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  4. The focal lengths of the objective and eye piece of a telescope are respectively 200 cm and 4 cm. The moon subtends an angle of 0.5° at the eye. If it is looked through the telescope, the angle subtended by the moon's image will be

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Q. The focal lengths of the objective and eye piece of a telescope are respectively $200 \,cm$ and $4\, cm$. The moon subtends an angle of $0.5^{\circ}$ at the eye. If it is looked through the telescope, the angle subtended by the moon's image will be

Ray Optics and Optical Instruments

Solution:

Magnifying power $=\frac{ f _{0}}{ f _{e}}$
$\Rightarrow \frac{\beta}{\alpha}=\frac{ f _{0}}{ f } $
$\Rightarrow \beta=\left( f _{0} / f _{ e }\right) \alpha$
$=50 \times 0.5 $
$\Rightarrow \beta=25^{\circ}$