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  4. The focal length of objective of a telescope is 50cm and eye-piece is 5cm . The telescope is focused from a distinct vision on a scale 2m away. The separation between the objective and the eye-piece is, if final image is formed at the least distance of distinct vision,

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Q. The focal length of objective of a telescope is $50cm$ and eye-piece is $5cm$ . The telescope is focused from a distinct vision on a scale $2m$ away. The separation between the objective and the eye-piece is, if final image is formed at the least distance of distinct vision,

NTA AbhyasNTA Abhyas 2020

Solution:

$L=VO+\left|U_{e}\right|$
$\frac{1}{V_{0}}-\frac{1}{u_{0}}=\frac{1}{f_{0}}\text{,}\frac{1}{V_{0}}-\frac{1}{u_{e}}=\frac{1}{f_{e}}$
$\frac{1}{V_{0}}=\frac{1}{50}-\frac{1}{206}\text{, }\frac{1}{- 25}-\frac{1}{u_{e}}=\frac{1}{5}$
$V_{0}=\frac{200}{3}cm\text{,}u_{e}=\frac{- 25}{6}cm$
$L=\frac{200}{3}+\frac{25}{6}\Rightarrow L=70.83=71cm.$