Can you see a much more magnified image through the lens if you adjust the distance of the lens from your hand?
Yes, we can see magnified image through a lens by adjusting the distance between the object and the lens, condition is that the lens must be converging type. For example think of a magnifying glass used to see very small things.
Magnified glass is generally a biconvex lens and for having a magnified image the object is adjusted to be between focus and optical center of lens. The image thus formed is virtual, erect and magnified.
Refer to the ray diagram given below for the case mentioned above.
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