Understanding How Magnifying Glasses Work

[nonequilibrium]

So I'm using Serway, not the thing you should expect a lot of insight from, but I do try.

Anyway, I know how convergent lenses work. So here is the following usual case:

[PLAIN]http://www1.union.edu/newmanj/lasers/Geometrical_Optics/ConvLensCase2.gif

You see the convergent lens creates a bigger thing to look at. On the other hand, the bigger thing is also farther away. I just assumed the being-bigger part weighed up to the being-farther-away part. But now my book has come to "The Simple Magnifier" and states "The size of the image formed at the retina depends on the angle theta subtended by the object at the eye."

Does it just postulate this? Is it evident? Okay, it does sound very intuïtive. But anyway, the book goes on to say that we can't see things closer than about 25cm (I'm sorry if you use other units, but you know what I'm talking about: the near point). It then suggests that we use magnifying glasses so we can put objects closer than 25 cm, cause the magnifier will create a virtual image that is farther away than 25 cm (but larger) which is visable. So basically, they say, a magnifying class is not useful for making an angle larger, it's actually there to make larger angles possible (because it then says, if your eye were RIGHT behind the lens, the smaller object and the larger image form the same angle (from their peaks to your eye), it's just that you can't see the small object, but you can see the larger image[note: ignore the colored lines on the image, they're meaningless for my discussion]).

This seems very weird. I can take a magnifying glas and hold it half a meter away from me, hovering 10 cm above some map and I see the letters on the map in bigger letters. But following the book's logic, it shouldn't make a difference, because I can actually see the map because it's far enough. (of course the book doesn't actually state this, but it does seem to follow out of their reasoning, doesn't it?) Or does a magnifying glas simply have two distinct uses:

1) make more angles possible when an object is too close
2) make objects look bigger. (<-- this one does sound subtle, is it bigger in this case because my eye is far from the magnifying glas and so the angle of the virtual image is way bigger than that from the actual letters on the map?)

I'm a bit confused... I hope somebody else gets my confusion.

Thank you,
mr. vodka

 

[jtbell]

Put a lens with a focal length of about 5 cm close to your eye, or close to your eyeglasses, if you wear them. Put an object on the other side of the lens and adjust its position so you see a nice sharp magnified image. The object will probably be in the range of 5 to 6 cm from your eye.

Now remove the lens while keeping the object in the same place. What do you see?

When I do it, I see the object directly, and it appears to be the same angular size as the image was, but it's a fuzzy blob because I can't focus my eye on something that close.

That's the point of the simple magnifier: to place the image far enough away so your eye can focus on it. If we could focus our eyes on things that are arbitrarily close, we wouldn't need magnifying glasses. We'd just hold things very close to our eyes in order to see very fine details.

 

[nonequilibrium]

Indeed jtbell (thank you for replying), I also did that experiment this morning and got the same. It seems to be a nice example and experimental proof of what my book was saying.

But don't you agree this is only one way to use a magnifier? (if not, I'm very confused) Because here we hold the magnifier as close to our eyes as possible. In this case it doesn't magnify it, it sharpens it, as it were. On the other hand, we can also use a magnifying glass to... magnify :p Hold a lens half a meter away from you 10 cm's over a map and you see the map is bigger. On first notice, it seems weird in comparison, because here there IS a magnification, while in our experiment there wasn't. Is the key element here that we're far from the magnifying glas and thus here the main effect we notice from the magnifying glas is that we notice the image is bigger? In our first experiment, that was a demonstration for the fact that the image is farther away. So these are very distinct (but both useful) ways of using a magnifier, right?