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. `2.3 `and `12.0`
D. `2.3` and `3.0`

Answer

A

Explanation

When final image if formed at infinity, then
Length of the tube `=v_(o)+f_(a)=v_(o)=f_(e)`
`implies 15=v_(o)+3impliesv_(o)=12 cm`
For objective lens `(1)/(f)=(1)/(v_(o))-(1)/(u_(o))`
`implies(1)/((+2))=(1)/((+12))-(1)/(u_(o))impliesu_(o)=-2.4cm`