How to collect results:
Results table:
Graph:
Fair Test: We must make sure that the same equipment is used. For example if we take more than one lesson to do the experiment, the same glass block must be used because different glass blocks may have different sizes and other features. Also I must repeat the experiment. At the beginning I'm going to do a practice experiment for which the obtained results I will not count. Then I will do the experiment twice, recording the data and later I will find the average of the two for each result. If the two results are very different from each other I will repeat the experiment again and make sure I have accurate results.
The thickness of the material and the type of material must be the kept constant. Only the incidence ray may change.
Accuracy:
I must use a sharp pencil to be more precise, mm ruler to work in millimetres for more precision, large-scale protractor in order to achieve grater accuracy. I must also use a ray box producing a narrow ray.
The light ray may be wide. I must always place my line in the middle of the light ray to avoid any mistakes.
To have valid evidence I am repeating every measure I make twice and finding the average.
For the angle of incidence I am also taking readings for 8 points at every 10-degree interval. I could be even more accurate by taking a reading at every 5-degree interval, however this would take too long.
Safety: We must not forget that we are working in a dark room in order to see the light ray. Special care must be taken as accidents can occur in the dark so unused objects must be put away. Also the ray box may be hot and care should be taken when handling it.
Prediction: My prediction is that as the angle of incidence increases, the sideways displacement also increases. This is because:
- Preliminary experiment: We have done in class an experiment to show the change of the angle of refraction of a light ray through a glass block against the angle of incidence.
If we take away the angle of refraction (r) from the angle of incidence (i) we will get a direct connection between the result and the sideways displacement.
Diagram 2:
The results show that as the angle of incidence increases, i -r also increases. This helps us to see that as i increases, the sideways displacement also increases. Underneath is the table of results and graph from my preliminary experiment of i-r.
- Scientific explanation: When the angle of incidence is 0, there is no sideways displacement (as shown in diagram). As I increase, d must also increase.
We can calculate the sideways displacement: I am going to calculate the sideways displacement for i=30 degrees:
1. To find out what r is. I know that the refractive index of glass is 1.52 from a preliminary experiment:
Sin i (angle of incidence) =n (refractive index)
Sin r (angle of refraction)
Sin 30 = 1.52 (what I got from preliminary experiment)
Sin r
Sin r = Sin 30 = 0.333
1.5
r = Sin-1(0.333) = 19.45
2. To get the distance AB: (Shown on diagram 2)
6 =Cos. r
AB
6 =Cos. 19.45
AB
AB= 6 = 6.36
Cos. 19.45
3. To get distance D and therefore find sideways displacement:
D = Sin (i-r)
AB
D = Sin (30-19.45)
6.36
D= 6.36xSin10.55
D=1.16
I can do the same for an angle of incidence of 60 degrees:
Sin i (angle of incidence) =n (refractive index)
Sin r (angle of refraction)
Sin 60 = 1.52 (what I got from preliminary experiment)
Sin r
Sin r = Sin 60 = 0.57
1.52
r = Sin-1(0.57) = 34.75
6 =Cos. r
AB
6 =Cos. 34.75
AB
AB= 6 = 7.30
Cos. 34.75
D = Sin (i-r)
AB
D = Sin (60-34.75)
7.3
D= 7.3xSin25.25
D=3.11
I have made a graph (in excel) showing my predicted values of sideways displacement against angle of incidence. According to my calculations shown by the graph I predict that as the angle of incidence increases, the sideways displacement also increases if you shine a light ray through a glass block. As shown by the graph, this displacement is proportional.
Obtaining Evidence
Table to show my two results and average in the experiment to show the sideways displacement of a light ray through a glass block when changing the angle of incidence.
I carried out the experiment as planned. Above is my results table.
Complications: It was difficult to get results for angle of incidences of 80 degrease.
I had to be very careful in not moving the glass block at all.
Analysis and Conclusion
My graph is a gentle curve upward. It shows that as the angle of incidence increases, the sideways displacement also increases not proportionally but more rapidly because the graph is not a straight line.
My conclusion is that as the angle of incidence increases, the sideways displacement also increases. However the rate of increase increases as the angle of incidence increases
Prediction and results:
On the same graph I have put the predicted and obtained results. My line of best fit is the same shape, which means the results agree with my prediction however there my line of results is above my line of prediction. This can be due to the different refractive index because I didn't use the exact refractive index in my prediction.
Rate of increase: I have used the graph to find out the rate of increase:
I (degrees) d (mm)
20 7 18 = 2.57
7
40 18
1:2.57 This is the ratio of sideways displacement of two angles (one twice bigger than the other). This shows that as the angle of incidence doubles, the sideways displacement will be 2.57 times greater. I have repeated this calculation two more times:
I (degrees) d (mm)
30 12 32
12 =2.67
60 32
1:2.67
I (degrees) d (mm)
40 18 50 =2.78
18
80 50
1:2.78
We can see that as the difference between the angles increases by 10 degrees, the ratio of the distances becomes bigger by 0.1.
The sideways displacement is not directly proportional to the angle of incidence because the ratio is not 1:2. Instead as the angle of incidence increases, the sideways displacement increases even more each time.
Scientific explaining conclusion:
Evaluation
The experiment did work well and confirmed my prediction
Quality:
My results were accurate because the line on my graph is a smooth curve. Also the obtained results were very similar to my predicted results because the two lines on my graph have the same shape.
Anomalies:
I had no major anomalies however I got a few minor variations. My main once were the obtained results of the sideways displacement of angle 10 and 20 degrees. This did not effect my experiment conclusion and evaluation because my line of best fit overcame this problem by not going exactly through the points.
I had these minor anomalies because:
- It's very difficult to measure angles exactly. Measuring a tiny fraction wrong may mean a large difference in results.
- The light ray was wide and each time I had to approximately measure the middle of it which my not have been completely precise.
- The ruler I used was only in millimetres and therefore may not have been completely precise. Also it is difficult to measure fractions of millimetres with the naked eye.
Improvements:
The experiment could not have been improved in a major way however tiny improvements could mean I could get more accurate results:
- I could use a narrower gap in the slide of the ray box, which would produce a narrower ray, and therefore it would be easier to mark the ray.
- If the ray box was longer, this would mean the distance between the bulb and the slide is greater which would also produce a narrower ray.
- I could use a bigger protractor with a larger scale, which would make my angle measuring more precise.
- I could also take a reading for every 5 degrees angle of incidence, which would make my results more exact and reliable.
- I could use a magnifying glass to take accurately my readings of the compass and ruler.
Reliability:
I had no major variations between my two readings.
My results table:
My first difference is on angle of incidence 40 degrees.
My second one is on angle of incidence 60 degrees.
My third one is on angle of incidence 70 degrees.
I can find out which one had the greatest percentage difference by doing the following calculation:
%Variation = (Difference / average value) x 100
- For i=40degrees: (2/19)x100 =10.53%
- For i=60degrees: (0.5/33.75)x100 =1.48%
- For i=70degrees: ( 2/44)x100 =4.55%
My largest percentage variation is 10.53% for angle of incidence of 40 degrees. This is not a large percentage variation, which shows my results were accurate.
Suitability:
My experiment was suitable because it produced the results I was looking for. Although I could make minor improvement on the whole I could not on the whole do it in a better way.
Sufficient for conclusion:
The results I got were sufficiently good to enable me to produce a definite conclusion that: The sideways displacement of a light ray through a glass block increases proportionally but more rapidly as the angle of incidence increases. Especially because of the very good agreement with my predicted results (as can be seen from graph.)
Further work in detail:
The path of a light ray through any material depends on:
- The angle of incidence. (done)
- The wavelength of the ray.
- The refractive index of the material.
- The thickness of the material.
To investigate this topic better I would need to do an experiment for more than just one of these factors. For e.g. I could change the thickness of the material:
An experiment to show the sideways displacement of a light ray through a glass block changes as the thickness of the material changes.
Simple Plan:
To change the thickness of the material I would need to use more than one glass block. I could place two glass blocks next to each other. I could repeat this by changing the positions of the blocks and therefore achieving different thickness.
To achieve different thickness, I am going to use two glass blocks. I am going to put them in different ways:
Here are some examples of how I can arrange the blocks in order to achieve different thickness:
I can arrange the glass blocks in many ways but I have chosen 6 that will give me enough variation:
1 - 20mm
2 - 6mm
3 - 11mm
4 - 8mm
5 - 13mm
6 - 17mm
Difficulties:
- There will be a small gap between the two glass blocks that are joined together. I can try to avoid any major problems in my results by placing the two glass blocks as close as possible next to each other.
- I will not know what angle of incidence can use in order to get clear results for all the widths I am going to use. To overcome this problem I need to do a preliminary experiment with using the largest width I am planning to have on my actual experiment. I need to see which is the largest angle of incidence I will be able to use in it. I must use this angle of incidence all through my actual experiment to make it a fair test.
Method: I am going to carry out an experiment similar to the one I originally did with the difference that this time I am going to have instead of one glass block, two joined together in different ways producing different thickness. For each thickness I will record the results. This time I will not change the angle of incidence but leave it constant all the way.
Diagram:
Fair Test, Accuracy and Precision: I will change nothing else but the thickness of the material. The angle of incidence will remain the same. I will repeat the experiment twice for each thickness and produce an average. I will use same methods of achieving precision as I did in the first experiment.
Prediction:
My prediction is that as the thickness of the glass block increases, the sideways displacement will also increases.
We can see that from the diagram. I used the yellow ray to show how the sideways displacement would have decreased as the thickness halves. We can conclude from the diagram that as the thickness doubles, the sideways displacement also doubles and therefore the two are directly proportional.
As the thickness increases, there will be more space the ray has to travel through and because the original ray and the diffracted ray travel at different directions, they will get further away from each other causing the sideways displacement to increase.
Explanation:
