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An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eye piece is 36 \mathrm{~cm} and the final image is formed at infinity. The focal length \mathrm{f_{0}} of the objective and the length \mathrm{f_{e}} of the eye piece are   

Option: 1

f_{0}=45 \mathrm{~cm}$ and $f_{e}=-9 \mathrm{~cm}


Option: 2

f_{0}=50 \mathrm{~cm}$ and $f_{e}=10 \mathrm{~cm}


Option: 3

f_{0}=7.2 \mathrm{~cm}$ and $f_{e}=5 \mathrm{~cm}


Option: 4

f_{0}=30 \mathrm{~cm}$ and $f_{e}=6 \mathrm{~cm}


Answers (1)

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 We know that, \mathrm{f}_{0}+\mathrm{f}_{\mathrm{e}}=36 \quad \ldots(1)

Where \mathrm{\ell=} length of the tube \mathrm{=36 \mathrm{~cm}}
\mathrm{\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}=\mathrm{m}=5}\quad \ldots(2)

Where \mathrm{\mathrm{m}=} magnification \mathrm{=5}

Solving (1) and (2) we obtain,

\mathrm{5 f_{e}+f_{e}=36}

\Rightarrow \quad f_{e}=6 \mathrm{~cm}$ and $f_{0}=5 f_{e}=30 \mathrm{~cm}

\therefore \left ( D \right )

Posted by

Ritika Harsh

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