Field of view inversions

    Caption: A schematic diagram of a Porro prism viewed in cross section.

    Features:

    1. A Porro prism (in cross section as seen in the diagram) is a right-triangle isosceles triangle: i.e., is a right triangle with two 45° angles.

    2. The common usage for a Porro prism is to give 1 total internal reflection using the long side of the prism (as illustrated in the diagram) or to give 2 total internal reflections using the 2 short sides of the prism.

      Total internal reflection reflectivity is usually high compared to ordinary mirrors (see Wikipedia: Total internal reflection: Applications). The higher the reflectivity, the less light is absorbed in the reflection process.

    3. In the diagram, the reflection is, in fact, a plane reflection with the plane being the long side of the prism.

      The reflection plane is perpendicular to the symmetry plane of the prism which is also the plane of the diagram.

    4. The plane reflection plus the rotation of the observer (illustrated by an eye) results in the peculiar mirror inversion the observer sees. It's mirror inversion around the horizontal diameter of the field of view (FOV) as the observer would see it.

      So A is above B without the Porro prism and B' is above A' with the Porro prism.

      Of course, the observer could put A' above B' just by rotating their eye around the vertical by 180°.

    5. The plane reflection inversion is actually the intrinsic inversion independent of the observer orientation. It is a front to back inversion about the reflection plane. The behavior of plane reflection plus observer orientation giving mirror inversion is explicated in figure optics_reflection_plane.html.

    6. Porro prism are used in some star diagonals such as those that come with Celestron C8 telescopes.

      One could use a plane mirror to do the reflection in a star diagonal. But the high reflectivity of the Porro prism usually makes it the preferred choice.

    7. A Porro prism (or something similar) that uses the short sides to create 2 plane reflections is used in some binoculars.

    Credit/Permission: © David Jeffery, 2015 / Own work.
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