Final answer:
The magnification of a magnifying lens with a focal length of 10 cm, held 3 cm from the eye and the object at 12 cm from the eye, can be approximated as 3.5x by adapting the standard formula to the given distances.
Step-by-step explanation:
The question pertains to the concept of magnification in optics, particularly concerning a magnifying lens. Magnification is defined as the ratio of the height of the image (as seen through the lens) to the height of the object itself. The formula for the magnification (M) of a simple magnifier when the image is at the near point for the standard eye (25 cm from the eye) is given by M = 1 + (25 cm / f), where 'f' is the focal length of the lens.
Here, the focal length of the magnifying lens is given as 10 cm (f = 10 cm). However, the object distance from the eye is not the near point, but it is provided as 12 cm. To correctly determine the magnification for this case, we can adapt the formula as M = 1 + (D / f), where 'D' is the distance from the eye at which the object appears clearly without strain. We use the accommodation of the eye to focus on objects at different distances, and the usual nearest clear vision distance, the near point, is approximately 25 cm for an average adult.
To compute the magnification, we substitute our values into the formula: M = 1 + (D / f) = 1 + (25 cm / 10 cm) = 1 + 2.5 = 3.5. Thus, for a magnifying lens with a focal length of 10 cm held 3 cm from the eye and the object at 12 cm from the eye, the magnification would be 3.5x, though this value would be reached assuming that the eye adjusts to place the image at the near point.
It should be noted that the provided condition does not represent the standard situation for the simple magnifier equation, as the object distance does not match the near point. Therefore, the provided magnification formula does not directly apply, but an approximation can be considered if we assume that the eye is adjusting to bring the image into focus at the near point distance.