A square card of side length 1 mm is being seen through a magnifying lens of focal length 10 cm. The card is placed at a distance of 9 cm from the lens. The appaent area of the card thorugh the lens is

Options

A. `1 cm^(2)`
B. `0.81 cm^(2)`
C. `0.27 cm^(2)`
D. `0.60 cm^(2)`

Answer

A

Explanation

Area of square card= `1mmxx1mm=1mm^(2)`
Focal length of magnifying lens (converging lens),
`f=+10` cm
Objective distance, `u=-9` cm
According to thin lens formula, `(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)=(1)/(f)+(1)/(u)=(1)/(+10cm)+(1)/(-9cm)=(1)/(10cm)-(1)/(9cm)`
or `v=-90` cm
Magnification, `M=(v)/(u)=(-90cm)/(-9cm)=10`
`:.` Apparent area of the card through the lens
`=10xx10xx1mm^(2)=100mm^(2)=1cm^(2)`