An astronomical telesope has objective and eyepiece of focal lengths `40cm` and `4 cm` respectively. To view an object `200cm` away from the objective, the lenses must be separated by a distance `:`

Options

A. `46.0 cm`
B. `50.0 cm`
C. `54.0 cm`
D. `37.3 cm`

Answer

C

Explanation

`f_(o)=+40cm, f_(e)=4cm`
`u_(o)=-200cm`
`(1)/(v_(o))-(1)/(u_(o))=(1)/(f_(o))`
`(1)/(v_(o))=(1)/(40)-(1)/(200)`
`(1)/(v_(o))=(5-1)/(200)=(4)/(200)=(1)/(50)`
Image found at right side of the objective lens,
`v_(o)=+50cm`
This image will appear as object for eyepiece
`L=|v_(o)|+|f_(e)|`
`=50+4`
`=54cm`