A square wire of side `3.0 cm` is placed `25 cm` away from a concave mirror of focal length `10 cm`. What is the area enclosed by the image of the wire ? The centre of the wire is on the axis of the mirror, with its two sides normal to the axis.

Options

A. `7.5cm^2`
B. `6.0cm^2`
C. `4.0cm^2`
D. `3.0cm^2`

Answer

C

Explanation

`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(v)+(1)/(-25)=(1)/(-10)`
`(1)/(v)=-(1)/(10)+(1)/(25)=(-5+2)/(50)=(-3)/(50)`
`v=-(50)/(3)`cm
`m=-(v)/(u)=-((-50)/(3))/(-25)=-(2)/(3)`
`("Area of image")/("area of object")=m^2implies(A_i)/(A_O)=(-(2)/(3))^2`
`(A_i)/(3xx3)=(4)/(9)impliesA_i=4cm^2`