A telescope using light having wavelength 5000 Å and using lenses of focal lengths 2.5 cm and 30 cm. If the diameter of the aperature of the objective is 10 cm, then the resolving limit of telescope is

Options

A. `6.1xx10^(-6)`rad
B. `5.0xx10^(-6)`rad
C. `8.3xx10^(-4)`rad
D. `7.3xx10^(-3)`rad

Explanation

To find the resolving limit of the telescope, we will use the formula for the resolving power of a telescope, which is given by:

\[ R = \frac{1.22 \lambda}{A} \]

where:
- \( R \) is the resolving limit,
- \( \lambda \) is the wavelength of light,
- \( A \) is the diameter of the aperture.

### Step 1: Convert the Wavelength to Meters
The wavelength is given as \( 5000 \) Å (angstroms). We need to convert this to meters.

\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### Step 2: Convert the Diameter of the Aperture to Meters
The diameter of the aperture is given as \( 10 \, \text{cm} \). We need to convert this to meters as well.

\[ A = 10 \, \text{cm} = 10 \times 10^{-2} \, \text{m} = 0.1 \, \text{m} \]

### Step 3: Substitute Values into the Resolving Limit Formula
Now we can substitute the values of \( \lambda \) and \( A \) into the resolving limit formula.

\[ R = \frac{1.22 \times (5 \times 10^{-7})}{0.1} \]

### Step 4: Calculate the Resolving Limit
Now we perform the calculation.

\[ R = \frac{1.22 \times 5 \times 10^{-7}}{0.1} = 1.22 \times 5 \times 10^{-6} \]

Calculating \( 1.22 \times 5 \):

\[ 1.22 \times 5 = 6.1 \]

Thus,

\[ R = 6.1 \times 10^{-6} \, \text{radians} \]

### Final Answer
The resolving limit of the telescope is:

\[ R = 6.1 \times 10^{-6} \, \text{radians} \]