A cardsheet divided into squares each of size `1 mm^(2)` is being viewed at a distance of `9 cm` through a magnifying glass (a conerging lens of focal length `10 cm`) held close to the eye.
(a) What is the magnification produced by the lenas ? How much is the area of each square to 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.