Diameter of the objective of a telescope is 200cm. What is the resolving power of a telescope? Take wavelength of light =5000Å.

Options

A. `6.56xx10^(6)`
B. `3.28xx10^(5)`
C. `1xx10^(6)`
D. `3.28xx10^(6)`

Explanation

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

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

where:
- \( R \) is the resolving power,
- \( D \) is the diameter of the telescope's objective,
- \( \lambda \) is the wavelength of light.

### Step 1: Convert the diameter from centimeters to meters.
Given:
- Diameter \( D = 200 \) cm

To convert centimeters to meters:
\[ D = 200 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 2 \, \text{m} \]

### Step 2: Convert the wavelength from angstroms to meters.
Given:
- Wavelength \( \lambda = 5000 \) Å

To convert angstroms to meters:
\[ \lambda = 5000 \, \text{Å} \times \frac{1 \times 10^{-10} \, \text{m}}{1 \, \text{Å}} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### Step 3: Substitute the values into the resolving power formula.
Now substituting \( D \) and \( \lambda \) into the formula:
\[ R = \frac{2 \, \text{m}}{1.22 \times 5 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate the denominator.
Calculating the denominator:
\[ 1.22 \times 5 = 6.1 \]
Thus, the denominator becomes:
\[ 6.1 \times 10^{-7} \, \text{m} \]

### Step 5: Calculate the resolving power.
Now substituting back into the formula:
\[ R = \frac{2}{6.1 \times 10^{-7}} = \frac{2}{6.1} \times 10^{7} \]
Calculating \( \frac{2}{6.1} \):
\[ \frac{2}{6.1} \approx 0.328 \]
Thus:
\[ R \approx 0.328 \times 10^{7} \approx 3.28 \times 10^{6} \]

### Final Answer:
The resolving power of the telescope is approximately \( 3.28 \times 10^{6} \).

---