If we assume a lens has no thickness, the following equation relating the focal length f, the object length u and the image length v can be derived:
The following points must be noted.
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If either of u, v are imaginary then the corresponding values of u, v are negative.
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The value of f is positive for a concave or converging lens and negative for a convex or diverging lens.
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u or v are negative if rays of light must be constructed back to the position of the object or image. It is possible for an image to have a negative value.
Example:. The diagram below illustrates the formation of an image by a concave or converging lens. The object is further from the lens than the focal length and real. The focal length f is also real because the lens is concave.
If f=20 cm and u=50 cm,
