A card sheet divided into squares each of size `1 mm^(2)` is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 10 cm) held close to the eye.
(a) What is the magnification produced by the lens? How much is the area of each square in the virtual image?
(b) What is the angular magnification (magnifying power) of the lens?
(c) Is the magnification in (a) equal to the magnifying power in (b)? Explain.

Explanation

`(1)/(v)+(1)/(9)=(1)/(10)`
i.e., `v=-90cm`.
Magnitude of magnification `= 90//9 = 10`.
Each square in the virtual image has an area `10 xx 10 xx 1 mm^(2) = 100 mm^(2) = 1 cm^(2)`
(b) Magnifying power `= 25//9 = 2.8`
(c) No, magnification of an image by a lens and angular magnification (or magnifying power) of an optical instrument are two separate things. The latter is the ratio of the angular size of the object (which is equal to the angular size of the image even if the image is magnified) to the angular size of the object if placed at the near point (25 cm). Thus, magnification magnitude is `|(v//u)|` and magnifying power is `(25// |u|)`. Only when the image is located at the near point `|v| = 25 cm,` are the two quantities equal.