The diameter of the lens of a telescope is 0.61 m and the wavelength of light used is 5000 Å. The resolution power of the telescope is

Options

A. `2xx10^(6)`
B. `10^(6)`
C. `2xx10^(4)`
D. `2xx10^(2)`

Answer

To find the resolution power of the telescope, we can use the formula for the resolution power given by:

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

where:
- \( R \) is the resolution power,
- \( D \) is the diameter of the telescope,
- \( \lambda \) is the wavelength of light used.

### Step-by-Step Solution:

1. **Identify the given values:**
- Diameter of the lens \( D = 0.61 \, \text{m} \)
- Wavelength of light \( \lambda = 5000 \, \text{Å} \)

2. **Convert the wavelength from angstroms to meters:**
- \( 1 \, \text{Å} = 10^{-10} \, \text{m} \)
- Therefore, \( 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)

3. **Substitute the values into the resolution power formula:**
\[ R = \frac{0.61}{1.22 \times (5 \times 10^{-7})} \]

4. **Calculate the denominator:**
- First, calculate \( 1.22 \times (5 \times 10^{-7}) \):
\[ 1.22 \times 5 = 6.1 \]
\[ 6.1 \times 10^{-7} = 6.1 \times 10^{-7} \]

5. **Now substitute back into the formula:**
\[ R = \frac{0.61}{6.1 \times 10^{-7}} \]

6. **Perform the division:**
\[ R = 0.61 \div 6.1 \times 10^{7} = \frac{0.61}{6.1} \times 10^{7} \]
- Calculate \( \frac{0.61}{6.1} \):
\[ \frac{0.61}{6.1} \approx 0.1 \]
- Therefore:
\[ R \approx 0.1 \times 10^{7} = 1 \times 10^{6} \]

7. **Final result:**
- The resolution power of the telescope is \( R \approx 10^6 \).