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

(a) Given, object distance, `u=-9cm`,
Image distance, `v=?`,
Focal length, `f=10cm`
Since `(1)/(v)-(1)/(u)=(1)/(f)rArr (1)/(v)+(1)/(9)=(1)/(10)`
`rArr" "v=-90cm`
`therefore" Magnitude of magnification"`
`m=(v)/(u)=(90)/(9)=10`
Each square on the virtual image has an area
`=m^(2)xx"Area of object"=100xx1mm^(2)`
`=100mm^(2)=1cm^(2)`
(b) Magnifying power `=D//u=25//9=2.77`
(c ) No, the magnification of image by a lens and the angular magnification (or magnifying power) of an optical instrument are two separate entities.
The magnification magnitude is `|(v//u)|` and magnifying power is `(25//|u|)`. When the image is located at the near point i.e. `|v|=25cm` the two quantities becomes equal.