Final answer:
To obtain a magnification of 10x with a 2.1 cm-focal length magnifying glass, it should be held approximately at its focal length (2.1 cm) from the object, assuming the standard near point distance of 25 cm for comfortable viewing with the human eye.
Step-by-step explanation:
To calculate the distance at which a 2.1 cm-focal length magnifying glass should be held from an object to achieve a magnification of 10x, we use the lens formula for magnification: M = 1 + (D/f), where M is the magnification, D is the distance of the near point (the closest an average human eye can comfortably see an object, typically 25 cm), and f is the focal length of the lens.
In this case, to achieve a magnification of 10x, we need the equation to look like 10 = 1 + (25 cm / 2.1 cm). By solving for f, we get: 10 - 1 = 25 cm / 2.1 cm, which gives us 9 = 25 cm / 2.1 cm, and therefore the distance (d) at which the magnifying glass must be held from the object is 2.1 cm. Note that this is under the assumption that the eye is very close to the lens, such that the distance between the lens and the eye, which is 5.0 cm in the given question, doesn't significantly affect the approximated calculation.