Correct Answer - C
On screen real image is obtained
`m=-3,u=-x,m=-(v)/(u)`
`-3=-(v)/(-x)impliesv=-3x`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(-3x)+(1)/(-x)=-(4)/(3x)` …..(i)
As size of image is decreased i.e., object is moved away.
`m=-2,u=-(x+6),v=-2(x+6)`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(-2(x+6))+(1)/(-(x+6))=(-3)/(2(x+6))` ..(ii)
`-(4)/(3x)=-(3)/(2(x+6))implies8(x+6)=9x`
`x=48cm`
`(1)/(f)=-(4)/(3x)=-(4)/(3xx48)impliesf=-36cm`