Question:easy

An astronomical telescope in normal adjustment has magnifying power \(5\) for distant objects. The separation between the objective and the eyepiece is \(36\) cm. The focal lengths of the objective and the eyepiece are respectively

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For an astronomical telescope in normal adjustment: \[ M=\frac{f_o}{f_e} \] \[ L=f_o+f_e \] Solve the two equations simultaneously.
Updated On: Jun 16, 2026
  • \(30\) cm, \(30\) cm
  • \(30\) cm, \(6\) cm
  • \(6\) cm, \(30\) cm
  • \(6\) cm, \(6\) cm
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Recall the two telescope facts.
In normal adjustment the magnifying power is $M = \frac{f_o}{f_e}$ and the tube length is $L = f_o + f_e$, where $f_o$ is the objective focal length and $f_e$ the eyepiece focal length.
Step 2: List what we know.
$M = 5$ and $L = 36$ cm.
Step 3: Use the magnification to link the two lenses.
From $M = 5$ we get $f_o = 5 f_e$.
Step 4: Substitute into the length equation.
\[ f_o + f_e = 36 \;\Rightarrow\; 5f_e + f_e = 36 \]
Step 5: Solve for the eyepiece.
$6 f_e = 36$, so $f_e = 6$ cm.
Step 6: Back-substitute for the objective.
$f_o = 5 \times 6 = 30$ cm. The objective is the longer focal length lens, as expected for a telescope.
\[ \boxed{f_o = 30\ \text{cm},\quad f_e = 6\ \text{cm}} \]
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