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Determination of Focal Length of Convex Lens using u–v Method

The relation between u, v and f for a convex lens is,

v-1 + u-1 = f-1

Using the proper sign convention, u is negative, u negative, v and f are positive. So we have,

218_convex lens derivation.jpg

Comparing with y = mx + c, graph between v-1 & u-1  is negative with slope –1 and intercept  f-1 .The corresponding graph is as shown in figure.

Proceeding in the similar manner as discussed in case of a concave mirror the focal length of the lens can be calculated by measuring the coordinates of either of the points A, B and C.

1676_u v graph.jpg

u–v Graph
The u versus v graph is a hyperbola as shown in figure. By measuring the coordinates of point C whose coordinates are (2f, 2f) we can calculate the focal length of the lens.

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