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

Answer

B

Explanation

Here `f_(0)=40cm,f_(e)=4cm`
Tube length (l) =Distance between lenses `=v_(0)+f_(e)` For objective lens,
`u_(0)=-200cm,v_(0)= ?`
`(1)/(v_(0))-(1)/(u_(0))=(1)/(f_(0)) "or" (1)/(v_(0))-(1)/(-200)=(1)/(40)`
or `(1)/(v_(0))=(1)/(40)-(1)/(200)=(4)/(200):.v_(0)=50cm`
`:.l=50+4=54cm`