Angular width of central maxima of a single slit diffraction pattern is independent of

Options

A. slit width
B. frequency of the light used
C. wavelength of the light used
D. distance between slit and screen

Explanation

To determine the factor that the angular width of the central maxima of a single slit diffraction pattern is independent of, we can analyze the relationship between the parameters involved in the diffraction pattern.

### Step-by-Step Solution:

1. **Understanding the Diffraction Pattern**:
The angular width of the central maxima in a single slit diffraction pattern is defined by the angle θ at which the first minimum occurs on either side of the central maximum. The condition for the first minimum is given by:
\[ d \sin \theta = \lambda \]
where \(d\) is the width of the slit, \(\lambda\) is the wavelength of the light used, and \(\theta\) is the angle.

2. **Rearranging the Equation**:
From the equation \(d \sin \theta = \lambda\), we can express \(\sin \theta\) as:
\[ \sin \theta = \frac{\lambda}{d} \]
Therefore, the angle θ can be approximated (for small angles) as:
\[ \theta \approx \sin^{-1}\left(\frac{\lambda}{d}\right) \]

3. **Identifying Dependencies**:
From the above relationship, we can see that:
- The angular width θ depends on the wavelength \(\lambda\) of the light used.
- The angular width θ also depends on the slit width \(d\).

4. **Considering Other Factors**:
The question asks for the factor that the angular width is independent of. The options provided include:
- Slit width (d)
- Frequency of the light used
- Wavelength of the light used
- Distance between the slit and the screen

We have established that the angular width depends on both the slit width and the wavelength.

5. **Analyzing the Distance**:
The distance between the slit and the screen does not appear in the equation for determining the angle θ. Therefore, it does not affect the angular width of the central maxima.

6. **Conclusion**:
The angular width of the central maxima of a single slit diffraction pattern is independent of the distance between the slit and the screen.

### Final Answer:
The angular width of the central maxima of a single slit diffraction pattern is independent of the **distance between the slit and the screen**.