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° at the eye. If it is looked through the telescope, the angle subtended by the moons image will be

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° at the eye. If it is looked through the telescope, the angle subtended by the moons image will be (A)  100°  (B)  50°  (C)  25°  (D)  10°

Tardigrade Admin · Accepted Answer

Given, fo=100 cm, fe=2 cm Visual angle subtended by moon (α )=0.5o Visual angle subtended at eye with moons image (β )=? Magnifying power of telescope (M)=(β /α )=(fo/fe) ∴ β =α . (f0/fe) =0.5 × (100/2) =25o

Q. 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

$100^{\circ}$

$50^{\circ}$

$25^{\circ}$

$10^{\circ}$

Given, $f_{o} = 100 c m, f_{e} = 2 c m$ Visual angle subtended by moon $(α) = 0.5^{o}$ Visual angle subtended at eye with moons image $(β) = ?$ Magnifying power of telescope $(M) = \frac{β}{α} = \frac{f _{o}}{f _{e}}$ $∴ β = α . \frac{f _{0}}{f _{e}} = 0.5 \times \frac{100}{2} = 25^{o}$

Q. 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∘ at the eye. If it is looked through the telescope, the angle subtended by the moons image will be

100∘

50∘

25∘

10∘