size, of the image. For now we will consider the case of a thin lens, so any references to distances relative to the lens are to the center of the lens. There are more complicated rules for studying image formation for thick lenses, which will not be needed here. In addition to the focal length $f,$ the other important parameters are as follows.

$d_o$ : The object distance is the distance from the object to the lens.

$d_i$ : The image distance is the distance from the image to the lens.

$h_o$ : The object height is the height of the object measured.

$h_i$ : The image height is the height of the image.

For the heights, we treat the positive direction to be up$,$ or above the principal axis. The object distance is always positive, ${?}^2$ while the image distance is positive if it is to the right of the lens, and negative if to the left.

Consider the following diagrams shown below which each show the principal rays $1$ and $3$ coming from the same object a distance $d_o$ from the lens. The shaded triangles in each diagram are similar to each other. ${?}^3$

$f,d_i-f.$

Use the similar triangles in the figure above to relate the image height $h_i$ to the object height $h_o$ in terms of $d_i$ and $f.[$Note that $-h_i$ is a positive number because the image is below the principal axis, so