The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is…
The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm. It is focused on a scale at a distance 2 m from it. The distance of objective lens from eye lens to see the clear image is
38.3 cm
48.3 cm
58.3 cm
22.5 cm
Solution
for a telescope,
$\mathrm{f}_{\mathrm{o}}=30 \mathrm{~cm}, \mathrm{f}_{\mathrm{e}}=3 \mathrm{~cm}, \mathrm{u}_{\mathrm{o}}=-200 \mathrm{~cm}$
For objective lens,
$\begin{aligned}
& \frac{1}{f_o}=\frac{1}{v_0}-\frac{1}{u_o} \\
& \Rightarrow \frac{1}{30}=\frac{1}{v_o}-\frac{1}{-200} \Rightarrow \frac{1}{v_0}=\frac{1}{30}-\frac{1}{200}
\end{aligned}$
$\therefore \quad \mathrm{v}_{\mathrm{o}}=35.3 \mathrm{~cm}$ To see clear image, it should be formed at infinity.
$\therefore$ Distance between objective and eye lens is
$\mathrm{L}=\mathrm{v}_{\mathrm{o}}+\mathrm{f}_{\mathrm{e}}=35.3+3=38.3 \mathrm{~cm}$