The focal length of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision is

Options

A. 45 cm
B. 55 cm
C. `275/6`cm
D. `325/6 cm`

Answer

D

Explanation

Length of telescope is given by, `v_(0) + u_(e)`
For object, `1/v_(0) -1/u_(0)=1/f_(0)`
`1/v_(0) -1/infty=1/50`
For eye, `1/v_(e) -1/u_(e)=1/f_(e)`
`implies 1/u_(e) =1/(D) + 1/f_(e)=1/D +1/5= 1/25 + 1/5`
Length of telescope,` v_(0)+ u_(e)= 50 +25/6= 325/6 cm`