If aperture diameter of the lens of a telescope is 1.25 m and wavelength of light used is 5000 Å, its resolving power is

Options

A. `2.05xx10^(6)`
B. `2.5xx10^(5)`
C. `4.1xx10^(5)`
D. `4.1xx10^(6)`

Answer

To find the resolving power of the telescope, we can use the formula for the resolving power (RP) of a telescope, which is given by:

\[ RP = \frac{d}{1.22 \lambda} \]

where:
- \( d \) is the diameter of the telescope's aperture,
- \( \lambda \) is the wavelength of light used.

### Step 1: Identify the given values
- Diameter of the lens \( d = 1.25 \, \text{m} \)
- Wavelength of light \( \lambda = 5000 \, \text{Å} \)

### Step 2: Convert the wavelength from angstroms to meters
1 angstrom (Å) = \( 10^{-10} \) meters, so:
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### Step 3: Substitute the values into the formula
Now substitute \( d \) and \( \lambda \) into the resolving power formula:
\[ RP = \frac{1.25 \, \text{m}}{1.22 \times 5 \times 10^{-7} \, \text{m}} \]

### Step 4: Calculate the denominator
First, calculate \( 1.22 \times 5 \):
\[ 1.22 \times 5 = 6.1 \]
Now, multiply by \( 10^{-7} \):
\[ 6.1 \times 10^{-7} \, \text{m} \]

### Step 5: Calculate the resolving power
Now substitute back into the equation:
\[ RP = \frac{1.25}{6.1 \times 10^{-7}} \approx 2.049 \times 10^{6} \]

### Step 6: Round the result
Rounding \( 2.049 \times 10^{6} \) gives:
\[ RP \approx 2.05 \times 10^{6} \]

### Conclusion
The resolving power of the telescope is approximately \( 2.05 \times 10^{6} \) (unitless).