A card sheet divided into squares each of size 1 `mm^(3)` viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm ) held close to the eye.
a. What is the magnification produced by lenas ? 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

a . F = 10 cm, u = -9 cm
`(1)/(v) - (1)/(u) =(1)/(f)`
`(1)/(v)= (1)/(f) + (1)/(u) = (1)/(10) - (1)/(9) = - (1)/(90) therefore v = - 90 ` cm
Linear magnification = `(v)/(u) = (-90)/(9) = 10 `
Area of each square in the image = `(1 mm xx 10)^(2) = 100 mm^(2) = 1 cm^(2)`
b. angular magnification - `(D)/(|u|) = (25)/(9) = 2.8 `
c. No. If the image is located near the least distance of distinct vision (v = D = 25 cm ) , the two quantities in (a) and (b) are equal .