# If you are told an image is real and you know it was made by a single optic (either a lens or a mirror), which of the following must be true?

The image distance is positive. The image distance is negative. The image is inverted. The image is upright. The image height is positive. The image height is negative. The magnification of the image is positive. The magnification of the image is negative. It was made by a converging optic. It was made by a diverging optic. The focal length of the optic is positive. The focal length of the optic is negative.

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 Is this homework or are You going to test our knowledge? – Georg Apr 9 '11 at 21:18 Too localized perhaps? – David Zaslavsky♦ Apr 9 '11 at 23:11

All those statements are potentially true. None of them is logically necessary. This can be seen from the lens equation $\frac{1}{d_{o}}+ \frac{1}{d_{i}} = \frac{1}{f}$, remembering the convention that the focal length is positive for a converging lens and negative for a diverging lens. All that remains is to draw a few ray diagrams to get a sense for the inversion of the image. (or using the derived result${}^{1}$ $M=-\frac{d_{i}}{d_{o}}$, where M is the magnification of the lens.
${}^{1}$It's easiest to get THIS result from noting that the ray from the top of the object will pass through the center of the lens undeflected, and also gets mapped to the top of the image. So the ray going from the object to the lens creates a similar triangle to the one formed going from the lens to the image.