The resolving power of a telescope whose lens has a diameter of 1.22 m for a wavelength of `5000 Å` is

Options

A. `2xx10^(5)`
B. `2xx10^(6)`
C. `2xx10^(2)`
D. `2xx10^(4)`

Explanation

To find the resolving power of a telescope with a given lens diameter and wavelength, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the lens (D) = 1.22 m
- Wavelength (λ) = 5000 Å = \(5000 \times 10^{-10}\) m

### Step 2: Write down the formula for resolving power
The resolving power (R) of a telescope can be calculated using the formula:
\[ R = \frac{D}{\lambda} \]
where \(D\) is the diameter of the lens and \(\lambda\) is the wavelength of light.

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ R = \frac{1.22 \, \text{m}}{5000 \times 10^{-10} \, \text{m}} \]

### Step 4: Simplify the expression
Calculating the denominator:
\[ 5000 \times 10^{-10} = 5 \times 10^{-7} \, \text{m} \]
Now substituting this back into the equation:
\[ R = \frac{1.22}{5 \times 10^{-7}} \]

### Step 5: Perform the division
Calculating the value:
\[ R = \frac{1.22}{5} \times 10^{7} = 0.244 \times 10^{7} = 2.44 \times 10^{6} \]

### Step 6: Final result
Thus, the resolving power of the telescope is approximately:
\[ R \approx 2.44 \times 10^{6} \]

### Step 7: Conclusion
The correct answer is \(2.44 \times 10^{6}\).

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