I cannot give you any simple scaling rule, though it certainly is true that usually, small creatures have disproportionately large eyes. The eyes of mice tend to bulge conspicuously.

This applies even more strongly in creatures that when they are adult, have a given size of eye. It is difficult for most designs of eye to grow in constant proportion of size. So for example, small children often seem to be all eyes. It is not so much that one cannot make an eye small enough to fit a baby, but rather that if a baby had small eyes, it would not be easy to grow them larger.

In some insects, such as caterpillars, the larvae actually might be blind, or alternatively have very small eyes, such as half a dozen simple eyes, where as the adult moth might have comparatively huge eyes compromising tens of thousands of component eyes, each as complex as one of those simple eyes. But in such life histories, the entire organ very nearly gets restructured from scratch in between those two stages.

It certainly is true that in a very small eyes there are limits to what one can do with light, but when you see what tiny creatures can have perfectly functional eyes, you soon realise that the limiting factors are not so much the fundamental physics, as the practical structure.

Exactly why squid have such enormous eyes, I do not know. It might well have something to do with their habit of sheltering deep and rising to the surface only at night. But otherr animals have similar habits, so that cannot be the whole story. Squid also are short-lived creatures, so their eyes need not last more than a year or two. Possibly they simply have eyes built on a scheme that permits easier scaling than our eyes, so why not grow them large if it happens to be useful?

Whales however have the normal mammalian constraints, and there is little visual advantage for them to have large eyes, besides which lucky whales live long, and to be lucky you don't want large, vulnerable eyes. In summary, their eyes cannot easily grow large, and they don't need to be very large, and if they did grow large, they would be too vulnerable.

Or so it seems to me.  

Cheers,

Jon

[ Did Jon Richfield sleep in today? ]

Basically, the optics of the eye are not scaleable. The lens has to be a fairly gooey transparent substance, and there are probably few choices of solute in the watery base. If the dilution of the lens material is high (i.e. close to pure water) then the refractive index is probably subject to greater fluctuations. So the physics of refraction dictates the front-to-back eye dimension quite strictly.

There is no gained advantage in a larger eye, and the disadvantages would include more weight, a bigger external area that could be damaged, a decrease in the skull capacity, and a lens that sags slightly under gravity and distorts the image.

Animals with small skulls give up a huge proportion of the skull capacity to have eyes as large as they can. A cat's eyes barely fit in. An owl turns its head because its eyes have no room to rotate in its skull. Smaller animals make do with monochrome vision, poorer resolution, no night vision, or composite non-moveable non-focus eyes.

I did read once that a hawk could read a newspaper from 1000 feet up. Smart hawks they have nowadays - probably South African.