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In a laboratory four convex lenses $L_1, L_2, L_3$ and $L_4$ of focal lengths $2,4,6$ and 8 cm , respectively are available. Two of these lenses form a telescope of length 10 cm and magnifying power 4. The objective and eye lenses are respectively
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Verified Answer
The correct answer is:
$L_4, L_1$
$\begin{gathered}
\text { Length of tube }=10 \mathrm{~cm} \\
\qquad \begin{array}{c}
f_o+f_e=10 \mathrm{~cm} \\
\text { Magnification } m=\frac{f_o}{f_e}=4 \\
f_o=4 f_e
\end{array}
\end{gathered}$
Putting in Eq. (i),
or
$5 f_{\varepsilon}=10 \mathrm{~cm}$
and
$\begin{aligned}
& f_e=2 \mathrm{~cm} \\
& f_o=8 \mathrm{~cm} \\
& f_o=8 \mathrm{~cm}, f_e=2 \mathrm{~cm}
\end{aligned}$
Hence, $L_4$ and $L_1$ will be used.
\text { Length of tube }=10 \mathrm{~cm} \\
\qquad \begin{array}{c}
f_o+f_e=10 \mathrm{~cm} \\
\text { Magnification } m=\frac{f_o}{f_e}=4 \\
f_o=4 f_e
\end{array}
\end{gathered}$
Putting in Eq. (i),
or
$5 f_{\varepsilon}=10 \mathrm{~cm}$
and
$\begin{aligned}
& f_e=2 \mathrm{~cm} \\
& f_o=8 \mathrm{~cm} \\
& f_o=8 \mathrm{~cm}, f_e=2 \mathrm{~cm}
\end{aligned}$
Hence, $L_4$ and $L_1$ will be used.
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