The equation can also be used for curved mirrors a s well as lenses. Note that converging lenses and mirrors have positive focal lengths, whereas diverging lenses and mirrors have negative focal lengths.
- Rough preliminary work proposed
The preliminary work that I have proposed is to look carefully at a camera and to work out how it gets the rays to a focus at a particular point, and where that point is. I will look at the system in lots of
detail which will ensure that I know how rays work, and how they are brought to a focus, and what causes the rays to be brought to a focus at a particular point.
I know that in a camera there is a convex lens, which is used to form a small, inverted real image on photographic film. The film is usually kept in darkness, and it contain a light sensitive chemical called silver bromide. When you press the button, a shutter in front of the film opens and shuts again. This exposes the film to light for a brief moment only. Different intensities and colours of light across the image cause varying chemical changes in the film. This can later be developed, fixed and used in printing a photograph. We have to look carefully at a camera to work out how it gets the rays to a focus at a particular point, and where that point is.
- Rough preliminary work done
The preliminary work that I have done, is to check the amount of light reaching the film. This is controlled by the diaphragm. This alters the aperture of the hole through which the light passes. Increasing the aperture lets more light into the camera, but it can also lead to some focusing problems. High quality cameras have expensive multi-element lenses which produce sharply focused images even at wide apertures.
When I used the camera I wondered how it worked and how the rays were formed on the screen, so I took the camera apart. I discovered that the rays which entered the camera went through a convex lens, this causes then to diverge, and be brought to a focus at a particular point called the focal point. The focal length is the distance from the lens to the focal point.
- Outcome of rough preliminary work done
I discovered form the preliminary work that I did, all the rays from one point going through an optical system will meet at one point. To avoid blurring this is where we must put the film on the screen.
- Conclusions from rough preliminary work
From the preliminary work, I can conclude that a camera has a convex lens, which brings the rays to a focus. The rays going through the system, are all bought to a focus at the same time, and the distance is called the focal length. The film must be placed at the focal point, to avoid the picture form being blurred.
- Detailed theory and how it is relevant
I know that cameras can give us a sharp image, because of rays which start at one particular point go through the optical system at one point. This creates am image on the focal point. I know that every lens has a focal lens. Concave lenses are very similar to concave mirrors, in the way in which they form images, they have the same properties to form images. A concave lens forms an upright,
virtual image of any object placed in front of it. The image is always smaller than the object and closer to the lens than the original image. Changing the position of the object changes the position and size of the image which is formed, but the basic form of the diagram stays unchanged.
For distant objects, the film must lie at the principal focus of the lens if the image is to bein sharp focus. For closer objects, the distance between the lens and the film must be increased. Accurate focusing of the image is achieved by screwing the lens backwards or forwards in its holder to suit the particular object distance.
- The independent variables that might be relevant
The formula that I worked out was, 1/u + 1/v = 1/f . The problem therefore involves three variables (v, u and f). V is the dependable variable, which makes v the function of u and f. In turn f depends on the shape of the lens, and what the lens is made of.
- The independent variables I shall vary
As v is the dependant variable, the independent variables I will have are, u and f. I would like to investigate how v depends on u and f, and I will several convex lenses of different of different focal lengths. I will change u and f separately.
- Ensuring a fair test
A fair test involves changing independent variables one at a time, or separately. We can then be sure that changes in the dependant variable are caused only by changes in the independent variable
that we are changing. To ensure a fair test I will only change the independent variables, and I will make sure that they are changes one at a time, or separately.
e.g. When we will be dealing with a particular lens, f is constant therefore any change in v will be caused only by changes in u.
Subsequently I may repeat the experiment using several lenses. If I do this I will keep u fixed, in order to discover the dependant of v and f.
- Equipment choice for precise data
- I will have use a white screen, not lined or graph paper, this will ensure that the image will be brighter, and the brightness will be judged more easily.
- I will use my eyes to see the brightness and the sharpness of the image. I will also keep one eye shut, so that the image is clearer.
- For large v values I will use a piece of string, which will stretch all the way from the lens to the rear wall. I will make sure that the string is not stretchable and will not effect the values that I record.
- Procedural strategy proposed for precise data
I will allow v values ranging form 0-8 metres. For each lens I will take 10 pairs of readings ( of u and v) thus making sure that the data is reliable and accurate. I will process these readings immediately, to check that they are consistent. Any anomalous readings I will repeat so that I have accurate readings and data. How do I know when the image is sharp? I will use my eyes to see if the image is clear, and if when I move the lens, if the image gets clearer or sharper. If it does then I will continue to move the lens until the image is as clear as it will get. Is there a range of acceptable definition? I’ll move the object a little to check this out. This will be me my uncertainty of u.
e.g. u = 7.9cm ± 0.2cm.
I will make sure that the lamp is very bright, so that the image is bright and easy to see.
- Safety of persons and equipment
I will make the room dark, so all the bags will have to be under desks. I will also make sure that there are no objects on the desks or floor that people could touch and possibly hurt themselves by touching or knocking.
- Special measurement routines for precise data
I will measure from the centre of the lens. I must allow for the lens thickness. I will repeatedly check that the screen is not crumpled, so that the image will be crumpled and will not look sharp. When I view the image I will make sure that I have one eye shut, this will make it easier to see the sharpness of the image.
- Repeated readings proposed
For each lens, I will record 10 pairs of readings. I will repeat them myself and invite people to do the same readings to check that mine are accurate. If there is agreement it suggests that the data I have recorded is reliable.
I will look at my data graphically, so that I can check the data points on the graph. If they lie on a smooth line with little scatter, I will be inclined tot think that the reliability is good.
- Analysis proposed linked to theory
The analysis that I proposed to do is to, have a lens, with a screen of white paper, and a light. I will change the independent variables of u and f at separate times, this will ensure that I will be able to work out the dependant variable of v.
When I draw the graph of my results I will use the formula u + v / uv = f . This will ensure that I will have a straight line, which makes it easier to check and evaluate.
