An object is 2.3 cm tall, and 5.5 cm from a converging lens. The image is upright and 9.0 cm tall. What is the focal length of the lens?

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The object is 2.3 cm tall, and 5.5 cm from a converging lens. The image is upright and 9.0 cm tall.

The magnification due to the lens is `M = -9/2.3` . In terms of the distance of the object from the lens d, and the focal length f, the magnification is given by `M = f/(f - d)`

Using the values given in the problem and the magnification that has been derived:

`-9/2.3 = f/(f - 5.5)`

=> `-9f + 49.5 = 2.3f`

=> `11.3f = 49.5`

=> `f ~~ 4.38`

The focal length of the lens is approximately 4.38 cm.

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