By increasing the diameter of the objective of telescope, we can increase its range, why ?

Answer

### Step-by-Step Solution:

1. **Understanding the Objective of a Telescope**: The objective lens of a telescope is responsible for gathering light from distant objects. The diameter of this lens plays a crucial role in how much light it can collect.

2. **Effect of Diameter on Light Gathering**: When the diameter of the objective lens is increased, the area of the lens also increases. The area \( A \) of a circular lens can be calculated using the formula:
\[ A = \pi \left( \frac{d}{2} \right)^2 = \frac{\pi d^2}{4} \]
where \( d \) is the diameter of the lens. As \( d \) increases, \( A \) increases.

3. **More Light Collection**: A larger area means that the telescope can collect more light from the same distant object. This is crucial for observing faint objects in the universe, as more light results in a clearer and brighter image.

4. **Focusing on a Larger Area**: With more light gathered, the telescope can focus on a larger area of the sky. This means that it can resolve finer details and observe objects that are further away.

5. **Increase in Range**: The ability to gather more light and focus on a larger area directly translates to an increase in the range of the telescope. This means that the telescope can observe objects that are farther away than it could with a smaller diameter objective.

6. **Conclusion**: Therefore, by increasing the diameter of the objective of a telescope, we effectively increase its range due to the enhanced light-gathering capability and improved resolution.