The limit of resolution of a 100 cm telescope for `lambda=5000Å` is equal to

Options

A. `61xx10^(-8)" rad"`
B. `6.1xx10^(-8)" rad"`
C. `12.2xx10^(-8)" rad"`
D. `122xx10^(-8)" rad"`

Answer

To find the limit of resolution of a telescope, we can use the formula:

\[ \Delta \theta = \frac{1.22 \lambda}{D} \]

where:
- \(\Delta \theta\) is the limit of resolution in radians,
- \(\lambda\) is the wavelength of light,
- \(D\) is the diameter of the telescope.

### Step-by-Step Solution:

1. **Identify the given values**:
- Diameter of the telescope, \(D = 100 \text{ cm} = 1 \text{ m}\)
- Wavelength, \(\lambda = 5000 \text{ Å} = 5000 \times 10^{-10} \text{ m} = 5 \times 10^{-7} \text{ m}\)

2. **Substitute the values into the resolution formula**:
\[ \Delta \theta = \frac{1.22 \times (5 \times 10^{-7})}{1} \]

3. **Calculate the limit of resolution**:
\[ \Delta \theta = 1.22 \times 5 \times 10^{-7} \]
\[ \Delta \theta = 6.1 \times 10^{-7} \text{ radians} \]

4. **Express the result in a more convenient form**:
\[ \Delta \theta = 61 \times 10^{-8} \text{ radians} \]

5. **Final answer**:
The limit of resolution of the telescope is:
\[ \Delta \theta = 61 \times 10^{-8} \text{ radians} \]