The image size will approach to infinity when the object move closer to the focus point (p->f), however, the image will move to infinity at the same time (q->∞).

But the ratio q/p will approach a constant value.

1/p+1/q=1/f, so q=pf/(p-f) so M=-q/p=-f/(p-f)

Let the height of the object is h, the height of the image will be H=q/p*h;

Without the len, we will put the object at the best viewing distance(about 25cm for normal eye) where we can see the object clearly.

So the viewing angle for the object is θ=h/25cm;

The view angle change to θ'=H/(|q|+d)=q/p*h/(q-d)≒h/p≒h/f

So the viewing angle being magnified by a factor of

θ'/θ=(h/f) / (h/25cm) =25cm/f -- the so called magnify power.

You can drag the focus point (red dot), object ,eye and lens position horizontally.

Play with it and find out the differences. :-)

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To magnify a small object: put the object in front of a convex lens to form a real image (2f>p>f). Then add the second convex lens, so that the image is near the focus point of the second lens (p2

For an object very far away, it will form a real image almost at the focus point for the first convex lens. Also adjust the second convex lens, so the the real image is near the focus point of the second lens. And you have a telescope.

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