Sideways Displacement of a Light Ray

• As a ray of light enters glass it slows down
• Side (A) of the ray slows first
• (A) travels a shorter distance inside glass than (B) does outside
• This has the effect  of bending the ray towards the normal

When the angle of incidence is greater that 0 degrees, the ray bends towards the normal as it enters the glass block.

Thirdly, I need to examine my preliminary experiment:

• according to these results I can say that:

As (i) increases, the difference between (i) and ( r) becomes greater, so the refracted ray becomes more out of line with the incident ray, and the sideways displacement increases.

And finally, it is important to say that sideways displacement depends on (i) - ( r).

 

To show it on an example, I will use the results from my preliminary work:

To assume that angle (i) = 15, then (r) = 12 and (i-r) = 3.

If we increase (i) - the angle (r) and therefore angle (i-r) increase as well, for example:

(i) = 45 , (r) = 30, (i-r) = 15.

This happens, because:

Those two angles are equal (the ones that marked with         ) .

I predict, according to my scientific knowledge, that the sideways displacement of the light ray depends on the angle of incidence and therefore, if the angle of incidence will increase, the sideways displacement will increase as well.

(i) - ( r) shows  that light is changing it's path, but it doesn't mean that sideways displacement is  proportional to the angle of incidence. The preliminary results show the difference between the angle of incidence and the refracted angle, which might help to explain, that even at that stage, when the light ray is going through the glass block there is a difference, so that when the ray of light actually does go out of the glass there is  difference between where the light actually goes and how it should have gone without the glass, which is called sideways displacement. This is shown on the diagram below :

Using my preliminary experiment I can actually make a prediction on what the sideways displacement will be. If I take a table of results and draw a diagram with all the appropriate information and then plot a graph.

So that my diagrams would look like this:

As I can clearly see from my hand-drawn diagrams, the sideways displacement increases as the angle of incidence gets bigger. I also plotted a graph, basing on the results that I have got from the diagrams, in order to underline my prediction.

It is important to bear in mind, that the diagrams are all of the same size (i.e. the rectangles that represent glass blocks are all of the same size), and the results that I got are not proportional, i.e. sideways displacement of a light ray is not proportional to the angle of incidence.

Obtaining evidence.

I have carried out the experiment carefully, following my plan. I changed the table, where I recorded the results, because the table, that I decided to use in my plan was not suitable for this particular experiment. This can be explained by the fact that, for example, my last angle of incidence was meant to be 105°, but this can not be done on practice, because otherwise the ray of light would have to go through the glass block, entering it from another side. It would happen, because the "normal" is perpendicular to the glass block, therefore to make sure, that it would be a fair test, I could allow the ray of light to go in the glass block just in the angle not greater than 90°. And if I would take the results, that were in my previous table, I could not make a fair test, because I would be able to take just 5 results. The evidence of it, is the fact that, it would not be possible to take two last results ( 90° and 105° ), because if I would put the ray of light at the angle of 90°, the ray of light would just go by the side of the glass block. This reasons resulted in fact, that I have changed my table for results completely, changing the angles of incidence, that I used in practice.

To record my results in an adequate way I have a table, to show my practical observations in a "numerous" way.

Table of results:

It is important to mension that the average of three results, that are clearly shown in the table above, are not very precise, because in some cases ( e.g.20° , 50° and 60° of the angle of incidence) the actual average should be with two decimal places ( e.g. 0.73, but not just 0.7). But I have put everything to one decimal place, because the other results are with one decimal place and the results in the table should be of the same number of decimal places, so that it is a clear table.

I have also measured the glass block and it's dimensions are:

• length      = 11.2 cm
• width       =   6.2 cm
• thickness  =  1.8 cm

Safety:    

I used the following equipment :

• ray box
• glass block
• piece of white blank paper
• sharp pencil
• protractor
• ruler

Following my safe instructions, I carried out the experiment without any mistakes. When I started my experiment, I set up everything and I made sure that glass block is put onto the piece of paper, so it would not be scratched or damaged anyhow. The apparatus (the ray box, the glass block, the piece of white blank paper, on which I carried out my experiment) was situated on the free area and nothing was on the edge of the table, where I did the experiment. The ray box eventually became hot, but even here I was careful enough to work with it. Using the equipment, I was careful in moving it, so that everything was safe.

My experiment is sufficient , because I carried out the experiment and nothing went out of control and I was following my plan, therefore I took enough results and recorded them clearly. This also means that I do not need to repeat anything and nothing stayed undone in my experiment. The sufficiency of my experiment might be proved by the fact that I have done it and I can base my following coursework on the results that I have got.

Accuracy  

To make sure that my experiment is accurate I have followed the instructions of my plan. To be precise, I took a very thin and sharp pencil and tried to make the ray of light as thin as possible by putting it not in a very long distance away from the glass block. Also to make sure that the results will be accurate, I kept the ray box at the same distance away from the glass block for each of the angles of incidence. I put the ruler to the ray of light ( to show it's path on the piece of paper) as precise as it was possible. The make accurate results I did the same experiment three times on a different pieces of blank white paper and took the average of those results.

My results are systematic , because as it is clearly shown in my table, I started with the angle of incidence equals to 10° and so every next angle of incidence that I used ( in order to follow the fair test instructions) was increased by this 10° . The evidence of this is proved by the fact, that if you take any angle of incidence, that I used in my experiment, you can find out that the difference between the two nearest angles of incidence is 10°. For example, the third angle of incidence, that I have measured is 30° and the fourth angle of incidence is 40°, therefore 40° - 30° = 10° . As it is clear from my explanations , the angles of incidence are not chosen by random, but it was the results of preparation for this experiment.

I have repeated  my experiment three times, in order to make a fair test, so that  can base the rest of my investigation on this results. To make sure that the results will be clear, I have done the experiment three times on the different pieces of paper, which gave me the opportunity to find an average of those three results, that I have clearly recorded in my table of results.

The precision of my experiment can be checked by following factors:

• sharpness of my pencil
• the thickness of the ray of light
• the precise line, which shows the path of light ray

Firstly, I have drawn the line around the glass block on the piece of white paper, so that I knew the precise position of the glass block and it stayed the same. Next, I made sure that the ray box stayed at the same distance away from the glass block and I have shortened this distance as far as possible, so that the ray of light was as thick as possible and it thickness didn’t change through out the experiment, because I kept the ray box on the same distance away from the glass block, exept of moving it, in order to change the angle of incidence.

Analysing and concluding.

I have done a hand-drawn graph, according to my results, that I got from the experiment.

The following graph is the computer version of my hand drawn graph :

This graph shows that the sideways displacement increases, when you increase the angle of incidence. However, those two values are not proportional to each other.

 As I have said already, I also have the hand-drawn graph and I will use it in order to base my concluding on it.

Firstly, I have drawn the line of best fit   and it is a curve ,  because those values are not proportional to each other. The curve goes smooth, which underlines my accurate observations.

As I can see from my graph, it starts at the point when the angle of incidence equals to 0° and the sideways displacement equals to zero as well and it is sensible, because if you do not send a ray of light at all, there will be no sideways displacement.

To make sure, that my statement is right about the theory, that sideways displacement increases with the angle of incidence, I make a calculation to see whether the difference between any two values of the angle of incidence (comparing to the sideways displacement) is the same.

Use of graph and calculations corresponded to it:

I am taking the results from my graph:

If the angle of incidence is 10°, then the sideways displacement equals to 0.3 cm

If the angle of incidence is 25°, then the sideways displacement equals to 0.95 cm

So the difference between them is 0.95 - 0.3 = 0.65 cm

If the angle of incidence is 15°, then the sideways displacement equals to 0.5 cm

If the angle of incidence is 30°, then the sideways displacement equals to 1.2 cm

So the difference between them is  1.2-0.5    = 0.7 cm

If the angle of incidence is 20°, then the sideways displacement equals to 0.7 cm

If the angle of incidence is 35°, then the sideways displacement equals to 1.5 cm

So the difference between them is  1.5 - 0.7   = 0.8 cm

If I will go on, the difference between the sideways displacement, which occurs when the angle of incidence assuming is (i) and the angle of incidence assuming is (i)+15°, will be increasing, because pattern of this graph is like that.

To prove it in another way, I can draw tangents to  points on my graph ( to the every second value of angle of incidence from 10-70 - i.e. if angle of incidence = (i), then the next point to which I draw a tangent to, is (i)+20°).

So I have got the following results:

angle of incidence = 10° , the "acceleration" = 0.35/9 = 0.038

angle of incidence = 30° , the "acceleration" = 0.45/8 = 0.056

angle of incidence = 50° , the "acceleration" = 0.6/8   = 0.075

angle of incidence = 70° , the "acceleration" = 0.5/4   = 0.125

Here - once again as I increase the angle of incidence the difference between the previous sideways displacement and the next one increases. Those results also prove that inclination increases too.

Conclusion:

My conclusion consists of two main factors that have been proved through out my experiment. Firstly, it is that the sideways displacement increases as well as the angle of incidence.  In particular, during the experiment, and also looking at the hand-drawn diagrams of my experiment that I have carefully carried out, I can see as I increased the angle of incidence , the sideways displacement of the light ray become bigger too.  

Secondly, I have proved that the sideways displacement of the light ray is not proportional to the angle of incidence. This is shown in the calculations, that I based on the hand-drawn graph. And this is obvious from my scientific knowledge.

Science:

If you have ever half submerged a straight stick into water, you have probably noticed that the stick appears bent at the point it enters the water. This optical effect is due to refraction. As light passes from one transparent medium to another, it changes speed, and bends. How much this happens depends on the refractive index of the mediums and the angle between the light ray and the line perpendicular (normal) to the surface separating the two mediums (medium/medium interface). Each medium has a different refractive index .The angle between the light ray and the normal as it leaves a medium is called the angle of incidence. The angle between the light ray and the normal as it enters a medium is called the angle of refraction.

The amount of bending which a light ray experiences can be expressed in terms of the angle of refraction (more accurately, by the difference between the angle of refraction and the angle of incidence.  

For any given angle of incidence, the angle of refraction is dependent upon the speeds of light in each of the two materials; the speed is in turn dependent upon the optical density and the index of refraction values of the two materials.

The equation is known as the Snell's Law equation and is expressed as follows.

where ("theta i") = angle of incidence

           ("theta r") = angle of refraction

ni = index of refraction of the incident medium

nr = index of refraction of the refractive medium

As with any equation in physics, the Snell's Law equation is valued for its predictive ability. If any three of the four variables in the equation are known, the fourth variable can be predicted if appropriate problem-solving skills are employed.

So according to this scientific knowledge it is easy to explain, why the ray of light bends, which appears to be the base for explaining the sideways displacement.

Now list the relevant equation (Snell's Law), substitute known values into the equation, and perform the proper algebraic steps to solve for the unknown.

So now I will actually take the result from my experiment that I have just done:

ni = 1.00 (from the table above)

nr = 1.52(from the table above)

   

= 40 degrees

Following the formula of the Snell's Law( see above) :

1.00 * sine (40 degrees) = 1.52 * sine (theta r)

0.6428 = 1.52 * sine (theta r)

0.423 = sine (theta r)

sine-1 (0.423) = sine-1 ( sine (theta r))

25 degrees = theta r

Proper algebra yields the answer of 25 degrees for the angle of refraction. And this is a precise calculation, because if I actually measure it on the experiment paper ( where my experiment is recorded) the result will be the same.

 I will do another example, with angle of incidence = 50 degrees.

1.00 * sine (50 degrees) = 1.52 * sine (theta r)

0.7660 = 1.52 * sine (theta r)

0.504 = sine (theta r)

sine-1 (0.504) = sine-1 ( sine (theta r))

30 degrees = theta r

And this once again appears to be true, because on the paper with the experiment, the same result is found.To prove it, I have shown this on the sheet number 1( where I I have done the experiment for the first time).

Link to prediction:

In my prediction I have included the scientific knowledge, which can be also said in another way, but still have the following meaning:

The same two conditions, which are necessary for bending the path of the line of students, are also necessary for bending the direction of a light ray. Light refracts at a boundary because of a change in speed. Their is a distinct cause-effect relationship; the change in speed is the cause and the change in direction (refraction) is the effect.

The transmission of light across a boundary between two medium is accompanied by a change in both the speed and wavelength of the wave. The light wave not only changes directions at the boundary, it also speeds up or slows down and transforms into a wave with a larger or a shorter wavelength. The only time that a wave can be transmitted across a boundary, change its speed, and still not refract is when the light wave approaches the boundary in a direction which is perpendicular to it. As long as the light wave changes speed and approaches the boundary at an angle, refraction is observed.

Basically, the results, that I have got from my experiment, support my prediction, because as I have increased the angle of incidence, the sideways displacement increased  as well, exactly like I have predicted it.

To show the clear link to prediction, I , first of all, compare the graphs, that I have drawn for the prediction and for actual experiment, which is based on the results that I have got. The difference to spot between them is that the graph, which shows the results of the actual experiment, is that the inclination of the graph is bigger, comparing to the graph that I have plotted on the same axis, which shows the predictable results. This means, that the sideways displacement becomes bigger, as the angle of incidence increase, faster, and not as I have predicted. For example, from the graphs I can see that the sideways displacement is 1.2 cm, when the angle of incidence is 30° in the actual experiment and in the predicted graph the sideways is of the same value, when the angle of incidence equals 45°. Basically, those graphs show that in general my prediction is right, because both of the graphs are curves and both of them show that the sideways displacement increases with the angle of incidence. The differences in those two graphs might be explained by following factors:

• the thickness of the glass that I have used in the preliminary experiment might be not the same.
• doing the preliminary experiment I have used the D-shaped glass block, so that I have not actually measured the sideways displacement, because it was not possible to do, but I drew it, basing on the results of the preliminary experiment,  on the piece of paper, so that I did not see the ray of light, but only imagined it, basing on my own knowledge.

Taking an account for those factors, I would say, that my experimental results do match with my prediction.

Evaluating evidence.

Quality of my experiment was good, because I have followed all instructions in my prediction. I also paid a lot of attention to make sure that I have done a fair test, by measuring the sideways displacement three times with the same angle of incidence, for example. I can state that my experiment was reliable, because I didn't have any results, that didn't fit into the expected pattern that I have described earlier in this investigation. My results were accurate, because they all are close to the line of best fit (the accurately drawn curve). As it is clear from my table of results, that I have completed (in the "Obtaining evidence") it is clear that there is an agreement between the repeated results (nor of them are far away from the first result) and I have eventually gained the evidence from my results, that they are sufficient enough in order to support a firm conclusion. This was achieved by covering a large enough range of values of the variables.

I did not have any anomalies , all my results ( the average of three results) were on the curve of best fit and it means that observations were accurate and careful. Quality is proved, because everything I have done can be used to analyse it with care. The results do underline my prediction and this proves the quality, that is produced by my experiment.

Suitability of my experiment is at the good level, because:

• my conclusion was based on those results that I have got from my experiment
• a good range of results was used
• the equipment that I have used in my experiment stayed the same through out the experiment
• nothing was damaged or went out of control
• I have followed the instructions of safety and a fair test
• my graph, that I have drawn is based on my results, that I have got from my experiment, is smooth
• my graph also shows the clear trend

Reliability  

My experiment is reliable, because:

• I have measured the sideways displacement 3 times for the same angle of incidence on different pieces of paper
• I have found the average of those 3 results, so that the graph that I have plotted, is based on reliable results
• I have kept the fair test through out the experiment, in particular, I have varied just one of the factors - the angle of incidence
• I made sure that the glass block stayed on the same place, by marking it position on the blank piece of paper with a sharp pencil

The experiment is sufficient for conclusion, because:

• my results have showed a clear pattern

 

Improvements to be made, that can provide additional evidence for the conclusion that I have drawn:

• Take more results ( for example, I could measure the sideways displacement for the angle of incidence equals 80°)
• Take a ray box with a thinner ray of light, so the results would be more precise ( or I could have kept the ray box closer to the glass block)
• To draw a best fit curve more accurate, I could take the results more often ( for example, measure the sideways displacement every 5°, but not just every 10° as I did)

The futher work, that can be done on the same topic:

• Next sensible work to do would be to investigate  how the sideways displacement varies with the thickness of a glass block.
• I have produced a mini-plan below :

Aim - to find out how the sideways displacement of a light ray depends on various factors.

Factors to vary -

• the angle of incidence
• type of material (glass, plastic, water, etc.)
• thickness of the material

I will vary the thickness of a material and other factors and the equipment will stay the same for a fair test.

Equipment -  

• 2 glass blocks (the material, through which the ray light will go)
• 1 ray box ( to produce a ray light, which should be as thin as possible)
• 1 protractor ( to measure the angles)
• 1 ruler (to measure the dimensions of the glass block)
• 1 sharp pencil

• 1 piece of blank white paper

I will take 2 glass blocks, because, I need about 6 different thickness' of glass block to make a fair test. Instead of taking 6-7 different glass blocks, which would also produce difficulties with the equipment, I could take one glass block and make the ray of light go through it at three different sides, e.g.

Instructions -

• fix the glass block on the blank piece of paper
• draw a perpendicular line("the normal") to the side of the glass block
• fix the ray  box  near the glass block
• draw a line to show the position of the ray box to make sure that the ray box will stay on the same position (same distance away from the glass block) during the experiment
• measure the angle of incidence ( how far away is the ray of light from "the normal")  (i)

• measure the sideways displacement
• record the results into the appropriate table
• repeat the experiment for the same thickness of a glass block
• if needed, repeat the experiment for the same thickness of a glass block one more time ( if the difference between result 1 and result 2 is big)
• record the results into the appropriate table
• repeat steps 6-10 for 5-6 different thickness' of glass blocks

Table for the results-

Safety -

• the whole experiment should be done in the free area (without any external objects: books, pencil-boxes, etc.)

• experiment should be done on straight horizontal surface, so that any parts of the equipment will not go over the edge (e.g. of the table, where the experiment is carried out)
• I must be careful with the equipment, because :

• the glass is easy to break or scratch, so I will not keep it near the edge of the table and I will make sure that it is in a safe position.
• the ray box is connected to the plug, so I have to be careful with the electricity, also during the experiment the ray box might get hot, so I will be careful in touching it.

• I will be careful in moving the equipment, so that everything will be safe

• if something  goes wrong - ask the teacher

Prediction -