Question

The focal lengths of the objective and eye piece of an astronomical telescope are `25 cm and 2.5 cm` respectively. The telescope is fucussed on an object `1.5 m` from objective, the final image being formed `25 cm` from eye of the observer. Calculate the length of the telescope.

Answer 1

Here, `f_(0) = 25 cm, f_(e) = 2.5 cm`.
`u_(0) = - 1.5 m = - 150 cm., v_(e) = - 25 cm, L = ?`
As `(1)/(v_(0)) - (1)/(u_(0)) = (1)/(f_(0))`
`:. (1)/(v_(0)) = (1)/(f_(0)) + (1)/(u_(0)) = (1)/(25) - (1)/(150) = (6 - 1)/(150)`
`v_(0) = (150)/(5) = 30 cm`
Again, as `(1)/(v_(e)) - (1)/(u_(e)) = (1)/(f_(e))`
`:. (1)/(u_(e)) = (1)/(v_(e)) - (1)/(f_(e)) = (1)/(-25) - (1)/(2.5)`
`= (-1 - 10)/(25) = (-11)/(25)`
`u_(e) = (- 25)/(11) = - 2.27 cm`
Length of telescope, `L = |v_(0)| + |u_(e)|`
`= 30 + 2.27 = 32.27 cm`