An astronomical telescope comprises an objective lens and an eyepiece lens. The telescope's tube length is the sum of the focal lengths of these two lenses. Given:
Focal length of the objective lens, \( f_o = 10 \, \text{m} = 1000 \, \text{cm} \)
Focal length of the eyepiece lens, \( f_e = 10 \, \text{cm} \)
The tube length, \( L \), is calculated as:
\( L = f_o + f_e \)
Substituting the provided values:
\( L = 1000 \, \text{cm} + 10 \, \text{cm} = 1010 \, \text{cm} \)
The magnification \( M \) is determined using the formula:
\( M = \frac{f_o}{f_e} \)
With the given values:
\( M = \frac{1000 \, \text{cm}}{10 \, \text{cm}} = 100 \)
Consequently, the tube length measures 1010 cm, and the magnification is 100. The final answer is: 1010 cm, 100