The diameter of objective of a telescope is `1m`. Its resolving limit for the light of wave length `4538 Å`, will be

Options

A. `5.54xx10^(-7)rad`
B. `2.54xx10^(-4)rad`
C. `6.54xx10^(-7)rad`
D. None of these

Explanation

To find the resolving limit of a telescope, we can use the formula for resolving power given by:

\[ RL = \frac{1.22 \lambda}{D} \]

Where:
- \( RL \) is the resolving limit,
- \( \lambda \) is the wavelength of light,
- \( D \) is the diameter of the telescope's objective.

### Step 1: Identify the values
- The diameter \( D \) of the telescope is given as \( 1 \, \text{m} \).
- The wavelength \( \lambda \) is given as \( 4538 \, \text{Å} \).

### Step 2: Convert the wavelength to meters
Since \( 1 \, \text{Å} = 10^{-10} \, \text{m} \), we convert \( \lambda \):

\[ \lambda = 4538 \, \text{Å} = 4538 \times 10^{-10} \, \text{m} = 4.538 \times 10^{-7} \, \text{m} \]

### Step 3: Substitute the values into the formula
Now we can substitute the values of \( \lambda \) and \( D \) into the resolving limit formula:

\[ RL = \frac{1.22 \times (4.538 \times 10^{-7})}{1} \]

### Step 4: Calculate the resolving limit
Now, we perform the multiplication:

\[ RL = 1.22 \times 4.538 \times 10^{-7} \]

Calculating this gives:

\[ RL \approx 5.54 \times 10^{-7} \, \text{radians} \]

### Conclusion
The resolving limit for the telescope is approximately:

\[ RL \approx 5.54 \times 10^{-7} \, \text{radians} \]

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