Graphs for convex and concave lenses

(Real is positive sign convention)

Figure 1 shows a graph where the reciprocal of the image distance is plotted against the reciprocal of the object distance. The graph is a straight line that intercepts both axes at 1/f where f is the focal length of the lens. Since the object is real this graph is for a convex lens.

Figure 2 shows a graph of the object distance plotted against the image distance for both convex and concave lenses. Both real and virtual objects and images are shown.

Enlarged view of an object distance (u) against image distance (v) graph

The focal length of the lens is 10 cm.

The graph is completely symmetrical so that when u= 2f v also equals 2f.

Minimum distance

The next graph shows the distance between the object and image (u+v) plotted against the object distance (u) (it could equally well have been v).

The minimum value for (u+v) is 4f when u=v=2f. This means that no image can be formed with a convex lens of focal length 10 cm if the object and the screen are closer than 40 cm.