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

Area of each piece `= 1mm^2`
`therefore u = - 9 cm , f= + 10 cm` (convex lens)
Lens formula,
`1/f = 1/v - 1/u`
` therefore 1/v = 1/f + 1/u`
`therefore 1/v = 1/10 + 1/(-9) = (9-10)/(90) = (-1)/(90)`
`therefore v = - 90 cm `
`therefore` Value of magnification
`m = v/(|u|) = 90/9 = 10 `
`rArr` Area of each piece in virtual image,
`A. = (10)^2 xx 1 = 100 mm^2`
`= 1 cm^2`
(b) Magnifiying power ,
`M = (D)/(|u|) = (25)/(9) = 2.8`
(c) No, magnification of lesn and angular magnification of optical instrument both are different.
`rArr` Value of magnification `= (|v|)/(|u|)` and angular magnification (magnifying power) ` = (D)/(|u|) = (25)/(|u|)`
`rArr` Only when image is obtained at near point, then `|v|` = 25 cm and hence magnification and magnifying power are same.