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Proving the lens formula.

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Jack Webdale        02/05/2007     Page

Proving the lens formula

Background information

When light passes from air to a denser material it slows down. In a concave lens the light has to travel further through the middle then through the sides. This has the affect of pushing the waves back in the middle and forward around the edge therefore effectively adding curvature to the wave. A similar thing happens when passing through a concave lens but obviously vice-versa, taking away curvature of the wave.

The curvature that the lens adds or takes away is the Power of the lens, measured in dioptres. P=1/f, P is the power of the lens and f is the focal length. The focal length of a lens is the distance from a lens to its focal point, which is where the image of a distant object is formed. The shorter the focal length the more powerful the lens.

The following formula is what I am going to attempt to prove that it is valid. It is used to give the focal length, and hence where the image is focused.


Where v is the distance from the lens to its focal point, u is the distance from the object to the lens and 1/f is the power of the lens. This follows from the above, the power shows how much curvature is added to the wave. As a wave moves further away from an object the curvature of it decreases.

This formula may also help me with my progress, as I can use it to calculate the magnification of the lens.

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Before I begin the real experiment, I have chosen to perform a preliminary experiment to discover a suitable range of distances I will get results from. I will also have an idea of the power of the lens, so I can judge it’s minimum and maximum distances to get a clear image on the sheet. To do this I will set-up the apparatus as shown in the diagram of apparatus, And I have chosen to make the Object and the lamp a constant position, due to the wires etc and difficulty of shifting it about all the time. Therefore, the Lens and the image sheet are the elements that I will move to focus the image.

Preliminary research

I began with a crude test, to get an approximate result for the focal length of the lens. I simply got a piece of paper, put it against a ruler, and with the lens; I placed it in front of a window, and focussed the image on the paper. I then had a measurement of approximately 15 cm. This would help me greatly in my experiment, as it would indicate immediately any results way off the mark, considering the variables and errors. I then also set up the apparatus as shown in the diagram, and used them to determine what distances I would use in my experiment. I placed a metre rule on the bench, and put on one end, the screen that the image would focus, and at the other, the object. I decided that I would not exceed this Object to Image (U – V)

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1/v = (-1)1/u+1/f. From this statement the gradient of the line is always –1, and this is always the case whatever the reciprocal of the focal length. Also, due to the –1 gradient, the X-axis intercept is also the reciprocal of the focal length. With the graph, I can determine the experiment was successful, as the straight line travels through both axis and at almost the same points. On the Y-Axis 1.167cm and on the X-axis 0.066cm. They both give a focal length of approximately 14.9cm

Knowing that the focal length is approximately 15cm, I can conclude that my experiment was successful, and thus proves that the lens formula 1/U + 1/V = 1/F is valid.

I decided not to put error bars on my graph, as I was not using the whole values of v and u, where I knew the errors spread over a 0.5cm distance for each measurement taken. However, even though I took middle values of v, it is still evident that errors took place. If I were to repeat the experiment, I would choose to take two values of u, the object distance as well as v then take the middle value. This may also reduce the chance of inaccuracy due to the human eye. There are little ways in which I could improve this experiment, except take many readings of a result, then take an average value. Doing this for every measurement taken, however, would be very time consuming, and if one reading happened to be far out, the average would not be that accurate.

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