If the wavelength of light used is 6000 Å. The angular resolution of telescope of objective lens having diameter 10 cm is ______ rad.

Options

A. `7.55 xx 10^(-6)`
B. `6.10 xx 10^(-6)`
C. `6.55 xx 10^(-6)`
D. `7.32 xx 10^(-6)`

Answer

To solve the problem of finding the angular resolution of a telescope with a given wavelength and diameter of the objective lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Angular Resolution**:
The angular resolution (Δθ) of a telescope can be calculated using the formula:
\[ \Delta \theta = \frac{1.22 \lambda}{D} \]
where:
- \( \Delta \theta \) is the angular resolution in radians,
- \( \lambda \) is the wavelength of light,
- \( D \) is the diameter of the objective lens.

2. **Convert Wavelength from Angstroms to Meters**:
Given that the wavelength of light is 6000 Å (angstroms), we need to convert this to meters:
\[ 1 \text{ Å} = 10^{-10} \text{ m} \]
Therefore,
\[ \lambda = 6000 \text{ Å} = 6000 \times 10^{-10} \text{ m} = 6.0 \times 10^{-7} \text{ m} \]

3. **Convert Diameter from Centimeters to Meters**:
The diameter of the objective lens is given as 10 cm. We convert this to meters:
\[ D = 10 \text{ cm} = 10 \times 10^{-2} \text{ m} = 0.1 \text{ m} \]

4. **Substitute Values into the Angular Resolution Formula**:
Now we can substitute the values of \( \lambda \) and \( D \) into the angular resolution formula:
\[ \Delta \theta = \frac{1.22 \times (6.0 \times 10^{-7})}{0.1} \]

5. **Calculate the Angular Resolution**:
Performing the calculation:
\[ \Delta \theta = \frac{1.22 \times 6.0 \times 10^{-7}}{0.1} = \frac{7.32 \times 10^{-7}}{0.1} = 7.32 \times 10^{-6} \text{ rad} \]

6. **Final Result**:
Thus, the angular resolution of the telescope is:
\[ \Delta \theta = 7.32 \times 10^{-6} \text{ rad} \]

### Answer:
The angular resolution of the telescope is \( 7.32 \times 10^{-6} \) radians.

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