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.

Explanation

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 - )/(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`.