Question

The focal lengths of the objective and eye-piece of a telescope are respectively 100 cm and 2 cm. The moon substends an angle of $ 0.5{}^\circ $ at the eye. If it is looked through the telescope, the angle subtended by the moons image will be

• A. $ 100{}^\circ $
• B. $ 50{}^\circ $
• C. $ 25{}^\circ $
• D. $ 10{}^\circ $

Answer 1

Answer: (C)

Given, $ {{f}_{o}}=100\,\,cm,\,\,{{f}_{e}}=2\,\,cm $ Visual angle subtended by moon $ (\alpha )={{0.5}^{o}} $ Visual angle subtended at eye with moons image $ (\beta )=? $ Magnifying power of telescope $ (M)=\frac{\beta }{\alpha }=\frac{{{f}_{o}}}{{{f}_{e}}} $ $ \therefore \,\,\,\,\,\,\,\beta =\alpha \,.\,\frac{{{f}_{0}}}{{{f}_{e}}}\,=0.5\,\times \,\frac{100}{2}\,={{25}^{o}} $