The focal lengths of the objective and the eyepiece of an astronomical telescope are 40 cm and 5 cm respectively. It is focussed on a scale at a distance of 2 m. The final image is formed at infinity. What is the separation between the two lenses ?

Options

A. 45 cm
B. 50 cm
C. 55 cm
D. 60 cm

Answer

C

Explanation

`f_(o)=40cm, f_(e)=5 cm`
For the objective `u_(o)=-200 cm`
`therefore (1)/(v_(o)) -(1)/(u_(o))=(1)/(f_(o))`
`therefore (1)/(v_(o))= -(1)/(200)+(1)/(40)=(4)/(200)=(1)/(50)`
`therefore v_(o)=50 cm`
In an astronomical telescope, when the final image is formed at infinity, the image fourmed by the objective is at the focal length of the eyepiece.
`therefore` The distance between the objective and the eyepiece `=v_(o)+f_(e)=50 cm +5 cm=55 cm.`