Thursday, February 2, 2012

A Simple Imager

One can create a simple model for the eye by treating it as a camera with a variable focal length. The image distance is fixed at 2 cm and the focal length required ranges from 2 cm for an object at ∞ and 1.8 cm for an object distance of 18 cm from the lens.

We can solve the thin lens formula for the focal length in terms of o and i.

Assuming an image distance of 2 cm one can plot the required focal length as a function of the object distance.

If one looks at an object 1 cm in diameter at various distances from the imager its image will be 20 μ, 200 μ and 2 mm for 10 m, 1 m and 10 cm respectively. The symbol μ represents a micron or 10-6 m. The results show how small images in the human eye can be. The acuity of the model compares well with that of the fovea of the eye with a maximum of about 50 cones per 100 microns.

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