To investigate the relationship between u and v for a convex lens.

For a focal length of 10 centimetres

u

v

20

20.7

00

0.2

The image is bigger than when the focal length was 5 centimetres but it is still too small. The image is also clearer but is still too blurred. The range is wider but again is not big enough because the differences are hard to measure.

For a focal length of 15 centimetres

u

v

20

70.5

00

29.4

The image is big enough to be easily measured and the image is clear. The range is wide, easy to deal with and easy to measure the difference.

Conclusion

I conclude with the evidence collected in the preliminary investigations and with the evidence shown in my ideal results that the best lens to use for this experiment will be the lens with a focal lens of 15 centimetres. It has the wider range of results and the clearer image.

Second preliminary

My second preliminary will identify the exact focal length of the lens I have chosen to use for our experiment.

The way identified if the exact focal length of the lens I was going to use was to move the screen until there was no image. Because as soon as the screen is in front of the focal length there image becomes virtual. So therefore the last place where there is an image is 14.8 centimetres so the exact focal length of the lens is 14.8 centimetres.

In Conclusion to all the results of all my preliminaries I have decided to use a lens with the focal length of 15 centimetres. I have come to this decision on the basis that the image is clearer and the range of v is greater. However using my ideal results I have found that the range between the lower values of u will have to be small and the range between the lower values of u will have to be larger. For example the lower values will have to be 18-19-21-25 and the higher values will have to be 105-125-145-170-200. This is because the image for the smaller values is much larger and the value of v has a greater gap between each step than the higher values of u.

Diagram

Apparatus

* 12 volt lamp- to produce the light must be right next to the object so the maximum light gets through

* Object- a cross hair shape so it is easily identified and a clear image can be obtained each time

* Convex lens

* White Screen- so image can be clearly seen and observed

* Metre rule- to measure u and v

Method

First collect apparatus noted above. Set up apparatus as shown in the diagram making sure the object and the 12-volt lamp are very close together so the maximum light gets through. The lamp must have gone through a 12-volt power supply. For each value of u make sure the object is u centimetres from the centre of the lens using a metre rule to the nearest millimetre. Once this has been done use a vertical plain white screen to focus the image on. If there is a range of distance where there is an image keep moving the screen until the clearest possible image is present on the screen. Now measure the distance between the centre of the lens and the screen to the nearest millimetre and record the result. Repeat this procedure for all the values of u. Repeat the experiment three times for accuracy. Find an average result and record it. Graph the results in various ways.

Variables involved

Independent variable- the independent variable will be the values of u. I will use a range of 18 centimetres to 200 centimetres. Any greater than 200 centimetres and v gets too difficult to measure because the image is too small. Any smaller than 18 centimetres and the image gets too difficult to measure because it is too large and can not fit on to the screen.

Dependant variable- the dependant variable for this experiment will be the values of v. The wide range of u will mean that there will be a wide range of v for better results.

Controlled variables- the lens must always be kept the same as exact focal lengths of different lenses can vary. The power supply must be kept the same so any slight changes in power can be taken into account. The screen must be kept the same to make sure any slight differences do not take effect on the experiment.

Conclusion

My results prove that the greater the value of u the smaller the value of v is. As I said in my prediction if the values of u two times greater than the focal length of the lens, the image will be diminished. The value for v will be greater than the focal length of the lens, but not greater than two times the focal length of the lens. This has been proven by my results. I also predicted that the values of v less than two times the focal length but greater than the focal length the image will be magnified and the value for v will be greater than twice the focal length. The closer to the focal length v is the more magnified the image and the bigger the value of v. This has been proven by my results. I have found that u and v have a linear relationship. This is shown by my third graph. This shows a way of finding v or u. The only way you can balance this equation is for u to be 0 so therefore where the line crosses the y axis that is where v is.

/v=1/f-1/u.

There were no anomalous results in my experiment. This can be proved by the fact that on all graphs there are no points extremely outside of the line or curve of best fit.

Evaluation

My results are accurate and my experiment went well. There are some problems with the experiment. The first being that even though the object was pushed up to the lamp some light was still escaping. This could mean that the full amount of light is not going through the object therefore changing the distance of v. This problem can be solved by focusing the light so that it only goes through the object therefore increasing the light intensity. A second problem with the experiment is that the object is made of glass and this diverges the rays slightly so when the light reaches the lens not all the light then gets focused therefore changing the length of v. The way of remedying this problem would be to make the object out of a transparent material that would not bend the light. Or focus the light towards the centre of the object so the amount of light that is diverged is cut down. Further tests that could be done are the differences in different types of objects using different materials. Also seeing if the dimming the lights has on the experiment to see if the light intensity makes any difference to the results. The evidence of my results is not quite accurate enough to support my conclusion in full. However this not due to the experiment this is more down to human error. Also interpretation of where the image is at its clearest varies from person to person therefore making my results slightly inaccurate.