The reason that I chose an LDR is because, most importantly, it is a passive sensor and this means that I am able to change its sensitivity by using whetstone networks, amplifiers or by inserting it into a potential divider. The fact that it has a slow reaction time could perhaps be an advantage, since it means that I will be able to use moving coil meters or digital multimeters without having to worry about it change before I can take a reading. Finally, I ruled the phototransistor out purely because I feel that it is unnecessary to have those extra features when an LDR would be ample.
Meter
The other component whose choice I had to think about carefully was the meter that I chose to use. Without knowing the exact values of their resistance, I cannot make exact calculations. However, in our circuit, I have got the following set up:
Let us say that the value of the variable resistor is RV and that the value of the internal resistance of the meter is RM. Naturally, then
GV = (RV)-1
And
GM = (RM)-1.
Thus, the value of the total conductance of the combination of the variable and resistance of voltmeter is
GV + GM
We can therefore write the resistance to this then, as:
However, the value of the resistance that we are expecting to get is:
Therefore, in order to allow RV to be as close to the resistance that would be there without the meter. In order to do this, we want to minimise GM and hence maximise RM. Thus, our aim is to have a resistance with the highest resistance possible: A Digital Multimeter. An oscilloscope would also meet this requirement of a high resistance, but will also make it significantly harder to read results.
Resistor
The other decision that I had to make about the circuit was the inclusion of the variable resistor (which I am using a resistance substitution box to replicate). There are a number of reasons for this. The alternative circuit is below:
Firstly, there is the safety reason. In this circuit, if the LDR is placed in bright light and the resistance decreases dramatically; and the ammeter has a lower resistance, then there will be a very low resistance, and hence a very high current; potentially draining the battery, and damaging the ammeter and the LDR.
Secondly, there is also an issue in what I have to measure. In this circuit, I would have to measure the current of the circuit, as with only one component, all of the voltage will flow through that component despite its resistance (which can easily be shown via potential tracing) In a circuit where I am using a 12V supply, with a potentially high resistance, the current is going to be very small. This means that there is low percentage accuracy in what I achieve. Also, because of an ammeter’s resistance, when I place the ammeter in series with the LDR it could load the result for bright lights.
The final problem is sensitivity. With the resistor in the circuit, I am able to alter it in order to increase the sensitivity of the results that I get. With this circuit, however, that is not possible.
Since I have decided on the existence of the resistor, the next step would be to work out the value. Since I am using a resistance substitution box, I am limited to certain values. However, given the values of the resistor that are possible, and the EMF of 12V which we would achieve for a perfect battery, I can form the following formulae for the output potential difference, in terms of the values of resistance in the LDR, R. Firstly, I will work out the formulae for orders of magnitude, and then I will be able to further narrow it down.
Naturally I will have to measure it for my LDR, but internet reports on the internet seem to suggest that the intensity of light emitted from a 60W bulb is approximately 50 lux. Therefore, the intensity that I would be interested in is the value of resistance from 25 lux downwards. This graph, from seems to indicate that the resistance in the values that I need will be between 10 and 0.1 kΩ
As such, I am going to plot a calibration curve showing how equal changes in light intensity affect the voltage output over my desired range for each of the values I can choose from. The way values for resistance were calculated were by approximating the graph above with a regression line y = 100x-0.76
From this graph, you should be able to see the best resistor to pick. Clearly the two lower values of resistance will be ineffective. Because we are using this resistor where the intensity is much higher than 1kΩ then these two resistors will be loaded to easily. The other two resistors are much trickier to choose between. The former has much greater sensitivity over the lower end of our range, but lacks this sensitivity over the higher end of the range and also is very non-linear. The 10000Ω resistor is not as sensitive, but has constant sensitivity throughout.
However, there are two values between these on the resistance substitution boxes, so if we plot a graph for these values of resistance, we should be able to find out which of these resistors is optimal.
In my opinion, from this calibration curve, the best resistor to use is the 27kΩ value. This is because it is fairly linear making calculations slightly easier, but it also is sensitive over this range, particularly over the lower end, which deals with the problem of a percentage inaccuracy.
Safety
Naturally whenever you are working with electricity, there are problems that one must take care off. There are naturally some problems which are true for all electrical problems:
- Leave electrical equipment switched off when not in use.
- This will be done by simply removing one of the connecting leads which are connected to the cell.
- Always make sure there is some high resistance component in the circuit to prevent any short circuiting
- This is one of the purposes of the extra resistor in the circuit. However, it is slightly unnecessary due to the high resistances and low voltages in the circuit, meaning that there will always be a low current.
- Do not expose any of the circuitry to water, or any other conductive material.
- No water is being used in this experiment, so this should just be a case of being careful when around the sink.
- When using connecting leads, take them out gently to prevent damage, which could possibly break the circuit.
When using light, or light bulbs, there are also some issues that one must take care of:
- The light bulb gets hot, so it cannot be touched.
- This is slightly obvious, but none the less quite painful. It will simply be a case of being careful, but also turning the light bulb off when not in use to prevent it getting too hot.
- Since light bulbs are made of glass, they must be careful not to be dropped.
Since I am using a Polaroid, I must be careful with how I treat that since they are expensive and can be fragile
- Since the Polaroid is plastic, I must not put it too close to the light bulb at its hottest, to prevent it from melting.
- I will put the Polaroid as close to the LDR as possible, in order to not only prevent it from melting, but I also get the largest possible amount of light polarised.
- I must be careful not to insert anything with great force into the Polaroid
- I think the best way to do this is to hold the Polaroid at the edges using a boss and clamp, or possible sticking it in place with plastecine.
Physics Coursework
Using an LDR to detect the intensity of plane polarised light allowed through a Polaroid.
RESULTS
Results Tables
The first table corresponds to the pre-experiment I detailed in my coursework plan, which allows me to work out the resistances and the e.m.f. of certain components.
The second table gives me certain values which allow me to make calculations if I need to take into account of zero errors, for example.
For these two, I am doing a reading at the beginning and the end of my coursework practical which gives me the opportunity to take into account systematic drift, if it is changing over time.
The last table corresponds to my final coursework ideas. I am taking each reading three times, if I have time to remove possible inconsistencies. Taking 18 values 3 times is ambitious, so I have chosen to take a certain set of values (the ones on white rows) three times before I take the values of the grew rows, making sure that I do not have a limited set of values at the end of it.
Preliminary Readings
Actual Experiment
Physics Coursework
Using an LDR to detect the intensity of plane polarised light allowed through a Polaroid.
ANALYSIS
Firstly it is naturally important to be able to work out the intensity of the light as a function of the voltage that I have received. As such, I have made a larger copy of the calibration curve, which you should be able to see on the page before this. Based on the data sheet for the LDR that I found on the internet, I was able to produce resistance as a function of light intensity, and thus I was able to form this graph. Naturally when using a LDR such as this for this purpose, my ultimate aim is to find out a way of measuring angle based on this output p.d. By doing this experiment, I had two different ways to do this:
- By using my data, I could work out a formula for the light intensity let through a polaroid.
- Or, I could get a formula of the internet, and then use my data to comment on the effectiveness of my sensor.
I have chosen to do the latter. As such, on (a website intended to suggest to university lecturers how to include the subject of polarisation), I found the following formulae:
The former is a formula, from what I can gather, used to predict the intensity of an electric field passed through a polaroid. The latter, dealing with the intensity of the light, is what I require. The formula states that the amount of light let through (transmitted by) the polaroid is equal to the amount of light which collides with the polaroid, multiplied by the square of the cosine of the angle between the angle of the direction of polarisation of the wave, and the preferred plane of the polaroid. That is, in my diagram (left), the angle between the orange line (plane of polarisation) and yellow line (preferred plane of the polaroid).
Now, on to my results
The graph on the previous page, and the table of results somewhat earlier should lead you to the conclusion that these results are not what we expected.
What we would expect, given an angle a. Firstly, we need the intensity of the light let through the first polaroid, which should be equal to Iincidence from the formula we downloaded earlier. However, our formula only works with plane polarised light. However, this will be equal to half the intensity of the light that hits it, namely 25 lux.
From here, we can work out the value we expect for the intensity of the light:
From which, using our approximation earlier, of R = 100I-0.76
Then, using the potential divider equation, and a value of 27kΩ for the other resistor, we can work out the value we expect for the voltage:
The reason for the 1000000(25cos2(a)) is as our approximation gives us a value of kΩ, so we needed it to be just in ohms. This formula produces a graph looking something like this:
My results follow the same shape as the ideal results, however, are slightly less sensitive.
I think one of the reasons for this stems from the problem of ambient light. In my initial plan, I talked about using an ice cream tub to block ambient light, and while it blocked some ambient light, there was a problem of reflection:
Because the ice cream tub was shiny, it reflected light that was scattered by the light bulb. However, there is a way to rectify it. Since I have a calibration curve, I am able to work out the intensity of light for each angle. Since I have a result for crossed polaroids, which is supposed to equal zero, the light that has gotten to the LDR must be through ambient light. Hence, we require a reading for 7.30V, which is equal to approximately 9.5 lux. From this result, I am able to calculate the intensity of the light which should have been transmitted. Firstly, let’s work out intensity as a function of the voltage measured.
Therefore, for a given intensity, I, we have the value of our voltage. However, our intensities are too high by 9.5 lux so, we want this new value to be equal not to the actual intensity, but the intensity minus ambient light, therefore, substituting I with I - 9.5, we can work our way back from:
Which we can then change in terms of our angles to:
Physics Coursework
Using an LDR to detect the intensity of plane polarised light allowed through a Polaroid.
EVALUATION
So, after my excruciating mathematical analysis, it is time to talk about just how good the sensor actually was. I will be discussing the following things in my analysis:
- Resolution
- Response Time
- Systematic Drift
- Random Variation
- Sensitivity
Resolution
What is ‘resolution’?
According to , the resolution is “The size of the smallest element that can be separated from neighboring elements.” This means the smallest possible change in the output.
What did I require in terms of resolution?
Just like with sensitivity, it is always important to have a good resolution, as it means that the rest of the results are distinguishable. However, if my experiment were slightly inaccurate, then again, resolution would not be of the utmost importance
Were my needs met?
The smallest change in the voltmeter was 0.01V, which, using formulae worked out in my analysis, gives us a very high resolution, which is good. However, I feel that because I am using approximations so much, the resolution is damaged because our equipment is not sensitive enough to measure this smallest change.
Response Time
What is ‘response time’?
Response time is the time taken for the voltmeter to register the reading that I would like it to.
What did I require in terms of response time?
In terms of response time, I actually wanted a relatively slow response time, in terms of things such as phototransistors. Since I was not using a regulated power supply, it meant that the light was oscillating very quickly and a phototransistor or oscilloscope would have picked up on this.
How did my needs compare with the circuitry?
The response time, it turned out, worked very well. I positioned my light bulb, put the lid on the ice cream tub, and by the time I walked around to the voltmeter, it had registered the value that I required, so I could immediately move on to the next result.
Systematic Drift
What is ‘systematic drift’?
Systematic drift is defined as the change in results that can be achieved, due to something changing over time. In this case, for example, were I doing my experiment in the open air, then naturally change in temperature and ambient light would affect my coursework.
How was my circuitry affected by systematic drift?
Despite there being small fluctuations in my preliminary readings from the start to the end of my coursework, I do not feel this is significant as it is no greater than the fluctuations within the readings themselves. I was careful to stop this happening, however, by taking each reading in succession, then restarting, thereby taking the 0o reading both early, mid- and late afternoon to eliminate possible discrepancies, among other reasons.
Random Variation
What is random variation?
Random Variation is an unpredictable nature to the data, which is due to uncertain or random occurrences.
How was my circuitrHy affected by random variation?
In my circuits, there were no particularly large anomalies; therefore I can hope that there was no major variation. However, there are differences in the data which could be caused for many reasons. Firstly, the amount of ambient light can change depending on whether or not there is shade in the way of anything. Secondly, the conductivity of a wire is not always constant, so may allow a little more through, as shown by the sometimes flickering display on a voltmeter. There is also the fact that I will never be totally exact when measuring an angle, even if I do use totally precise equipment and am very careful, so there will always be some discrepancy.
Sensitivity
What is ‘sensitivity’?
According to , sensitivity is the “measure of the minimum difference that can be detected or viewed.” Thus, “A system with high sensitivity can detect very small temperature differences”
What do I want in terms of sensitivity?
Naturally in any sensor sensitivity is good, because this means that you are able to use it to a higher degree of accuracy. While this is very much appreciated, however, I feel that on my sensor, this is not absolutely vital. Although having a sensitive device is good as it will improve accuracy and precision, it is a little redundant having a device which is more accurate than another part of your experiment.
Is my Light Intensity sensor sensitive enough?
In my experiment with the light intensity, I obtained my numerical results from an approximation from a graph which is not particularly accurate in the first place. Even if my sensor was very sensitive, the numerical results that I will achieve will be made inaccurate when I try to convert them to lux using this graph.
Is my Angle sensor sensitive enough?
For the angle sensor, this is much more important as, although there are some minor inaccuracies, we are doing this experiment much more carefully, and we actually have figures that can back each other up, as shown from the detail in the differing graphs. As such, for this, sensitivity is important. If our results were ideal (i.e. there was no ambient light entering the system) then it is fair to say that it is sensitive, as seen from the Ideal Results graph on page 18. However, as it is, our results are not really sensitive for the lower values and the higher values. Up until 35o, the results all fall within 0.4V of each other, as do the results from 70o to 90o. Thus, in terms of sensitivity, this sensor was not very good. I could have improved this by using either a whetstone network; or by blocking out ambient light more effectively.