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Form 4 Physics online lessons on thin lenses

Determining focal length of a converging lens

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Answer Text:
Determining focal lengths:
1. Determining focal length of a converging lens
Experiment: To determine the focal length of a converging lens using the lens formula.
Procedure.
1. Set up the apparatus as shown below

2. Place the object at reasonable length from the screen until a real image is formed on the screen. Move the lens along the metre rule until a sharply focused image is obtained.
3. By changing the position of the object obtain several pairs of value of u and v and record your results as shown.

Discussion:
The value $frac{u v}{ u + v}$ is the focal length of the lens and the different sets of values give the average value of ‘f’.
Alternatively the value ‘f’ may be obtained by plotting a graph of $1 / v$ against $1 / u$ .
When plotted the following graph is obtained.
Since $1 / f = 1 / u + 1 / v$ , at the y-intercept $1 / u$ = 0, so that $1/ f = 1 / v$ or f = v.
The focal length may therefore be obtained by reading off the y-intercept and finding the reciprocal. Similarly at the x-intercept, $1 / v$ = 0, therefore
$1 / f = 1 / u$ or f = u hence the focal length can also be obtained by reading off the x-intercept and finding the reciprocal.