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Calculate the least value of the angular separation of two stars which can be resolved by a telescope of 200 cm aperture. If the aperture of the human eye be 2 mm and if the focal length of the eyepiece be 1 inch, what must be the minimum focal length of the objective if full resolving power of the telescope is to be utilized. Take $λ = 5000 \overset{0}{A}$

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6.7 × 10^–7 rad, 500 inches

1.65 × 10^–7 rad, 1000 inches

3.35 × 10^–7 rad, 1000 inches

None

answer is C.

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Detailed Solution

\Delta \theta = \frac{{1.22\lambda }}{a}\,;

$∆ θ = \frac{1.22 \times 5500 \times 10^{- 10}}{200 \times 10^{- 2}}$

M = \frac{{aperture\,of\,the\,objective({a_0})}}{{aperture\,\,of\,the\,eye}}\

= \frac{{200}}{{2 \times {{10}^{ - 1}}}} = 1000\, = \frac{{{f_0}}}{{{f_e}}} \Rightarrow {f_0} = 1000fe\

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