Calculate the resolving power of a telescope when light of wavelength `540 nm` is used. Diameter of objective lens is `6 cm`.

Explanation

To calculate the resolving power of a telescope, we can use the formula:

\[ R = \frac{T}{1.22 \lambda} \]

Where:
- \( R \) is the resolving power,
- \( T \) is the diameter of the objective lens,
- \( \lambda \) is the wavelength of light used.

### Step 1: Convert the diameter of the objective lens to meters
Given:
- Diameter \( T = 6 \, \text{cm} \)

To convert centimeters to meters:
\[ T = 6 \, \text{cm} = 6 \times 10^{-2} \, \text{m} = 0.06 \, \text{m} \]

### Step 2: Convert the wavelength from nanometers to meters
Given:
- Wavelength \( \lambda = 540 \, \text{nm} \)

To convert nanometers to meters:
\[ \lambda = 540 \, \text{nm} = 540 \times 10^{-9} \, \text{m} \]

### Step 3: Substitute the values into the resolving power formula
Now we can substitute \( T \) and \( \lambda \) into the resolving power formula:
\[ R = \frac{0.06}{1.22 \times 540 \times 10^{-9}} \]

### Step 4: Calculate the denominator
First, calculate \( 1.22 \times 540 \):
\[ 1.22 \times 540 = 658.8 \]

Then, multiply by \( 10^{-9} \):
\[ 1.22 \times 540 \times 10^{-9} = 658.8 \times 10^{-9} \, \text{m} \]

### Step 5: Calculate the resolving power
Now, substitute this back into the formula:
\[ R = \frac{0.06}{658.8 \times 10^{-9}} = \frac{0.06}{6.588 \times 10^{-7}} \]

Calculating this gives:
\[ R \approx 9.1 \times 10^{-4} \, \text{m} \]

### Final Answer
The resolving power of the telescope is approximately:
\[ R \approx 9.1 \times 10^{-4} \, \text{m} \]

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