Reduced Schematic Eye
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To make simple optical calculations a Reduced Schematic Eye, based on Gullstrand’s model, was later developed that approximately matches the ocular dimensions but simplifies the calculations by combining all the refracting surfaces into one power and location and all the refractive indices into one.
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In the real eye the cornea supplies 40 D and the lens 20 D of focusing power. In the simplified model they are combined as one focusing unit, located at H, with total focusing power (P) of 60 D. The index of refraction of the inside of the eye is taken as n’ = 1.33. Note total eye length in the reduced model is: 17mm + 5.5mm = 22.5mm.
The Nodal point, N, is the point through which light rays travel undeviated.
The numbers are slightly adjusted so the calculations are consistent.
The radius of curvature of the refracting surface can be calculated as follows, taking into account the interface between air and the eye:
The total length of the eye is calculated from the basic optical formula relating focal distance as the
reciprocal of lens power, and accounting for the index of refraction of the inside of the eye:
This is slightly shorter than the full schematic eye, which is 22.4 mm.
First focal point is calculated as:
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With this formulation we can make the simplified calculations relating object and image sizes.
To see an example go to how big is a 20/20 letter on the eye chart?