A astronomical telescope has objective and eyepiece of focal lenghts 40 cm 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be seperated by a distance

Options

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

Answer

A

Explanation

For the astronomical telescope `f_(o) gt f_(e)`
For the objective `u_(o)=-200cm ` and f=40 cm
`therefore (1)/(v_(o)) - (1)/(u_(o))=(1)/(f_(o)) therefore (1)/(v_(o)) =(1)/(f_(o)) +(1)/(u_(o))`
`therefore (1)/(v_(o)) =(1)/(40) -(1)/(200) =(5-1)/(200) =(1)/(50)`
`therefore v_(o)=50 cm`
`therefore` Distance between O and `E=v_(o)+r_(e)=50+4=54 cm`