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 solve the problem of finding the limit of resolution of a 100 cm telescope for a wavelength of \( \lambda = 5000 \) Å, we will follow these steps:

### Step 1: Understand the formula for the limit of resolution
The limit of resolution (\( \theta \)) for a telescope is given by the formula:
\[ \theta = \frac{1.22 \lambda}{D} \]
where:
- \( \theta \) is the limit of resolution in radians,
- \( \lambda \) is the wavelength of light (in cm),
- \( D \) is the diameter of the telescope (in cm).

### Step 2: Convert the wavelength from Ångstroms to centimeters
Given \( \lambda = 5000 \) Å, we need to convert this to centimeters.
1 Å = \( 10^{-8} \) cm, so:
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-8} \, \text{cm} = 5 \times 10^{-5} \, \text{cm} \]

### Step 3: Identify the diameter of the telescope
The diameter of the telescope is given as \( D = 100 \) cm.

### Step 4: Substitute the values into the formula
Now we can substitute \( \lambda \) and \( D \) into the limit of resolution formula:
\[ \theta = \frac{1.22 \times (5 \times 10^{-5} \, \text{cm})}{100 \, \text{cm}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \theta = \frac{1.22 \times 5 \times 10^{-5}}{100} = \frac{6.1 \times 10^{-5}}{100} = 6.1 \times 10^{-7} \, \text{radians} \]

### Step 6: Final result
Thus, the limit of resolution of the 100 cm telescope for \( \lambda = 5000 \) Å is:
\[ \theta \approx 6.1 \times 10^{-7} \, \text{radians} \]