Optics of the eye

Principle

There are a number of refracting surfaces in the eye, with the important ones the anterior surface of the cornea, and the lens.

Of these the cornea, because of the large difference in refractive index between air (1.0) and corneal tissue (1.37) is the more powerful, with a typical power of about 40 dioptre (dptr). The lens in the relaxed (not accommodated) state has a power of about 17 dptr. Accommodation may increase this, by about 14 dptr in children, less with increasing age. 

These several components may, by approximation, be thought of as equivalent to a single ideal lens. The resulting simplification is the reduced eye (see Fig. 1).

Location and strength of the ideal lens vary in literature but the following is a good approximation. Its principal plane is situated just behind the iris and so its distance to the retina (the axis length) is 20 mm, and its power is 50 dptr.

Fig. 1 The educed eye

Note that 50 dptr is less than the sum of the powers of cornea and lens. They are not close enough together for their powers to be additive. In the normal, resting reduced eye, somewhat arbitrarily, 36 dptr are due to the cornea and 14 dptr to the lens.

Both the axis length and the principal plane power are abstractions. However, the quantity power - 1/axis length (in m), the "net power" of the reduced eye, is concrete and measurable. To see this, note that the eye will see a sharp image when the image is focused on the retina, i.e. when the image distance is equal to the axis length. Replacing axis length by image distance and applying the lens formula (see Light: the ideal lens), under the condition of a sharply seen object, we find that the net power (in dptr, m^-1) is:

φ = 1/f = 1/d_object

The difference 1/d_object – 1/axis length directly gives the correction. Negativity means myopia and a negative lens equal to the absolute difference. With this correction the myopic eye will see clearly at infinite distance (the Foucault's principle, see Retinoscopy).

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More precisely the eye should by presented as a system with two principal planes (see The Ideal Lens), as illustrated in Fig. 2. It appears that the two principal planes are only 0.3 mm from each other. This is caused by the small differences between most eye media and the small refractive contribution of the lens. Therefore, for most applications the reduced eye with one principal plane is adequate.

Fig. 2 The reduced eye with two principal planes.

The power of the reduced eye of Fig. 2 is:

φ = 1/f = 1/0.017= 58.8 dptr or φ = 1.33/(0.024 – 0.0013 – 0.0003) = 59.4 dptr,

where 1.33 is the mean refractive index of the eye.