In a Young’s double slit experiment, the source illuminating the slits is changed from blue to violet. The width of the fringes

Options

A. Increases
B. Decreases
C. Becomes unequal
D. Remains same

Answer

To solve the problem regarding the change in fringe width when the light source in a Young's double slit experiment is changed from blue to violet, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Fringe Width**:
The fringe width (β) in a Young's double slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of the light used
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the two slits

2. **Identify the Wavelengths**:
- The wavelength of blue light is greater than that of violet light.
- Generally, the order of wavelengths in the visible spectrum is: Red > Orange > Yellow > Green > Blue > Indigo > Violet.
- Therefore, we can denote:
- \( \lambda_{blue} > \lambda_{violet} \)

3. **Analyze the Effect of Changing Wavelength**:
- Since the fringe width (β) is directly proportional to the wavelength (λ), if the wavelength decreases, the fringe width will also decrease.
- Mathematically, if we replace \( \lambda \) with a smaller value (from blue to violet), we can conclude:
\[ \text{If } \lambda_{blue} > \lambda_{violet}, \text{ then } \beta_{blue} > \beta_{violet} \]

4. **Conclusion**:
- Since the wavelength is decreasing when changing from blue to violet, the fringe width will also decrease.
- Therefore, the final answer is that the width of the fringes decreases.

### Final Answer:
The width of the fringes decreases when the light source is changed from blue to violet.

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