Question

The magnifying power of a refracting type of astronomical telescope is $m$. If focal length of eyepiece is doubled then the magnifying power will become

• A. $2m$
• B. $\sqrt{2}m$
• C. $\frac{m}{2}$
• D. $\frac{m}{4}$

Hint:

Magnifying power is inversely proportional to the focal length of the eyepiece ($m \propto \frac{1}{f_e}$). Therefore, scaling the eyepiece focal length by any factor $k$ automatically scales the total magnification by a factor of $\frac{1}{k}$.

Answer 1

The Correct Option is C

Step 1: State the device.
For an astronomical refracting telescope in normal adjustment, the magnifying power is $m = \dfrac{f_o}{f_e}$, the ratio of objective to eyepiece focal length.
Step 2: Note what changes.
Only the eyepiece focal length is doubled; the objective focal length $f_o$ stays the same.
Step 3: Write the new eyepiece focal length.
$f_e' = 2f_e$.
Step 4: Write the new magnification.
$m' = \dfrac{f_o}{f_e'} = \dfrac{f_o}{2f_e}$.
Step 5: Express in terms of $m$.
$m' = \dfrac{1}{2}\cdot\dfrac{f_o}{f_e} = \dfrac{m}{2}$.
Step 6: Conclude.
Doubling the eyepiece focal length halves the magnifying power, so the answer is option (3).
\[ \boxed{m' = \frac{m}{2}} \]