The magnifying power of the astronomical telescope for normal adjustment is 50. The focal length of the eyepiece is 2 cm. The required length of the telescope for normal adjustment is:

A. 100 cm

B. 98 cm

C. 25 cm

D. 102 cm

To determine the required length of the telescope for normal adjustment, we can use the relationship between the magnifying power of the telescope, the focal lengths of the objective and eyepiece, and the overall length of the telescope. The magnifying power (M) of an astronomical telescope in normal adjustment is given by the formula:

Understanding the Formula

The formula for the magnifying power of a telescope is:

M = F_o / F_e

Where:

• M = magnifying power
• F_o = focal length of the objective lens
• F_e = focal length of the eyepiece lens

Given Values

From the problem, we know:

• M = 50
• F_e = 2 cm

Calculating the Focal Length of the Objective

We can rearrange the magnifying power formula to find the focal length of the objective:

F_o = M × F_e

Substituting the known values:

F_o = 50 × 2 cm = 100 cm

Finding the Length of the Telescope

The length of the telescope in normal adjustment is the sum of the focal lengths of the objective and the eyepiece:

Length of the telescope = F_o + F_e

Now, substituting the values we have:

Length = 100 cm + 2 cm = 102 cm

Final Answer

Therefore, the required length of the telescope for normal adjustment is 102 cm, which corresponds to option D.