Will magnifier work when touching a page?
No. It won't get the magnification effort when touching a page.
Because the magnifier need some distance between object and lens as focal length.
In order to achieve maximum magnification without distortion, the user should position the lens a proper distance from the object.
The distance from the 3x magnifier to the object viewed is about 8-10 cm. This distance offers user better viewing experience.
The focal length (working distance) is the ideal distance between the lens and the object, not too close (or the lens won't magnify) and not too far (or the image appears wavy). And if you hold the lens MUCH too far from the object, the image will appear upside down.
According to the almighty Wikipedia the 'normal' working distance for a lens is 10 inches. This is rather neat because (as you will see if you read the extra-technical stuff below) 10 inches is about 25cm, and 25cm X4 = 1 meter (near enough), and physicists use 1 meter as the definition of 'standard' focal length (not very practicable as a 'working distance')...but don't worry about that, all you need to know is - the way I calculate magnification now falls in line with the 'official' method you find online, like this:
1 inch = 10X magnification
2 inch = 5X magnification
2½ inch = 4X magnification
3 inch = 3.4X magnification
3½ inch = 2.8X magnification
4 inch = 2.5X magnification
5 inch = 2X magnification
6 inch = 1.7X magnification
7 inch = 1.5X magnification
8 inch = 1.3X magnification
9 inch = 1.1X magnification