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 \( R \) and is observing light of wavelength \( \lambda \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Limit of Resolution**:
The limit of resolution is the smallest angular separation between two point sources (like stars) that can be distinguished as separate. It is a measure of the resolving power of an optical instrument.

2. **Identify the Formula for Limit of Resolution**:
The formula for the limit of resolution \( \theta \) (in radians) for a circular aperture (like a telescope) is given by:
\[ \theta = \frac{1.22 \lambda}{R} \]
where:
- \( \theta \) is the limit of resolution,
- \( \lambda \) is the wavelength of the light,
- \( R \) is the diameter of the telescope's objective.

3. **Substitute the Given Values**:
In this problem, we have:
- Wavelength \( \lambda \) (as given),
- Diameter \( R \) (as given).
Thus, we can directly use the formula:
\[ \theta = \frac{1.22 \lambda}{R} \]

4. **Identify the Correct Option**:
From the options provided:
- Option 1: \( 0.305 \frac{\lambda}{R} \)
- Option 2: \( 0.61 \frac{\lambda}{R} \)
- Option 3: \( 1.22 \frac{\lambda}{R} \) (this matches our derived formula)
- Option 4: \( 2 \frac{\lambda}{R} \)

The correct answer is:
\[ \theta = 1.22 \frac{\lambda}{R} \]

### Final Answer:
The limit of resolution of the telescope is given by:
\[ \theta = 1.22 \frac{\lambda}{R} \]