Assume that light of wavelength 600 nm is coming from a star The limit of resolution of telescope whose objective has a diameter of 2 m is :

Options

A. `1.83 xx 10^(-7) ` rad
B. `7.32 xx 10^(-7) ` rad
C. `6.00 xx 10^(-7) ` rad
D. `3.66 xx 10^(-7)` rad

Explanation

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

\[ \theta_r = \frac{1.22 \cdot \lambda}{D} \]

where:
- θ_r is the limit of resolution in radians,
- λ is the wavelength of light (in meters),
- D is the diameter of the telescope's objective lens (in meters).

### Step-by-Step Solution:

1. **Identify the Wavelength (λ)**:
The problem states that the wavelength of light coming from the star is 600 nm. We need to convert this into meters.
\[ \lambda = 600 \text{ nm} = 600 \times 10^{-9} \text{ m} \]

2. **Identify the Diameter (D)**:
The diameter of the telescope's objective lens is given as 2 m.
\[ D = 2 \text{ m} \]

3. **Substitute Values into the Formula**:
Now we can substitute the values of λ and D into the formula for θ_r.
\[ \theta_r = 1.22 \cdot \frac{600 \times 10^{-9}}{2} \]

4. **Calculate θ_r**:
First, calculate the fraction:
\[ \frac{600 \times 10^{-9}}{2} = 300 \times 10^{-9} \text{ m} \]
Now, multiply by 1.22:
\[ \theta_r = 1.22 \cdot 300 \times 10^{-9} = 3.66 \times 10^{-7} \text{ radians} \]

5. **Final Result**:
The limit of resolution of the telescope is:
\[ \theta_r = 3.66 \times 10^{-7} \text{ radians} \]