An stronmical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of

Options

A. small focal length and large diameter
B. large focal length and small diameter
C. small focal length and small diameter
D. large focal length and large diameter

Answer

To determine the conditions under which an astronomical refracting telescope will have large angular magnification and high angular resolution, we need to analyze the properties of the objective lens used in the telescope.

### Step-by-Step Solution:

1. **Understanding Angular Magnification**:
- The angular magnification (M) of a telescope is given by the formula:
\[ M = -\frac{f_o}{f_e} \]
where \( f_o \) is the focal length of the objective lens and \( f_e \) is the focal length of the eyepiece lens.
- To achieve large angular magnification, we need a large value of \( f_o \) (focal length of the objective lens) compared to \( f_e \).

2. **Understanding Angular Resolution**:
- The angular resolution (θ) of a telescope is related to the diameter (D) of the objective lens and is given by the formula:
\[ \theta \approx \frac{1.22 \lambda}{D} \]
where \( \lambda \) is the wavelength of light used.
- A larger diameter (D) of the objective lens will lead to better angular resolution, as it reduces the value of θ.

3. **Combining the Conditions**:
- For an astronomical refracting telescope to have both large angular magnification and high angular resolution, we need:
- A **large focal length** \( f_o \) of the objective lens to increase magnification.
- A **large diameter** \( D \) of the objective lens to improve resolution.

4. **Conclusion**:
- Therefore, the objective lens of an astronomical refracting telescope should have both a **large focal length** and a **large diameter** to achieve the desired properties of large angular magnification and high angular resolution.

### Final Answer:
An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens with a **large focal length and large diameter**.

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