An astronomical telescope has an angular magnification of magnitude 5 for an object. The separation between the objective and the eye-piece is 36 cm . The final image is formed at infinity. The focal length f0 of the objective and fe of the eye-piece are

Question

An astronomical telescope has an angular magnification of magnitude 5 for an object. The separation between the objective and the eye-piece is 36 cm . The final image is formed at infinity. The focal length f0 of the objective and fe of the eye-piece are (A) 45cm and -9cm (B) 50cm and 10cm (C) 72cm and 2cm (D) 30cm and 6cm

Tardigrade Admin · Accepted Answer

Magnification, m=-5=(- f0/fe)⇒ f0=5fe ⇒ L=f0+fe=36 ⇒ 6fe=36∴ fe=6 cm ⇒ f0=5fe=30 cm

Q. An astronomical telescope has an angular magnification of magnitude $5$ for an object. The separation between the objective and the eye-piece is $36 c m$ . The final image is formed at infinity. The focal length $f_{0}$ of the objective and $f_{e}$ of the eye-piece are

$45 c m$ and $- 9 c m$

$50 c m$ and $10 c m$

$72 c m$ and $2 c m$

$30 c m$ and $6 c m$

Magnification, $m = - 5 = \frac{- f _{0}}{f _{e}} \Rightarrow f_{0} = 5 f_{e}$
$\Rightarrow L = f_{0} + f_{e} = 36$
$\Rightarrow 6 f_{e} = 36 ∴ f_{e} = 6 c m$
$\Rightarrow f_{0} = 5 f_{e} = 30 c m$

Q. An astronomical telescope has an angular magnification of magnitude 5 for an object. The separation between the objective and the eye-piece is 36cm . The final image is formed at infinity. The focal length f0​ of the objective and fe​ of the eye-piece are

45cm and −9cm

50cm and 10cm

72cm and 2cm

30cm and 6cm