Question

An astronomical telescope and a Galilean telescope use identical objective lenses. They have the same magnification, when both are in normal adjustment. The eyepiece of the astronomical telescope has a focal length $f.$

Answer 1

In normal adjustment,


tube length of an astronomical telescope is,

$L_A=f_0+f_e.....\left(1\right)$ and


tube length of the Galilean telescope is,

$L_G=f_0-f_e.....\left(2\right)$

Where, $f_0$ and $f_e$ are the focal lengths of the objective and the eyepiece respectively.

From (1) and (2) we get, tube length of the Galilean telescope is shorter than astronomical telescope.

Magnification, is same for both the telescopes,

$m=\frac{f_0}{f_e}$

The difference in between the two telescopes is,

$\left|\begin{array}{c}\Delta L\end{array}\right|=L_A-L_G$

$=f_0+f_e-(f_0-f_e)=2f_e$

Here, $f_e=f$

$\therefore \left|\begin{array}{c}\Delta L\end{array}\right|=2f$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ and $\left(C\right)$ is the correct answer.

Why this question? This has been given to understand the basic difference between Galilean telescope and astronomical telescope, which is very important from JEE prospective.