In order to increase the magnifying power of a telescope

Options

A. The objective should have large focal length and the eye-piece should have small
B. The objective should have small focal length and the eye-piece should have large
C. The focal lengths of both objective and eye- piece lens are small
D. The focal lengths of both objective and eye piece lens are large

Answer

To solve the question regarding how to increase the magnifying power of a telescope, we need to understand the formula for magnifying power (M) of a telescope, which is given by:

\[ M = \frac{F_0}{F_E} \]

where:
- \( F_0 \) is the focal length of the objective lens,
- \( F_E \) is the focal length of the eyepiece lens.

### Step-by-Step Solution:

1. **Identify the Formula**:
The magnifying power of a telescope is determined by the ratio of the focal lengths of the objective and the eyepiece.

2. **Understand the Effect of Focal Lengths**:
- A larger focal length of the objective lens (\( F_0 \)) will increase the magnifying power.
- A smaller focal length of the eyepiece lens (\( F_E \)) will also increase the magnifying power.

3. **Analyze Each Option**:
- **Option A**: The objective should have a large focal length. This is correct because a larger \( F_0 \) increases \( M \).
- **Option B**: The objective should have a small focal length and the eyepiece should have a large focal length. This is incorrect because a small \( F_0 \) decreases \( M \).
- **Option C**: Both objective and eyepiece have small focal lengths. This is incorrect as it would lead to a smaller \( M \).
- **Option D**: Both objective and eyepiece have large focal lengths. This is also incorrect as it would result in a smaller \( M \).

4. **Conclusion**:
The only option that correctly states how to increase the magnifying power of a telescope is **Option A**: The objective should have a large focal length.

### Final Answer:
The correct option is **A**: The objective should have a large focal length.