The focal length of the objective and eyepiece of an astronomical telescope for normal adjustments are 50 cm and 5 cm. The length of the telescope should be:

Options

A. 50 cm
B. 55 cm
C. 60 cm
D. 45 cm

Answer

To find the length of the astronomical telescope given the focal lengths of the objective and eyepiece, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Focal length of the objective lens, \( f_0 = 50 \, \text{cm} \)
- Focal length of the eyepiece lens, \( f_e = 5 \, \text{cm} \)

2. **Understand the Formula**:
The length of the telescope \( L \) for normal adjustment can be calculated using the formula:
\[ L = f_0 + f_e + d \]
where \( d \) is the distance of the final image formed by the eyepiece lens. For normal adjustment, we typically take \( d = 25 \, \text{cm} \).

3. **Substitute the Values**:
Substitute the values of \( f_0 \), \( f_e \), and \( d \) into the formula:
\[ L = 50 \, \text{cm} + 5 \, \text{cm} + 25 \, \text{cm} \]

4. **Calculate the Length**:
Now, perform the addition:
\[ L = 50 + 5 + 25 = 80 \, \text{cm} \]

5. **Final Result**:
Therefore, the length of the telescope is:
\[ L = 80 \, \text{cm} \]