The aperture of telescope is of 1m diameter and wavelength of light incident on the on the paerture is `5500 A^(0)` . The angular limit if resolution of the telescope is

Options

A. `6.71xx10^(-7)` radian
B. `3.35 xx10^(-7)` radians
C. `6.71 xx10^(-5)` radian
D. `3.35 xx10^(-5)` radians

Answer

To solve the problem, we need to find the angular limit of resolution of a telescope using the given parameters: the diameter of the aperture (D) and the wavelength of light (λ).

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Diameter of the aperture (D) = 1 m
- Wavelength of light (λ) = 5500 Å (angstroms)

**Step 2: Convert the wavelength from angstroms to meters.**
1 angstrom = \(10^{-10}\) meters, so:
\[ \lambda = 5500 \, \text{Å} = 5500 \times 10^{-10} \, \text{m} = 5.5 \times 10^{-7} \, \text{m} \]

**Step 3: Use the formula for the angular limit of resolution.**
The formula for the angular limit of resolution (θ) is given by:
\[ \theta = \frac{1.22 \lambda}{D} \]

**Step 4: Substitute the values into the formula.**
Substituting λ and D into the formula:
\[ \theta = \frac{1.22 \times 5.5 \times 10^{-7}}{1} \]

**Step 5: Calculate the value of θ.**
Calculating the above expression:
\[ \theta = 1.22 \times 5.5 \times 10^{-7} = 6.71 \times 10^{-7} \, \text{radians} \]

**Step 6: State the final answer.**
The angular limit of resolution of the telescope is:
\[ \theta \approx 6.71 \times 10^{-7} \, \text{radians} \]