Re: what is the far point for a person suffering from hypermetropia?

Light from the outside world enters the eye through the lens, a portion of tissue which can be changed in shape by muscles surrounding the eye. After light rays pass through the lens, they move through the main body of the eye and finally fall on the retina at the back surface of the eye.

People with good vision can use their muscles to control the shape of the lens so that light from very distant objects comes to a focus on the retina, and, with minor adjustments of the muscles, so that light from nearby objects comes to a focus on the retina. These people can see objects at any distance in sharp focus.

People with hypermetropia have a problem: no matter how hard their eye muscles squeeze, they cannot cause the lens of their eyes to grow round enough to bring light from nearby objects into focus on the retina. However, they can cause light from distant objects to come into focus on the retina. Because they can focus on distant objects, but not nearby ones, they are sometimes called "far-sighted."

Now, you ask about the "far point" of vision. What does this mean? I'm not an opthamologist, so I can't say for sure, but the following is my guess.

People with good, normal vision have lenses which come to a relatively flat shape when they relax all their eye muscles. For many people, this relaxed shape of the lens causes light from objects at very large distances to come to a focus -- or nearly come to a focus -- on the retina. That means that it is "easy" to watch distant events, like clouds moving across the sky or people playing in a park far away from you. On the other hand, in order to focus on very close objects, such as the head of a pin held just a few inches away from the eye, these people with ordinary vision must squeeze very hard with their eye muscles to push the lens into the proper shape. It is not easy to hold the muscles steady like this, and often people grow uncomfortable if forced to focus on very close objects for more than a few minutes. [Note added by MadSci Admin: There is what appears to be a correct description of the function of the eye's focussing muscles and fibers here at Wikipedia.]

Now, a person with hypermetropia cannot focus at all on a pin held a few inches from the eye. When they squeeze their eye muscles as hard as they can, they might bring light from objects at intermediate distances to a focus on their retinas; for example, a person might be able to focus on objects five feet away, but no closer. When these people relax their eye muscles fully, so that the lens reaches its flattest shape, light from objects at infinity will _not_ be focused on the retina. In fact, light from no ordinary objects at all will be focused: everything will be somewhat blurry. By squeezing just a bit with their eye muscles, however, people with hypermetropia can bring objects at infinity into focus. In other words, they have to work just a little bit to see distant objects clearly, while people with perfect vision can see those objects with no muscular effort at all.

You wrote: .. then does its far point increase? is its far point beyond infinity?

It's not clear to me what the phrase "beyond infinity" means, but perhaps one could make the argument: light from nearby objects diverges as it moves towards our eyes, light from more distant objects diverges less, and light from objects at infinity doesn't diverge at all (the rays are parallel). An object "beyond infinity" should have light rays which converge a bit as they approach our eyes. If you agree with this line of reasoning, then you could say that a person with hypermetropia does indeed have eyes which, in a relaxed state, will focus "beyond infinity."

The only way for a person with hypermetropia to focus on distant objects with totally relaxed eye muscles is for him to wear some sort of eyeglasses with slightly CONVERGING lenses. A magnifying glass is an example of a converging lens: it brings parallel light rays to a focus. The problem with a hypermetropiac eye is that the lens is a bit too weak to bring parallel rays to focus on the retina. By placing a slightly converging lens in front of the eye, the parallel light rays from a very distant will start to move towards each other a bit before they reach the lens of the eye. That means that the eye's lens doesn't have to do all the bending to bring them to a focus on the retina.