Ray Diagrams
Ray diagrams provide an intuitive way to analyze how lenses and mirrors form images. For example, the applet below illustrates ray diagrams for the case of a converging lens. You can move the object around: watch for your mouse cursor to change shape when it is moved over the arrow tip, then click-drag the object to a new location. By moving the object, you can observe both real and virtual images.
The applet below illustrates ray diagrams for diverging lenses. In this case, the image is always virtual.
Lensmaker’s Formula
With the proper sign conventions (see text), the same formula may be used to analyze images formed by thin lenses and mirrors:
where so is the object distance, si is the image distance, and f is the focal length. Negative image distances correspond to virtual images, and positive image distances correspond to real images.
The focal length for a converging optic is defined to be the distance from the optic to point where incoming parallel rays are focused. For a diverging optic, it is negative, and defined as the distance from the optic to the point where parallel rays appear to diverge from (virtual focal point).
Magnification
Let hi = image size and ho = object size. Then
M = hi/ho = -si/so
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Magnifications for inverted images are negative.