Someone told me that reading glasses (a priori with a magnifying glass effect only) improve one's eyesight of objects lying in the long range distance. I am really sceptic about it since everything is blurry if I look at objects through those glasses! Is it possible (for this particular person at least)?
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I don't think this is possible. Suppose that your unaided eye can focus on objects over some range of distanced from $d_1$ (closest) to $d_2$ (furthest). Putting a converging lens in front of your eye reduces both $d_1$ and $d_2$. That is, it shifts the range of distances over which you can focus closer to you, not further. Here's the geometric-optics proof of this. Varying the distance at which you can focus is equivalent to varying the effective focal length of your eye. If $D$ is the diameter of your eye, and $d$ is the distance of the object you're focusing on, then the focal length is given by $$ {1\over f}={1\over d}+{1\over D}. $$ When you put on your reading glasses, the effective $f$ is decreased, or to put it another way, the effective power of the lens, $1/f$, is increased. (To be specific, $1/f_{\rm new}=1/f_{\rm old}+1/f_{\rm lens}$.) So the left side of the equation becomes larger. $D$ doesn't change, so $1/d$ must become larger. So $d$, the distance to which you focus, becomes less. |
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