# Topic 33. Focusing the Lens, Part 2. Bi-Prisms

A second method for detecting when the lens has been focused on the desired object uses a pair of prisms mounted in opposite directions on the image screen.  This configuration is sometimes called a biprism, although that name is also used for other configurations of two prisms that have nothing to do with focusing a camera.

The method depends on the properties of a single thin prism as shown in the following figure.

A user whose eye is looking down through the prism from above sees an object below the prism as if it were located along the straight path shown by the blue line. In fact, the ray that reaches the user’s eye was refracted twice by the prism and actually followed the path shown by the green line. The angle of divergence between the blue path and the green path is a constant value – it depends only on the index of refraction of the prism and on its shape.

If the user is looking at an object located at position “0” then the user actually sees a point on the object that is to the left of the straight line path because the ray that actually enters the user’s eye was refracted as shown. As the object moves away from the bottom of the prism towards positions “1” and “2” the point on the object whose rays strike the user’s eye moves further and further to the left as shown in the figure. The user thinks that the object is sliding to the right, since parts of it that were further and further to the left are coming into the view point which looks to be directly under the user’s eye. On the other hand, when the object moves upward so that it is directly underneath the prism, the difference between the green ray and the blue ray is very small so that the user sees an object point that really is directly on the straight line of sight. (The difference between the blue path and the green path has been exaggerated in this figure by separating the two rays for clarity.)

We now combine two identical prisms of this type with one of them slanted to the right and one of them slanted to the left. We arrange the configuration so that the top half of the object sends it rays through one of the prisms and the bottom half of the object sends its rays through the other one.

As the object moves away from the bottom plane of the prisms, the two halves of the image appear to move in opposite directions, since the prisms tilts are opposite. Conversely, as the object moves closer to the bottom plane of the prism, the two halves of the image move closer together. If the prisms are thin and no too tilted, the two halves of the image will line up exactly with each other when the object plane is exactly at the common base plane of the two prisms.

In practice, the two prisms are located on the imaging screen (this screen is where the main camera lens forms its image while the picture is being composed), and the image on this screen serves as the object for the two prisms. When the image produced by the main camera lens is located exactly on the imaging screen, the two halves of this image transmitted through the two prisms appear lined up. When the image produced by the main camera lens is not focused on the imaging screen, the two halves of the image transmitted through the two prisms are displaced in opposite directions, and the image seen by the user appears to be cut in half at its center with the upper and lower halves displaced relative to each other.

Some imaging screens contain additional very small pairs of these prisms called micro-prisms. Each pair functions in the same way – the image appears to be smooth and continuous when all of the little pieces are not displaced relative to each other and appears to be broken up into tiny disjoint parts when the image is out of focus.