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 find the angular resolution of a telescope, we can use 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.

### Step 1: Convert the wavelength from angstroms to meters
Given that the wavelength \(\lambda\) is 6000 Å (angstroms), we convert it to meters:

\[ \lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6.0 \times 10^{-7} \, \text{m} \]

### Step 2: Identify the diameter of the objective lens
The diameter \(D\) of the objective lens is given as 10 cm. We convert this to meters:

\[ D = 10 \, \text{cm} = 0.1 \, \text{m} \]

### Step 3: Substitute the values into the angular resolution formula
Now we can substitute the values of \(\lambda\) and \(D\) into the formula for angular resolution:

\[ \Delta \theta = \frac{1.22 \times (6.0 \times 10^{-7})}{0.1} \]

### Step 4: Calculate the angular resolution
Now we perform the calculation:

\[ \Delta \theta = \frac{1.22 \times 6.0 \times 10^{-7}}{0.1} = \frac{7.32 \times 10^{-7}}{0.1} = 7.32 \times 10^{-6} \, \text{radians} \]

### Final Answer
Thus, the angular resolution of the telescope is:

\[ \Delta \theta \approx 7.32 \times 10^{-6} \, \text{radians} \]

---