The resolving power of an astronomical telescope is 0.2 seconds. If the central half portion of the objective lens is covered, the resolving power will be

Options

A. (a)0.1 sec
B. (b)0.2sec
C. (c)1.0sec
D. (d)0.6 sec

Answer

To solve the problem, we need to determine how the resolving power of an astronomical telescope changes when the central half of the objective lens is covered.

### Step-by-step Solution:

1. **Understanding Resolving Power**:
The resolving power (RP) of an astronomical telescope is given by the formula:
\[ RP = \frac{d}{1.22 \lambda} \]
where \(d\) is the diameter of the objective lens and \(\lambda\) is the wavelength of light used.

2. **Given Information**:
- The initial resolving power \(RP_1 = 0.2\) seconds.
- The diameter of the objective lens is \(d\).

3. **Effect of Covering the Lens**:
When the central half of the objective lens is covered, the effective diameter of the lens becomes:
\[ d_2 = \frac{d}{2} \]

4. **New Resolving Power Calculation**:
Using the formula for resolving power, we can express the new resolving power \(RP_2\) when the diameter is halved:
\[ RP_2 = \frac{d_2}{1.22 \lambda} = \frac{\frac{d}{2}}{1.22 \lambda} = \frac{d}{2 \cdot 1.22 \lambda} \]

5. **Relating the Two Resolving Powers**:
Since \(RP_1 = \frac{d}{1.22 \lambda}\), we can relate \(RP_2\) to \(RP_1\):
\[ RP_2 = \frac{1}{2} \cdot RP_1 \]
Substituting \(RP_1 = 0.2\) seconds:
\[ RP_2 = \frac{1}{2} \cdot 0.2 = 0.1 \text{ seconds} \]

6. **Final Result**:
Thus, the resolving power when the central half of the objective lens is covered is:
\[ RP_2 = 0.1 \text{ seconds} \]

### Conclusion:
The resolving power of the telescope after covering the central half of the objective lens will be **0.1 seconds**.