Eye

The eye is the primary biological optical organ. It’s useful as an analytical tool in geometric optics.

Construction

It’s made up of a few constituent components:

The eye itself is around 20 mm wide.
The cornea is at the surface of the eyeball. We approximate it as a spherical boundary between two interfaces.
There’s a lens inside.
The eyeball is made up of a liquid called the humor.
There’s also an aperture, the opening of which is called the pupil.
And the retina, which functions effectively as an imaging sensor. It contains photoreceptive cells (cones and rods). The eye is capable of a few key acts:
Adaption — control of the pupil size.
Accommodation — adjustment of the lens’ focal length.

A few parameters associated with our vision:

Object focal length — is around 12 mm. It varies as the eye accommodates, but not by too much.
Near point — nearest position of distinct vision. For a healthy eye, we take it as $d = 25 cm$ .
- In other words, an object at the near point is at $s_{o} = 25 cm$ . This results in a specific image distance $s_{i}$ .
- If we add corrective lenses or contact lenses, this $s_{i}$ is fixed and we find a new $s_{o}$ .
Far point — furthest position of distinct vision. For a normal eye, we take it as $d = \infty$ .

Common conditions associated with the eye:

Myopia (near sightedness) — where the far point is less than $\infty$ . The result is that it creates a blur, since the rays don’t converge on the retina.
- We correct with a divergent lens (concave lens), such that the lens creates an upright virtual image (closer than the real object) that the eye treats as a real object.
Hyperopia — where the near point is greater than 25 cm.
- We correct with a convergent lens (convex lens). The lens creates an upright larger virtual image further away from the eye than the real object.
Astigmatism — where the cornea is asymmetric, i.e., $f_{x} \neq = f_{y}$ . We correct with cylindrical lenses.