For anastronomical telescope having an objective lens of focal length 10 m and eyepiece lens of focal length 10cm, the tube length and magnification respectively are

The correct option is: **1010cm,100**

To understand why this is the correct answer, let us break down the calculations for both the tube length and the magnification of an astronomical telescope in normal adjustment.

First, let us identify the given values from the problem statement:
- Focal length of the objective lens ($f_o$) = 10 m
- Focal length of the eyepiece lens ($f_e$) = 10 cm

To perform calculations, we must ensure all quantities are in the same unit. Let us convert the focal length of the objective lens from meters to centimeters:
$f_o=10\text{m}=10\times 100\text{cm}=1000\text{cm}$

**1. Tube Length (L):**
For an astronomical telescope in normal adjustment (where the final image is formed at infinity), the tube length is the distance between the objective lens and the eyepiece lens. This is equal to the sum of their focal lengths:

$L=f_o+f_e$

Substituting the values:
$L=1000\text{cm}+10\text{cm}=1010\text{cm}$

**2. Magnification (m):**
The magnifying power of an astronomical telescope in normal adjustment is given by the ratio of the focal length of the objective lens to the focal length of the eyepiece lens:

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

Substituting the values:
$m=\frac{1000\text{cm}}{10\text{cm}}=100$

Thus, the tube length is 1010 cm and the magnification is 100, which corresponds to the correct option.