Astronomial telescope has two lenses of focal power 0.5D and 20D. Then its magnifying power is:

Options

A. 10
B. 20
C. 80
D. 40

Explanation

To find the magnifying power of an astronomical telescope with two lenses of focal powers 0.5D and 20D, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Focal Powers**:
- The focal power of the first lens (objective lens) is \( P_1 = 0.5D \).
- The focal power of the second lens (eyepiece lens) is \( P_2 = 20D \).

2. **Understand the Formula for Magnifying Power**:
- The magnifying power (M) of an astronomical telescope is given by the formula:
\[ M = \frac{P_2}{P_1} \]
where \( P_2 \) is the power of the eyepiece and \( P_1 \) is the power of the objective lens.

3. **Substitute the Values into the Formula**:
- Substitute \( P_2 = 20D \) and \( P_1 = 0.5D \) into the formula:
\[ M = \frac{20D}{0.5D} \]

4. **Simplify the Expression**:
- The \( D \) units cancel out:
\[ M = \frac{20}{0.5} = 20 \times 2 = 40 \]

5. **Conclusion**:
- Therefore, the magnifying power of the telescope is \( M = 40 \).

### Final Answer:
The magnifying power of the astronomical telescope is **40**.

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