Notes by Dr. Optoglass: Eye Geometry

Topics Covered:

  • The Emsley model of the Eye
  • The Focal Length the Eye
  • The Total Retinal Area of the Eye

The health of the eye seems to demand a horizon. We are never tired, so long as we can see far enough – Ralph Waldo Emerson

The problem with drawing the geometry of the human eye is that it varies from individual to individual, and from moment to moment, depending on various factors. Since these notes are intended for videographers, cinematographers and photographers, it is not important to get into the more complex eye models.

For our purposes, we will stick to one of the widest known and simplest – the Emsley Reduced Schematic 1952. We will also ignore many of the eye’s imperfections as far as geometry is concerned and assume everything is straight and perfectly spherical. The results don’t very much as far as we are concerned, but if you seriously want to study the eye and make more precise calculations, you’ll need to adopt one of the more complex models.

This is what the Emsley Schematic looks like:
Emsley Schematic
The Emsley model simplifies the eye to a single lens model with one principle point (H) and one nodal point (N). It also disregards accommodation, which as we have seen earlier, is the changing of the lens’ size to focus on objects at different distances.

From the above diagram, we can see clearly that rays from infinity focus on the fovea, and therefore the focal length of the eye is 22.22mm. But in reality, since the eye accommodates, one could say that the focal length really varies from 16.67mm to 22.22mm. This is why, depending on the textbook or website you are reading, you might find values within this range.

Total Area of the Retina

The eye is almost a perfect sphere, and for all intents and purposes we can consider it such. Therefore, if we consider the diameter of the inner eye to be 22.22mm, the total area is approximately 1550 square mm.

The retina spans around 72% of this area, so the area of the retina is 1116 square mm. Since we see a little more horizontally than vertically (we’ll get to that soon), we can assume the ‘mapped’ area of the retina to be an ellipse rather than a sphere.

That’s what we’ll do next.

Takeaways:

  • The simplest model of the human eye is the Emsley model.
  • The focal length of the human eye can be said to be between 16.67 and 22.22mm.
  • The total area of the retina (assumed to be an ellipse when mapped) is approximately 1116 square mm.

Links for further study:

Next: Angle of View and Aspect Ratio
Previous: The Human Eye – Part III