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. $\frac{275}{6} cm$
• D. $\frac{325}{6}\,cm$

Answer 1

Answer: (D)

Here, $f_0 = 50\, cm$, $f_e = 5 \,cm, D = 25\, cm$
The length of the telescope when the image is formed at the least distance of distinct vision is
$L = f_0 + \frac{f_eD}{f_e+D}$
$ = 50 + \frac{5\times25}{5+25}$
$ = 50 +\frac{25}{6} $
$= \frac{325}{6}\,cm$