A sharp image needs the light to focus exactly on the retina

1. Two parts of the eye do the converging, the curved cornea at the front, which bends the light most, and the lens just behind it.
   1. The lens is squeezed and relaxed by the ciliary muscles, which is how a healthy eye changes its converging power for objects at different distances.
2. The retina is the light-sensitive screen at the back of the eye, and a real image has to land on it for the object to look sharp.
3. When the rays meet in front of the retina, or would only meet behind the retina, the light from each point of the object lands as a small disc rather than a point, and the whole image looks blurred.
4. The closest distance at which an eye can still form a sharp image is its near point, about $25cm$ for a normal eye.
5. The furthest distance it can focus is its far point, which for a normal eye is so far away that light arriving from there is a parallel beam.
6. A defect of vision moves the near point, the far point, or both, so part of the range of distances stops being sharp.
7. Spectacles fix a defect by bending the rays before they reach the cornea, which changes where the eye's own focusing sends them.

A short-sighted eye brings distant light to a point in front of the retina

1. The cornea and lens of such an eye converge the light too strongly, or the eyeball is too long from front to back, and often both.
2. Light from a distant object, a road sign $50m$ away for example, arrives as a parallel beam and is brought to a point in front of the retina.
   1. Past that point the rays cross and spread apart again, so each point of the sign has become a small patch of light by the time it reaches the retina and the writing looks blurred.
3. The far point has moved in from a very great distance to something finite, perhaps $2m$, and nothing beyond it can be made sharp.
4. The near point is normal or even closer than $25cm$, which is why a short-sighted person can usually read a book with no help at all.

A diverging lens spreads the rays so the eye focuses them further back

1. A diverging lens is thinner in the middle than at its edges, and it spreads a parallel beam out as though the light had come from a point on the near side of the lens.
2. Worn in front of the eye, it turns the parallel rays from a distant object into slightly diverging rays before they reach the cornea.
3. Diverging rays take more converging to bring to a point, so the eye's own focusing now brings them together further back, exactly on the retina, and the sign looks sharp.
   1. The same idea told in terms of images is that the diverging lens forms a virtual image of the distant object closer to the eye, at the eye's own far point, and the eye can focus on that image.
4. A more short-sighted eye needs a diverging lens of shorter focal length, because the rays have to be spread more before they enter the eye.

A long-sighted eye would focus light from a near object behind the retina

1. The cornea and lens of such an eye do not converge the light strongly enough, or the eyeball is too short from front to back.
2. Light from a near object, a page held at $25cm$ for example, reaches the eye strongly diverging, so it needs a great deal of converging to be pulled back to a point.
3. The eye cannot supply enough, so the rays are still travelling towards each other as they cross the retina and would only meet at a point behind the retina.
   1. Every point of the print therefore spreads into a patch on the retina, and the page looks blurred.
4. The near point has moved outwards, perhaps to $75cm$, which is why the page has to be held at arm's length before it comes clear.
5. The far point is usually still very far away, so distant objects stay sharp without help.

A converging lens pulls the focus forward onto the retina

1. A converging lens is thicker in the middle than at its edges and bends rays inwards, the behaviour you have already met in a magnifying glass.
2. Placed in front of the eye, it starts the light converging while it is still outside the eye, so the rays that arrive at the cornea are far less spread out than they were.
3. The eye has less converging left to do, so the point where the rays meet moves forward from behind the retina to on the retina, and the print is sharp again.
   1. Told in terms of images, the converging lens forms an enlarged virtual image of the page further away than the page itself, at or beyond the eye's near point, and the eye focuses on that image instead.
4. A near point that has only just moved out needs a converging lens of long focal length, while a badly long-sighted eye needs a much shorter one.