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#### Bi-Convex Lenses

This tutorial explores magnification by a simple bi-convex lens. To operate the tutorial, place your mouse cursor on the soldier, then click on the left-hand button and move him back and forth to view different levels of magnification.

For the purposes of this tutorial, we apply the following equation to describe lens action:

1 / f = 1 / p + 1 / q

where f is the focal length of the lens, p is the distance of the object being imaged with respect to the optical center of the lens, and q is the distance of the image to the optical center of the lens.

This tutorial examines what happens to the "real" image of an object as it is moved closer to a simple thin bi-convex lens. At points greater than two times the focal length of the lens, the image of an object is real, inverted, and smaller than the object. At two times the focal length, the image is the same size as the object and is real and inverted. At less than two times the focal length, the image is real, inverted, and magnified. When the object approaches closer than the focal length of the bi-convex lens, it appears to be on the same side of the lens as the object (25 centimeters from the eye). In this instance, the image is magnified and is now a virtual image.

Contributing Authors

Mortimer Abramowitz - Olympus America, Inc., Two Corporate Center Drive., Melville, New York, 11747.

Matthew J. Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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