The focal length of the objective and the eyepiece of a telescope are… | JEE Main 2013 (22 Apr, Shift 1)

Q48JEE Main 2013 · 22 APR · SHIFT 1Difficult

Optical Instruments & the Eye

The focal length of the objective and the eyepiece of a telescope are 50 cm and 5 cm respectively. If the telescope is focussed for distinct vision on a scale distant 2 m from its objective, then its magnifying power will be:

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Answer: (d)

Objective: $\dfrac{1}{v_o} = \dfrac{1}{50} - \dfrac{1}{200} = \dfrac{3}{200} \Rightarrow v_o = \dfrac{200}{3}$ cm, $m_o = -\dfrac{v_o}{u_o} = -\dfrac{1}{3}$ .
Eyepiece with image at $D = 25$ cm: $m_e = 1 + \dfrac{D}{f_e} = 1 + \dfrac{25}{5} = 6$ .
$M = m_o m_e = -\dfrac{1}{3} \times 6 = -2$ .
So the answer is (d) $-2$ .

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