on my diagram of the prism gives:

Sin 34.8° x 1.51 = Sin E

Sin 34.8° x 1.51 = 0.862

Sin-1 0.862 = 59.5°

Therefore E = 59.5°

The angle of deviation can now be calculated by considering the following triangle:

If the two angles “X” and “Y” are added together then this will give the angle represented by “δ”.

As can be seen on my larger image of my prism, the two angles X and Y are already on, and these can be found by adding the differences of the two incidence and refracted rays together, i.e.:

X + Y = δ

(I – R1) + (E – R2) = δ

(40 – 25.2) + (59.5 – 34.8) = δ

14.5 + 24.7 = 39.2°

Therefore 39.2° is the angle of deviation for the incidence ray of 40°.

Example Calculation 2

While using the above described method I also noticed another method to calculate the angle of deviation, which has less calculations, is shorter and is simpler to understand. In involves using the angle that is in the middle of the first refracted array and the second refracted ray. This angle will always be 120° because it will always be double the angle at the top of the prism (from geometry). Below is an example calculation to demonstrated this method:

Specified incidence ray angle = 50°

From Snells law, then it follows that:

Sin R1 = Sin I / n

Sin R1 = Sin 50 / 1.51

Sin R1 = 0.51

Sin-1 0.51 = 30.5°

Therefore R1 = 30.5°

Using the rule of geometry described above if I add 120° to this answer for R1 and subtract this from 180° I should be able to obtain an answer for the angle R2.

180 – (120 + R1) = R2

180 – (120 + 30.5) = 29.5°

Therefore R2 = 29.5°

To find the emergence ray I again need to resort to Snells Law, which this time gives:

Sin R2 x n = Sin E

Sin 29.5° x 1.51 = 0.744

Sin-1 0.744 = 48.1°

Therefore E = 48.1°

Now that I have all for values need to calculate the deviance I again have to use the fact that X + Y = δ:

(I – R1) + (E – R2) = δ

(50 – 30.5) + (48.1 – 29.5) = δ

19.5 +18.6= 38.1°

Below is a results table of the answers that I have gained for the angles sizes using the two above methods.

Results Table for Theoretical Modelling:

These are the calculated values for the prism, using the refractive index for the glass as 1.51. Any values before 30° are not possible because the refracted ray will appear at the wrong side of the prism. This factor makes the SINE of the angle bigger that 1 and therefore it is not possible to calculate a value for the emergence ray and also therefore not for the deviance either (as there is no emergence ray to calculate it from). The Incidence angle of 90° is also highlighted because although this value and other values above it are possible in calculation in practice the 90° angle would actually miss the prism and the values of the incidence ray above 90° would have to come from inside the prism itself. I have therefore chosen to take readings in the range of 30° - 85°. I will take one reading below 30° but this will only be taken to prove right my initial theory work and will not be taken into consideration in any conclusions that I draw.

Over the next two pages is two graphs plotted in the incident angle range of 30° - 85°, which show the predicted trend in the angle of deviation and the angle of incidence, and the other graph shows the predicted trend, in the variation of the angle of emergence and the angle of incidence.

As you can see from the graph of the Angle of Deviance plotted against the angle of incidence, it is a parabola that achieves a minimum value of 38° when the angle of incidence is 49°.

The graph is shaped like it is because, there are in fact two Incident rays on my prism, the one where light goes into the prism (The Incidence Ray, I) and the one where the light comes out of the prism (The Emergence Ray, E). Depending on which incident ray you use to find the angle of deviation, this will alter the size of the deviation, this means that every incident ray has in fact two angles of deviation, depending on which ray you choose to measure from.

This is why the graph is shaped like it is, because there are two different angles of Incidence for each angle of Deviation. For example the Incidence ray of 35° corresponds to a deviation angle of about 42°, and the Incidence angle of about 67° also corresponds to the same angle of Deviance (42°).

I have derived from this that if 35° is the angle of incidence, then 42° is the angle of Deviation, and this means that 67° is the angle of emergence, for an incident angle of 35°. This is also shown in my theoretical results, but in these results it is more accurate than reading off the graph because the graph hasn’t got a very accurate scale.

Therefore I can use the graph of the angles of Deviance plotted against the angles of Incidence to find the emergence angle for a specified angle of Incidence and vice-versa (the angle lies along the same line where, the deviance is again the same value – the other side of the curve).

At the bottom of the graph where the incidence angle is about 49°, this angle corresponds to the minimum angle of deviation (which is about 38°) and using the above stated theory the angle of Incidence would be exactly the same as the angle of emergence at this point. This also means that the two refracted rays inside the prism would also be exactly the same.

From the graph of the angle of Emergence plotted against the angle of incidence, I can see the incident ray and the correspond emergence angle, this means I can work out from the graph, which incident angle corresponds to which emergence angle and I am able to deduce which two values go together to have the same angle of deviance. (Shown on the deviance angle against incidence angle graph).

Equipment

Prism – This will be kept constant throughout the experiment, because different prism could have a slight difference in refractive index (from about 1.51 – 1.53). This being kept constant should hopefully make my results more accurate.

360° Protractor – To measure the angles, should be very accurate

Ray Box – A source of light to view how the light is refracted in the prism.

Sighting Pins – These will be plotted along the middle of the ray of light as the light tends to be diffracted into its spectrum when passed through a prism, so keeping the pins lined up down the middle, will make my results more accurate.

0.30m Ruler – to draw the lines where the ray enters and leaves the prism

Lab Pack – To power the ray box

Fair Test

As mentioned above the prism needs to be kept constant because the refractive index needs to be kept constant to ensure accuracy in my calculations. Ideally the protractor also needs to be kept constant because some will be of a better build quality that the others, and some will also be more accurate than others.

Variables

The only variable that I can really change is the angle of incidence, as this will give different angles of emergence and also different angles of deviation.

So the variables that I will keep the same are the prism, and the protractor, changing the lab pack and the ray box will have no effect on my results whatsoever as the light is only used as a guide for the lines of incidence and emergence to be drawn.

I could repeat the experiment for each different angles that I am going to take, but I feel that this would be too time consuming, and hopefully, the experiment will be done correctly the first time, but my results shod hopefully tell me this when I have taken them.

Safety

As observed form other practical done in the past, I know that the ray boxes can get extremely hot, so I will take care not to leave this on for too long, I will also keep the voltage below 12V because this is the maximum voltage that the ray box can handle, and even at this temperature the ray box can get very hot. Care with he sighting pins also has to be taken into account even though they are really a minor issue, they are still sharp so common sense should prevail when using them.

Method

Place a piece of white paper onto a flat piece of cardboard and make sure that it can’t easily slip off.
Place the prism flat on the paper and draw around it, making sure that it is an accurate drawing, using a sharp pencil
Draw a normal line at exactly 90° to the side of the prism, and then using a protractor measure the angle of incidence that you want to obtain readings for and then connect this up to the normal line, exactly where it strikes the prism.
Connect the ray box up to the lap pack and to the power up to about 12V this makes the light as bright as possible while also keeping the lab pack at a safe voltage.
Move the ray box quite close to the prism, and direct the slit of light down the line of incidence that has already been drawn. Moving the prism as close as possible ensures that the beam is small and accurate, and that not much dispersion (the spreading out of a light ray as it enters takes place, because even though the size of the slit is not very close to the wavelength of light, dispersion still occurs and the beam gets weaker towards the end.
Place sighting pins along the middle of the light where it comes out of the other side of the prism then move the prism out of the way and connect up the pin marks that you have left in the paper. This is now the emergence ray that you have just drawn. Add a normal line at 90° to where the emergence ray leaves the prism.
Measure the angle of emergence by lignin up your protractor with the normal line (remember that both the incident ray and the emergence ray will be measured relative to their own normal line). Not this angle down.
Extrapolate both the Incident Ray and the Emergence Ray, so that they meet inside the prism, measure this angle carefully with a protractor and then note this angle down. This is the angle of Deviation.
Repeat this experiment, from the incidence angle of 30° to the incidence 0angle of 85°, going up in 5° increments. Be sure to use a separate piece of paper for each different angle of incident so as not to get confused.

Diagram

Implementing

Actual Results Obtained

Before this page is all my actual results for each different angle of incidence that I measured. They are drawings of the prism itself and both the angles of incidence and the angles of emergence are labelled on them. These two lines are then extrapolated back, and I have used a protractor to measure the angle of Deviation. In my experiment I tried to make it as accurate as possible by keeping the two normals, perfectly at 90° to the rays, and the prism. I also placed the sighting pins down the middle of the light ray, as accurately as my eyes could perceive.

Table of Results Obtained

On the next two pages are the graphs that were seen in the planning section, but using the actual results obtained from the table above. These are:

Graph 1 = Angle of Emergence against angle of Incidence

Graph 2 = Angle of Deviation against Angle of Incidence

As you can see from both of them they are almost the same as seen in the planning section, except for as you would expect, slight bumps here and they because as usual in the actual practical work, the results always vary slightly from the theoretical results, but the general trend is still the same.

The Graph of the angle of deviation plotted against the angle of incidence for my actual results obtained is almost the same in terms of general shape, but its position is different. The minimum value of deviation for my theoretical results was about 38° while for my results that were obtained due to experiment the value was higher at about 41°. The minimum values of incidence also was located at different values of incidence – 49° for my calculations, and in the region of 50°-55° for my experimental results. A number of factors could have affected this and them will be explained in the following evaluation. A closer inspection of my results table above confirms the value of incidence which conforms to the minimum angle of deviation, it is 50° because as stated in my planning and calculations section, at the minimum value of deviation the values for the angles of incidence and the values for the angle of emergence will be exactly the same.

Conclusions

As the graphs show, my actual results that I obtained strongly agreed with my prediction. There were of the same basic shape, and even though they don’t match exactly I’d say that the experiment was a success.

My experiment showed that light was bent when it entered the prism, my experiment also proved Snells law works, because my actual results were so close to my predicted results.

Equipment set up properly

Patterns are same as in planning

Show relationship between incidences etc

Links conclusions with existing knowledge

Be consistent

Knowledge used to make deductions

Error margins

Patterns in results

Graphs

From graphs what happen

Anomalous?

Evaluation

I think that the way I conducted my experiment was quite efficient and suitable, as you can see from my results, they are very close to the original predicted values. But as always there is room for improvement, which is explained in more detail below.

Why My Results were slightly different from my calculated results

I think the main reasons why my results were slightly different from the results that I had calculated before are:

The refractive index of the prism. I only had an educated estimate of the refractive index of the prism by using the glass blocks of the same glass, and even these results were susceptible to human error among other things. If there was a way to measure accurately the refractive index of the prism, then I could better my calculations by using this value.
The accuracy of my results could have also played a part in this. This will be better explained in the sections below on ‘accuracy’ and ‘sources of error’.

Sources Of Error

The main sources of error in my practical experiment was the light ray itself, this is because as it dispersed and it became fainter it was harder to judge where the centre of the ray was, and therefore this made it more difficult to judge where to place the sighting pins. This could have affected my results greatly and could account for sections on my graph where the results are not exactly as predicted.

Another main source of error could have been human error because everyone would judge the angles on a protractor differently and what I thought was 50.5° could have been 50° or 51°. So I think that human error had a part to play in how accurate my results were.

I think a big source of error could have been how accurate the protractor was cut, the sides my have been different lengths or the build quality of the prism may have just been poor, but I have no actual evidence to base this on it is just an observation and an insight into what factors could have affected my results.

Accuracy

The things that made my practical experiment inaccurate were:

As explained in the ‘sources of error’ section above, human error must have played a part in making my experiment less accurate than it should have been, such as the reading of the protractor and the placing pins at the middle of the light beam due to the dispersion of the light that the prism caused.
The accuracy of the protractor - the lines that are printed onto the protractor that I used were quite large and it was hard to judge on which value the line lay. Also even though it had a slightly magnified are in the middle of it was extremely difficult to see if it lay on the normal and if it lay on the point where the two lines intersected.

Limitations + Improvements

If I were to repeat the experiment again I would change the ray box into a laser (such as a He:Ne laser), this is because as my angle of incidence became greater, the light ray became fainter and more dispersed. I couldn’t risk turning up the voltage more to obtain a brighter ray because I was already up to my safety limit of 12V. This made judging the centre of the light to draw an emergence line, extremely difficult. A laser beam wouldn’t spread out as much, because it can’t be dispersed into colours because usually laser beams are monochromatic. Laser beams are also usually more powerful, and therefore the beam wouldn’t become as faint as the light ray, when it protrudes from the other side of the prism.

I would also maintain a sharper pencil at all times as this would make angle measuring easier, and maintain a high degree of accuracy in my investigation.

I would try and obtain a angle measuring tool that is of a better standard that a protractor and measures to a higher degree of accuracy, to ensure that all my results were very reliable.

Reliability

Overall I think my results were very reliable, and they linked back very well to my initial calculations. I think there is room for improvement as there is in any case but overall I think that my investigation was conducted reliably and to as high a degree of accuracy as the involved apparatus permitted.

Anomalous results

There were no major anomalies in my results, but having said this the two graphs that I have prepared from my results show some points that do not fit the exact trend, but they are still acceptable. An example of this is on the graph of the angle of emergence plotted against the angle of incidence, the two values of incidence angles 35° and 60° show slight bumps, even thought he line should be a perfect curve. These two could have arisen to inaccuracy on my part or for one of the reasons stated in the above sections.

The second graph of angles of deviation plotted against the angles of incidence show no real anomalous results with all points fitting the general trend of the graph in the same way that my initial calculations did (i.e. a smooth curve).

To conclude I think that given the situation and the equipment provided, I made the best use of it and even through there was room for improvement, my collected results were of a high standard as shown when comparing to my calculated values.