Question

The magnifying power of a telescope with a tube length of $60cm$ is $5$. What is the focal length of its eyepiece?

• A. $10cm$
• B. $20cm$
• C. $30cm$
• D. $40cm$

Answer 1

The correct option is A

$10cm$

Step 1. Given data:

The magnifying power of the telescope $m=5$.

The length of the tube$=60cm$.

Step 2. Formula used:

$m=\frac{f_e}{f_o}$ where the focal length of the eyepiece lens is $f_e$, and the focal length of the objective lens is $f_o$

The total length of the telescope$=f_e+f_o$

Step 3. Calculating the focal length of the eyepiece,

$\begin{array}{rcl}m& =& \frac{f_o}{f_e}\\ & =& 5\\ f_o& =& 5f_e\end{array}$

And,

$\begin{array}{rcl}{f}_e+f_o& =& 60\\ & \Rightarrow & f_e+5f_e=60\\ & \Rightarrow & 6f_e=60\\ & \Rightarrow & f_e=\frac{60}{6}\\ & =& 10\\ & & \end{array}$

Thus the focal length of the eyepiece is$10cm$

Hence, option A is the correct answer.