The focal length of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively. The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity. The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectively

Options

A. 2.4 and 12.0
B. 2.4 and 15.0
C. 2.0 and 12.0
D. 2.0 and 3.0

Answer

A

Explanation

Here `f_(o)=2 cm and f_(e)=3cm`.
Using lens formula for eye piece
`rArr" "(-1)/(u_(e))+(1)/(prop)=(1)/(3) rArr u_(e)=-3cm`
But the distance between objective and eye piece is 15 cm (given)
`therefore" Distance of image formed by the objective"`
`=v=15-3=12cm`.
Let u be the object distance from objective, then for objective lens
`-(1)/(u_(0))+(1)/(v_(0))=(1)/(f_(0)) or (-1)/(u)+(1)/(12)=(1)/(2)`
`rArr" "(-1)/(u)=(1)/(2)-(1)/(12)=(5)/(12), u=-(12)/(5)=-2.4cm`