"An investigation into the factors affecting a lens."
Lenses
"An investigation into the factors affecting a lens."
Aim: To investigate the relationship between the distance between a lens and an object, and the distance a screen must be from the lens in order that it displays a focused image of that object on the screen.
Background knowledge:
In order to plan and my investigation, I am going to research the different types of lenses and the factors affecting them, and their uses. I hope that this will help me to plan and carry out a more successful investigation, and also help me formulate a hypothesis and understand my results better.
Lenses are optical devices that affect the passage of light through them by refraction. They can be made from almost any transparent materials, but the most common is glass. Lenses are used extensively in optical instruments such as cameras, telescopes and all sorts of projectors.
There are two main types of lens, convex (converging), and concave (diverging). Convex lenses are thicker in the centre, thinning out towards the edges, while concave lenses have thick edges and thin centres. A concave lens will refract light inwards, thus creating a smaller image while a convex lens will do the opposite, creating a larger image.
All lenses have an optical centre, where light can pass without being refracted and the principal axis of the lens passes though this point. At this point on the lens, the glass (or other material) is flat on both sides of the lens. When light passes through the lens anywhere except the optical centre, the rays are refracted, either towards the principal axis, in the case of a convex lens, or away from it, in concave lenses.
Lenses also have a focal point, which is the point at which the refracted rays converge with one another. In a convex lens this is on the opposite side of the lens to the object, but in a concave lens, where the refracted rays are directed away from the principal axis and will therefore never meet, the focal point is on the same side of the lens as the object, and is located by following the lines of the refracted light rays. This is a virtual focal point.
Because of this, a convex lens can be used to project an image onto a screen, the sort that would be used in a cinema projector, forming a "real image" which can be seen. A concave lens does not form any such image, it makes only a "virtual image" which cannot be displayed on a screen as it will be on the same side of the lens as the object.
In order to construct a ray diagram, you need to know the focal length of the lens you are using, as it will tell you where the rays must meet. To roughly estimate the focal length of a lens you can project an image of a light source, say a window, through a lens onto a card. The distance from the lens to the card, when the image is in focus gives the focal length. Ray diagrams are a simple way of demonstrating how light passes through a lens, and also why the effects happen.
Ray diagrams:
Convex Lens
Concave Lens
Considering the facts outlined above, I will have to use a convex lens in this investigation, as I require a real image - I must be able to see the image in order to investigate it. A concave lens would not create a real image and using one would make my investigation impossible to conduct.
I will be using a 10cm lens in my investigation, as it is one I have readily available and the focal length is not of importance so long as it remains constant. As a preliminary experiment, I checked the length of my ...
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Considering the facts outlined above, I will have to use a convex lens in this investigation, as I require a real image - I must be able to see the image in order to investigate it. A concave lens would not create a real image and using one would make my investigation impossible to conduct.
I will be using a 10cm lens in my investigation, as it is one I have readily available and the focal length is not of importance so long as it remains constant. As a preliminary experiment, I checked the length of my lens using the method described above and found it to be 10cm. I need to know this information so that I can construct ray diagrams and also ensure that the object and screen are kept beyond the focal point during the experiment, to produce a real image.
Variables: The following factors could affect a convex lens:
* Material of lens used.
* Focal point of lens used.
* Light levels.
* Size, shape and possibly colour of object used.
* Eyesight of observer.
* Angle of lens in relation to screen and object.
* Colour and surface of screen.
As I will only be investigating the effect of altering the distances between the lens, the object and the screen, I must ensure that the other factors are kept constant throughout.
The lens used will obviously affect the results, as different lenses have differing focal points, and varying the focal points would defy the objective of this investigation. Materials could also affect the passage of light through the lens, distorting or altering the image. To ensure that the test is kept fair I will use the same lens throughout. As I have said, I have chosen a lens with a focal length of 10cm for this experiment.
The light levels used will affect the way the image appears on the screen, and a brighter light source could make the image appear clearer, and therefore affect the point at which I judge it to be most focused. Background light could also change the point at which the observer thinks they see the image as properly focused. I will therefore use the same light source throughout to try and keep these factors as constant as possible. I will keep the light in the room as constant as I can by keeping all windows covered and blacked out.
The object must be kept constant, as varying this could have a serious effect on the experiment. Some objects may appear more focused than others, depending on their colour, texture and size and therefore the objectmust be the same throughout the experiment
The eyesight of the person observing is a key factor in the experiment as this is the factor that determines the point at which we consider the image focused. The same person must therefore observe the experiment each time to minimise any variation in judgement. They must also ensure that they don not call the image as "focused" when it is nearly focused or "good enough" they must be precise.
The angle at which the lens is held will also affect the experiment. If the angle is varied, the rays of light will pass through different parts of the lens each time, the level of refraction will therefore vary, and the results will be inaccurate.
The final factor is the surface and colour of the screen. A shiny surface would confuse the observer with reflections, especially if it were not flat while a "bobbled" surface would cause the image to distort and therefore the point at which it focuses would be harder to determine.
Hypothesis: The larger the distance between the lens and the object, the smaller the distance between the lens and a projected, focused and real image onto a screen. This is because, as shown in my measured ray diagrams (entitled "Prediction"), the focal point is shown to be farther away when the object is closer. The reason for this is that when an object is near a lens, the rays must strike the lens at a greater angle, therefore the effect of diffraction is less and the rays will take longer to meet on the other side of the lens. This can be better shown in a diagrammatic form:
Close object:
Distant object:
Prediction: I can use the following formula, which relates to my hypothesis, to generate a set of predicted results for my experiment. This is a quantitative prediction:
/v = 1/f - 1/u
v = the distance between the lens and the image.
f = the focal length of the lens.
u = the distance between the lens and the object.
In order to use this formula I need to know the values of f and u. For between the lens and the object I will use the lengths listed below- these are the u values for this experiment. I know the focal length of my lens, 10cm - this is my f value.
"u" values "f" value
1cm 10cm
2cm
3cm
4cm
5cm
Using the formula I gained the following predicted v values for a lens with a focal length of 10cm, using the u values shown above.
U value (cm)
/V
V value (cm)
1
0.009091
10
2
0.016667
60
3
0.023077
43
4
0.028571
35
5
0.033333
30
Using these forecast results, I will now plot a graph comparing the u value with the v value.
This graph shows a smooth curve, demonstrating a negative correlation between the length of u and that of v. This supports my hypothesis. I will now conduct an experiment to investigate my theory further.
Apparatus:
* Ruler
* Screen of thick white paper
* Photographic slide (as object)
* Lens (focal length of 10cm)
* Lens stand
* Clamp stand
* Power pack
* Ray box
Set-up diagram:
Method: I will set up equipment as shown above and then adjust the distance between the screen and the lens until the image shown on the screen is as clear as possible.
I will record the v value for each of the different u values. I will then repeat experiment thrice in order to ensure accuracy.
Accuracy: In order to ensure that my results are as accurate as possible, I will take care not to alter any of the control variables. Before I conduct the experiment, I will also clean the lens to remove any dirt or grease which could affect the refraction and projected image.. I will conduct the experiment in a blacked-out room in order to facilitate accurate observation of the image. I will conduct the experiment three times to show up any anomalies that may occur.
Safety: There are few safety risks involved in this experiment. Apart from the risk of burning from he lamp supplying the light or damaging vision through looking at the light source, the only other safety consideration is the use of electricity. Care must be taken to ensure that both the power source and the lamp are safe to use.
Results:
I obtained the following results from my tests:
U value (cm)
First run V (cm)
Second run V (cm)
Third run V (cm)
Average V (cm)
1
86
83
83
84
2
53
58
54
55
3
41.5
38
43
40.6
4
34
32
33
33
5
27
31
29
29
These results suggest that there is a negative correlation between the length of u and the length of v. I think that these are fairly accurate results as they all show similar trends and each run-through has produced similar results. I will now plot four graphs using the data obtained.
Conclusion: I can see from these graphs that the u and v are inversely proportional. They have an equation of approximately y=m/x.
By comparing these results with my quantitative prediction, I can see that the values are slightly higher for the quantitative prediction. These are plotted on a graph too.
I can see from this graph that the two curves are similar. The formula for calculating the results is therefore correct in this case. It is interesting to note that the difference between the predicted and actual results is greater the closer the object is to the lens. This is because the nearer you get to the lens; the more changes and inaccuracies affect the distance of the image of the image. This can be seen on my ray diagrams. It is because the angle of refraction becomes much steeper more easily at close ranges.
The reason for the negative correlation between the distance of the object from the lens and the distance of the image from it is that the rays of light must be bent by the lens. If the object is near the lens, the light rays from it will strike the outside of the lens at an acute angle (say, 45o), if the light is bent inwards by the lens by say, 30o then the rays will leave the lens at 75o inwards to it. If the object is far away, the light will strike the lens at a less acute angle, for example 80o. The light would be bent by the lens by 30o and would therefore leave the lens at 110o inwards, a much steeper angle. This can be seen both in the simple ray diagrams and the accurate ray-graphs in my prediction.
I can therefore conclude that my general hypothesis was proven but my quantitative prediction was not accurately met in that the results, although not dissimilar, were not as close as they could have been.
Evaluation: There are a number of possible problems with this experiment that may have caused the deviation of the results from the predicted ones. For example, the angle of the lens in the holder may have varied. This would cause the refraction to be different an would thus influence the results. Although I covered this in my plan, the holder I used was not satisfactory and a different one could be used for more accurate results. Another possibility and, indeed a problem, is the scope for possible human error.
The observer's judgement of when the image is focused is subject to many conditions. Any of these could change, or he could simply see the image differently, with no reason. This problem could be solved with the use of computer sensors and a simple object. The sensors could detect when the line between shadow and light is at its most defined (this indicating focus) and display the results on a computer.
The experiment is also subject to the condition of the lens. Although the lens is supposed to have a 10cm focal point, poor grinding or damage subsequent to its production may change this by a small amount. Although I did check this, the experiment I conducted was not very accurate and subject to the same problems that my main one was.
Grease, dust of small pieces of dirt on the lens could also affect the results, by changing the refraction if the light, much the same as if the lens were of poor quality. Although I wiped the lens before I executed the experiment, I did not clean it before each test so as not do dislodge the lens. Dirt could have built up on the lens as the experiment progressed and grease would not be removed with a simple wipe. If I were using a better stand, I could clean the lens thoroughly with a detergent and polish it without moving its position. This would make the test fairer but would only be of significance if the method of measuring and the other factors were much more precise.
Although I took care to blackout the room I was working in, the light intensity could still vary, both in the background light and also in the light source. I could use a darkroom and light sensors to measure the amounts of light at various points and to make sure that they are all zero. I could also use a sensor to measure the level of light emitted from the source and have a computer automatically adjust it so that the level is constant. A good quality bulb and a steady controlled power source would also be necessary to prevent varying light intensity from the source. Laser light could also be used and would be easier to measure and with computer instruments.
Despite this scope for inaccuracies, the investigation turned up no anomalies and the quality of the evidence is good. I think that the evidence gained from this supports both my hypothesis but the experiment could be repeated with better equipment (mentioned above) and a wider range of lengths. I could also repeat the experiment varying the angle of the lens, and the focal length of the lens to see if they have an effect on the images produced and if so, what the effects are.
Danny Smith 11B