An astronomical telescope has an angular magnification of magnitude 5 for distant object. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. The focal length `f_(0)` of the objective and the focal length `f_(0)` of the eyepiece are

Options

A. `f_(0) = 45 cm and f_(e) = - 9 cm`
B. `f_(0) = 50 cm and f_(e) = 10 cm`
C. `f_(0) = 7.2 cm and f_(e) = 5 cm`
D. `f_(0) = 30 cm and f_(e) = 6 cm`

Answer

D

Explanation

Here, Angular magnification of telescope
`= (f_(0))/(f_(e)) = 5`,
`:. f_(0) = 5 f_(e)` …(i)
Now, `f_(0) + f_(e) = 36 cm` …(ii)
On solving (i) and (ii), we get
`5 f_(e) + f_(e) = 36 cm`
`f_(e) = 6 cm, f_(0) = 30 cm`