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 `= 1 mm xx 1 mmm = 1 mm^(2)`
Focal length of magnifying lens, `f = +10 cm`
Object distance, `u = -9 cm`
According to thin lens formula
`1 /v = 1/f + 1/u = 1/(+10cm) + (1)/(-9 cm) = (1)/(10 cm) - (1)/(9 cm)`
or `v = - 90 cm`
Magnification , `m = v/u = (- 90 cm)/(-9 cm) = 10`
`:.` Apparent area of the card through the lens
`= 10 xx 10 xx 1 mm^(2) = 100 mm^(2) = 1 cm^(2)`