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

Options

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

Explanation

To solve the question regarding the requirements for an astronomical refracting telescope to have large angular magnification and high angular resolution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Magnification**:
- The formula for angular magnification (M) of a telescope is given by:
\[ M = \frac{F_o}{F_e} \]
where \( F_o \) is the focal length of the objective lens and \( F_e \) is the focal length of the eyepiece.

2. **Condition for Large Angular Magnification**:
- To achieve large angular magnification, the focal length of the objective lens \( F_o \) must be large while the focal length of the eyepiece \( F_e \) should be relatively smaller. This means:
\[ F_o \text{ should be large} \]

3. **Understanding Angular Resolution**:
- The resolution of a telescope is determined by the formula:
\[ \text{Resolution} \propto \frac{D}{\lambda} \]
where \( D \) is the diameter of the objective lens and \( \lambda \) is the wavelength of light.

4. **Condition for High Angular Resolution**:
- For high angular resolution, the diameter \( D \) of the objective lens must also be large. This leads to:
\[ D \text{ should be large} \]

5. **Conclusion**:
- Therefore, for an astronomical refracting telescope to have both large angular magnification and high angular resolution, it is necessary that:
- The focal length of the objective lens \( F_o \) is large.
- The diameter \( D \) of the objective lens is also large.

### Final Answer:
The objective lens of an astronomical refracting telescope should have a **large focal length and a large diameter**.

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