The Mathematics of Lenses tvwo class 3
Ray diagrams can be used to determine the image location, size, orientation and type of
image formed of objects when placed at a given location in front of a lens. The use of
these diagrams were demonstrated earlier. Ray diagrams provide useful information
about object-image relationships, yet fail to provide the information in a quantitative
form. While a ray diagram may help one determine the approximate location and size of
the image, it will not provide numerical information about image distance and object size.
To obtain this type of numerical information, it is necessary to use the lens equation and
the Magnification equation. The lens equation expresses the quantitative relationship
between the object distance (do), the image distance (di), and the focal length (f). The
equation is stated as follows:
(Dutch books: 1
, where v = voorwerpsafstand and b = beeldafstand)
The Magnification equation relates the ratio of the image distance and object distance to
the ratio of the image height (hi) and object height (ho). The magnification equation is
stated as follows:
(Dutch books: N
, where BB`= hoogte beeld, and LL`= hoogte voorwerp)
These two equations can be combined to yield information about the image distance and
image height if the object distance, object height, and focal length are known.
Now try to do the problems on the next page!