The focal length of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision is

Question

The focal length of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision is (A) 45 cm (B) 55 cm (C) (275/6) cm (D) (325/6) cm

Tardigrade Admin · Accepted Answer

Here, f0 = 50 cm, fe = 5 cm, D = 25 cm The length of the telescope when the image is formed at the least distance of distinct vision is L = f0 + (feD/fe+D) = 50 + (5×25/5+25) = 50 +(25/6) = (325/6) cm

Q. The focal length of the lenses of an astronomical telescope are $50 c m$ and $5 c m$ . The length of the telescope when the image is formed at the least distance of distinct vision is

$45 c m$

$55 c m$

$\frac{275}{6} c m$

$\frac{325}{6} c m$

Here, $f_{0} = 50 c m$ , $f_{e} = 5 c m, D = 25 c m$
The length of the telescope when the image is formed at the least distance of distinct vision is
$L = f_{0} + \frac{f _{e} D}{f _{e} + D}$
$= 50 + \frac{5 \times 25}{5 + 25}$
$= 50 + \frac{25}{6}$
$= \frac{325}{6} c m$

Q. The focal length of the lenses of an astronomical telescope are 50cm and 5cm. The length of the telescope when the image is formed at the least distance of distinct vision is

45cm

55cm

6275​cm

6325​cm