A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:

Options

A. a large aperture contributes to the quality and visiblity of the images.
B. a large area of the objective ensures better light gathering power
C. a large aperture provides a better resolution
D. all of the above

Answer

To determine why a lens of large focal length and large aperture is best suited as an objective of an astronomical telescope, we can analyze the properties of the lens and how they contribute to the performance of the telescope.

### Step-by-Step Solution:

1. **Understanding Focal Length**:
- A lens with a large focal length allows for a greater magnification of distant objects. This is essential for telescopes as they are used to observe celestial bodies that are very far away. The longer the focal length, the more the image is magnified.

**Hint**: Recall that focal length affects the magnification and clarity of images in telescopes.

2. **Understanding Aperture**:
- The aperture of a lens refers to its diameter. A larger aperture means that more light can enter the telescope. This is crucial for astronomical observations, especially for faint objects like distant stars and galaxies. More light leads to brighter images and better visibility.

**Hint**: Think about how light intensity affects image quality and visibility.

3. **Light Gathering Power**:
- The light gathering power of a telescope is directly proportional to the area of the lens (which is related to the square of the diameter). A larger area means that the telescope can collect more light, which enhances the overall quality of the images produced.

**Hint**: Remember that the area of a circle is proportional to the square of its radius (or diameter).

4. **Resolution**:
- The resolving power of a telescope is determined by the diameter of the aperture. The formula for resolving power is given by \( R = \frac{D}{1.22 \lambda} \), where \( D \) is the diameter of the aperture and \( \lambda \) is the wavelength of light. A larger aperture results in a higher resolving power, allowing the telescope to distinguish between two closely spaced objects more effectively.

**Hint**: Consider how resolution affects the clarity of details in the images observed through the telescope.

5. **Conclusion**:
- Therefore, a lens with a large focal length and large aperture is optimal for an astronomical telescope because it enhances magnification, increases light gathering power, improves image quality, and provides better resolution.

**Final Answer**: A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope because it improves visibility, light gathering power, and resolution.