Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm coming from a distance object, the limit of resolution of the telescope is close to :

Options

A. `1.5xx10^(-7) rad`
B. `2.0xx10^(-7) rad`
C. `3.0xx10^(-7) rad`
D. `4.5xx10^(-7) rad`

Answer

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

\[ \text{Limit of Resolution} (R) = \frac{1.22 \lambda}{d} \]

where:
- \( \lambda \) is the wavelength of light,
- \( d \) is the diameter of the objective lens.

### Step-by-Step Solution:

1. **Identify the given values:**
- Diameter of the objective lens, \( d = 250 \, \text{cm} \)
- Wavelength of light, \( \lambda = 600 \, \text{nm} \)

2. **Convert the units:**
- Convert the diameter from centimeters to meters:
\[ d = 250 \, \text{cm} = 250 \times 10^{-2} \, \text{m} = 2.5 \, \text{m} \]
- Convert the wavelength from nanometers to meters:
\[ \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} = 6.0 \times 10^{-7} \, \text{m} \]

3. **Substitute the values into the resolution formula:**
\[ R = \frac{1.22 \times 6.0 \times 10^{-7}}{2.5} \]

4. **Calculate the numerator:**
\[ 1.22 \times 6.0 = 7.32 \]

5. **Calculate the limit of resolution:**
\[ R = \frac{7.32 \times 10^{-7}}{2.5} = 2.928 \times 10^{-7} \, \text{m} \]

6. **Round the result:**
\[ R \approx 3.0 \times 10^{-7} \, \text{m} \]

### Final Answer:
The limit of resolution of the telescope is approximately \( 3.0 \times 10^{-7} \, \text{m} \).

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