## 20130111

### Presentation: thin lens equations

So far we have used ray tracings to analyze images created by converging and diverging lenses. In this presentation we will qualitatively analyze lenses using the thin lens equations.

First, relating the locations of the object and image for a lens.

The convention in ray tracings is for light to move from left-to-right, with the object located to the left of the lens, and the image (if real) would be located to the right of the lens. For this case the object distance do and the image distance di would both be positive. If the image is virtual, then it would be located to the left of the lens, and the image distance di would then be negative.

The thin lens equation relates the object distance do, image distance di, and lens focal length f.

The focal length f is defined to be positive for a converging lens, and negative for a diverging lens, and do and di follow the sign conventions discussed above. (For the sake of completeness, there is such a thing as a "virtual object," but will not be considered in this course.)

Second, linear magnification.

Linear magnification m is defined as the ratio of the image height compared to the object height. The linear magnification can be either positive or negative, depending if the image is upright compared to the original object, or inverted compared to the original object. This ratio of image versus object heights is also equal to the ratio of image versus object distances (with an obligatory negative sign).

So for an upright image, m is a positive quantity, regardless of being enlarged or diminished.

And for an inverted image, m is a negative quantity, again regardless of being enlarged or diminished.

The absolute value of linear magnification m is greater than 1 if the image is enlarged, regardless of being upright or inverted.

And for a diminished image, the absolute value of linear magnification m is less than 1 if the image is enlarged, regardless of being upright or inverted.