To look closely at a small object, such as an insect or a crystal, you bring it

Question

To look closely at a small object, such as an insect or a crystal, you bring it close to your eye, making the subtended angle and the retinal image as large as possible. But your eye cannot focus sharply on objects that are closer than the near point, so the angular size of an object is greatest when it is placed at the near point (25 cm away from a “normal” eye). To enlarge the object even more, one uses a magnifying glass, which is a converging lens that produces a virtual image that is larger and further away from the eye than the object is. The usefulness of the magnifying glass is given by the angular magnification

mang = '/

which is the ratio of the angular size of the image seen through a magnifier when the object is placed at the magnifier’s focal point to the largest angular size of the object (when you view it from the near point)1. Find the angular magnification of a magnifying glass made of a converging lens with a focal length of 5 cm, assuming that the person who uses it has perfect vision.

Explanation / Answer

angular magnification is:

m = theta'/theta

angular size of the object if h is the object distance from the lens, h = 5 cm since it is placed at the focal point.

theta = h/D

m = theta'/theta = h/f x D/h = D/f

D = 25 cm and f = 5 cm

m = 25/5 = 5

Hence, angular magnification = m = 5.

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