Question

If tube length of astronomical telescope is $105cm$ and magnifying power is $20$ for normal setting. The focal length of objective is

• A. 100 cm
• B. 10 cm
• C. 20 cm
• D. 25 cm

Answer 1

Answer: (A)

To see with relaxed eye, final image should be formed at infinity. The length of telescope is given by
$L=f_o+f_e$ ... (i)

and magnifying power
$M=\frac{f_o}{f_e}$ ... (ii)
Given, $L=105,M=20$
$\therefore f_o+f_e=105$ ... (iii)
$\frac{f_o}{f_e}=20$ ... (iv)
From Eqs. (iii) and (iv), we get
$20f_e+f_e=105$
$\Rightarrow 21f_e=105$
$\Rightarrow f_e=\frac{105}{21}=5cm$
$\Rightarrow f_o=105-5=100cm$