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

Question

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 (A) 100° (B) 50° (C) 25° (D) 10°

Tardigrade Admin · Accepted Answer

Magnifying power =( f 0/ f e) ⇒ (β/α)=( f 0/ f ) ⇒ β=( f 0 / f e ) α =50 × 0.5 ⇒ β=25°

Q. The focal lengths of the objective and eye piece of a telescope are respectively $200 c m$ and $4 c m$ . 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

$10 0^{\circ}$

$5 0^{\circ}$

$2 5^{\circ}$

$1 0^{\circ}$

Magnifying power $= \frac{f _{0}}{f _{e}}$
$\Rightarrow \frac{β}{α} = \frac{f _{0}}{f}$
$\Rightarrow β = (f_{0} / f_{e}) α$
$= 50 \times 0.5$
$\Rightarrow β = 2 5^{\circ}$

Q. The focal lengths of the objective and eye piece of a telescope are respectively 200cm and 4cm. 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

100∘

50∘

25∘

10∘