When diameter of objective of an astronomical telescope is doubled, its limit of resolution is

Options

A. (a) doubled
B. (b) quardrupled
C. ( c) halved
D. unaffected

Answer

To solve the problem of how the limit of resolution changes when the diameter of the objective of an astronomical telescope is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Limit of Resolution**:
The limit of resolution (θ) of a telescope is defined as the smallest angular separation that can be distinguished between two point sources. It is given by the formula:
\[ θ = \frac{1.22 \lambda}{D} \]
where \( \lambda \) is the wavelength of light used and \( D \) is the diameter of the objective lens.

2. **Identifying the Change in Diameter**:
According to the problem, the diameter \( D \) of the objective lens is doubled. Therefore, if the original diameter is \( D \), the new diameter \( D' \) becomes:
\[ D' = 2D \]

3. **Calculating the New Limit of Resolution**:
We can substitute the new diameter into the limit of resolution formula:
\[ θ' = \frac{1.22 \lambda}{D'} = \frac{1.22 \lambda}{2D} \]
This simplifies to:
\[ θ' = \frac{1.22 \lambda}{2D} = \frac{1}{2} \left( \frac{1.22 \lambda}{D} \right) = \frac{1}{2} θ \]

4. **Conclusion**:
Since the limit of resolution \( θ' \) is half of the original limit of resolution \( θ \), we conclude that when the diameter of the objective is doubled, the limit of resolution is halved.

### Final Answer:
When the diameter of the objective of an astronomical telescope is doubled, its limit of resolution is halved.

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