Question

An astronomical telescope arranged for normal adjustment has a magnification of $6$. If the length of the telescope is $35cm$, then the focal lengths of objective and eye piece respectively are:

• A. $30cm$, $5cm$
• B. $5cm$, $30cm$
• C. $40cm$, $5cm$
• D. $30cm$, $6cm$

Answer 1

The correct option is A $30cm$, $5cm$

Given : Magnification of telescope $M=-6$

Length of telescope $L=35cm$

Let the focal lengths of the objective and eye piece be $f_o$ and $f_e$.

Magnification in normal adjustment $M=\frac{-f_o}{f_e}$

$\therefore$ $-6=\frac{-f_o}{f_e}$ $⟹f_o=6f_e$ ............(1)

Length of telescope $L=f_o+f_e$

$35=6f_e+f_e$ $⟹f_e=5cm$

$⟹$ $f_o=6\times 5=30cm$