In a single slit diffraction pattern, if the light source is used of less wave length then previous one. Then width of the central fringe will be-

Options

A. less
B. increase
C. unchanged
D. none of the above

Answer

To solve the problem regarding the width of the central fringe in a single slit diffraction pattern when the wavelength of the light source is decreased, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Diffraction**: In a single slit diffraction pattern, light passing through a narrow slit spreads out and creates a pattern of bright and dark fringes on a screen. The central fringe is the brightest and widest.

2. **Identify the Condition for Minima**: The condition for the first minima in a single slit diffraction pattern is given by the formula:
\[ a \sin \theta = m \lambda \]
where \( a \) is the width of the slit, \( \lambda \) is the wavelength of the light, and \( m \) is the order of the minima (for the first minima, \( m = 1 \)).

3. **Relate Angular Position to Linear Position**: For small angles, we can use the approximation \( \sin \theta \approx \tan \theta \approx \frac{y}{D} \), where \( y \) is the distance from the central maximum to the first minima on the screen, and \( D \) is the distance from the slit to the screen.

4. **Substitute the Approximation**: Substituting the approximation into the minima condition gives:
\[ a \frac{y}{D} = \lambda \]
Rearranging this, we find:
\[ y = \frac{\lambda D}{a} \]

5. **Calculate the Width of the Central Fringe**: The width of the central fringe is the distance between the first minima on either side of the central maximum, which is:
\[ \text{Width of central fringe} = 2y = 2 \frac{\lambda D}{a} \]

6. **Analyze the Effect of Wavelength**: From the equation \( \text{Width} = \frac{2\lambda D}{a} \), we see that the width of the central fringe is directly proportional to the wavelength \( \lambda \). Therefore, if the wavelength decreases, the width of the central fringe will also decrease.

7. **Conclusion**: If the wavelength of the light source is less than the previous one, the width of the central fringe will be less. Thus, the answer is that the width of the central fringe will decrease.

### Final Answer:
The width of the central fringe will be less.