Light of wavelength `lamda` is coming from a star. What is the limit of resolution of a telescope whose objective has diameter?

Options

A. `(0.305 lamda)/r`
B. `(0.61 lamda)/r`
C. `(1.22 lamda)/r`
D. `(2 lamda)/r`

Answer

To find the limit of resolution of a telescope whose objective has a diameter \( R \) when light of wavelength \( \lambda \) is coming from a star, we can use the formula for the limit of resolution, which is derived from the Rayleigh criterion. Here are the steps to derive the solution:

### Step-by-Step Solution:

1. **Understand the Concept of Limit of Resolution**:
The limit of resolution refers to the smallest angular separation at which two point sources can be distinguished as separate entities. This is crucial for telescopes as it determines how well they can resolve two closely spaced stars.

2. **Use the Rayleigh Criterion**:
The Rayleigh criterion states that two point sources are just resolvable when the central maximum of one diffraction pattern coincides with the first minimum of the other. The formula for the limit of resolution \( \theta \) in radians is given by:
\[ \theta = \frac{1.22 \lambda}{R} \]
where \( \lambda \) is the wavelength of light and \( R \) is the diameter of the telescope's objective lens or mirror.

3. **Substitute the Values**:
In this case, we have the wavelength \( \lambda \) and the diameter \( R \) of the telescope's objective. Substitute these values into the formula:
\[ \theta = \frac{1.22 \lambda}{R} \]

4. **Interpret the Result**:
The result \( \theta \) gives us the limit of resolution in radians. A smaller value of \( \theta \) indicates better resolving power of the telescope, meaning it can distinguish between two closely spaced stars more effectively.

### Final Answer:
The limit of resolution of a telescope whose objective has diameter \( R \) for light of wavelength \( \lambda \) is given by:
\[ \theta = \frac{1.22 \lambda}{R} \]