Farsightedness glasses beyond focal length

Question

As I understand, farsightedness glasses use convex lenses to create virtual image that is farther than the object (and thus past the near point of the user). However, this only happens if the object is within the focal length of the lens. If the object is beyond the focal length of the lens, no virtual image is formed (in fact real image would be formed on the other side of the lens). So what does someone see when wearing convergent glasses and looking beyond the glasses focal length? Can they see clearly there at all? If so, how?

Answer 1

The trick with converging eyeglasses is that the eye is closer to the lens than the focal length. The wearer is never in a position to view the (inverted) real image.

In the thin lens equation, $$ \frac1f = \frac1{d_i} + \frac1{d_o}, $$

the convention is that a “virtual image” has a negative image position $d_i$. A person who is wearing converging lenses to look at an object that’s far away will be trying to focus converging light rays, which would form an image somewhere behind the wearer’s head. In the thin lens equation for the eye, these converging rays correspond to a “virtual object,” with negative object position $d_o$.

If you wear converging lenses and hold a book near the focal length, the rays from that book exit the lens nearly parallel: slightly converging if the book is a little farther, and slightly diverging in the book is a little nearer. The image position position $d_i$ is bouncing around between negative infinity and positive infinity, but that’s a mathematical artifact due to asking about a hypothetical meeting point instead of the behavior of the light at the lens. The actual quantity in the thin lens equation, $\frac1{d_i}$, is varying smoothly around zero.

Note however that if you move the converging lens so that the real image forms before the eye, there is definitely a weird region. This is “easier done than said,” to misquote the adage. Go to a drugstore and get some inexpensive reading glasses, or get the magnifying lens from your soldering iron or your sewing kit. Hold it far from your eye and look out the window at a distant object: you’ll see the inverted real image. Hold the lens right up to your eye and look out the window: you’ll see the upright virtual image. Now smoothly move the lens from near your eye to far from your eye, and watch what happens as the image inverts.

Answer 2

Glasses, both near and far, are more often actually convex on the outside of the lens and concave on the users side of the lens.

As a glasses wearer, you are correct that glasses are always a bit of a compromise, far sighted lenses tend to be 'blury' at closer distances, but at a certain distance and beyond always look sharp, whereas near sighted lenses are still blury if too close, and rapidly are blury as the distance increases, but at a typical reading distance will be sharp.

I have different glasses for IT work and screens than for reading a book for exmple as the typical distances are different. Likewise I have seperate far sighted glasses for driving.