In our eyes, most of the focussing work is done by the cornea at the front of the eye. The lens only contributes about ten percent, and is just there to fine tune the focus for sharp images at different distances. When we are underwater though, the difference in refractive index between the surrounding water and the tissue of the cornea is much lower, so a given curvature doesn’t bend light as much. Our eyes are optimised for air and our lenses can’t adjust enough to make up the difference, so our vision is blurry underwater unless we wear goggles.
Fish can see clearly because their corneas are more spherical (a ‘fish-eye lens’) and so can focus more strongly, but this makes fish short-sighted in air. Penguins need to be able to see clearly on both land and underwater, so neither cornea shape will do. Instead they actually have corneas that are much flatter, even than ours. This takes almost all the focussing power away from the cornea and nearly all the work is done by the lens. To form a sharp image, the penguin’s eye must be able to change the shape of the lens a lot more than the lenses in either fish or human eyes do.
Penguins’ lenses are softer and the muscles can squeeze them up against the opening of the pupil. This makes them bulge outwards in very rounded shape. Diving birds use this technique as well but penguins are the masters.