In single slit experiment, if green light is instead of orange light then width of fringe will

Options

A. Remain same
B. Become narrower
C. Becomes twice
D. Becomes four-times

Answer

To solve the problem regarding the change in fringe width when using green light instead of orange light in a single slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Fringe Width**:
The fringe width (β) in a single slit diffraction pattern is given by the formula:
\[ \beta = \frac{\lambda D}{a} \]
where:
- \( \lambda \) is the wavelength of the light used,
- \( D \) is the distance from the slit to the screen,
- \( a \) is the width of the slit.

2. **Identify the Wavelengths**:
- Orange light has a longer wavelength (approximately 600-620 nm).
- Green light has a shorter wavelength (approximately 495-570 nm).

3. **Compare the Wavelengths**:
Since the wavelength of green light is shorter than that of orange light, we can conclude:
\[ \lambda_{green} < \lambda_{orange} \]

4. **Analyze the Effect on Fringe Width**:
From the fringe width formula, we see that fringe width is directly proportional to the wavelength. Therefore, if we replace orange light with green light:
\[ \beta_{green} < \beta_{orange} \]
This means that the fringe width will decrease when using green light.

5. **Conclusion**:
Since the fringe width decreases when switching from orange light to green light, we can conclude that the width of the fringe will become narrower.

### Final Answer:
The width of the fringe will become narrower when using green light instead of orange light.