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
A. The tube length of the two telescope differ by f
B. The tube length of the two telescope differ by 2f
C. The Galileans telescope has shorter tube length
D. The Galilean telescope has longer tube length

Answer 1

Hint: In order to solve this question, use the relation between focal length of both objective fo, focal length of eyepiece fe and the tube length L. If the tube length changes then the image formation between optic center and focus.

Complete step by step solution:
In normal adjustment, tube length (L) of an astronomical telescope is \[\left( {\mathop f\nolimits_o \, + \mathop f\nolimits_e } \right)\] --- (1)

Where \[{f_o}\] is the focal length of the objective lens \[{f_e}\] is the focal length of the eyepiece
In normal adjustment, tube length (L) of Galilean telescope is \[\left( {\mathop f\nolimits_o \, - \mathop f\nolimits_e } \right)\] ---- (2)

The magnification for both telescopes is

\[m = \dfrac{{\mathop f\nolimits_o }}{{\mathop f\nolimits_e }}\] Here \[l = 2{f_o}\]
From the equation (1) & (2)
The table length of both telescope differ by 2f
\[l = {f_o} + {{f}_e} + {f_o} - {{f}_e}\]
\[l = 2{f_o}\]
Also the Galilean telescope has shorter tube length compared to the astronomical telescope.

Hence, (b) and (c) options are correct.

Note: There are two types of telescope that are refracting and reflecting, that we use to observe the image by using visible light. But astronomical telescopes are generally used to observe celestial bodies. Galilean telescope, instrument for viewing distant objects.