In a Young's double-slit experiment, green light is incident on the two slits. The interference pattern is observed on a screen. Which one of the following changes would cause the observed fringes to be more closely spaced?

Options

A. Reducing the separation between the slits
B. Using blue light instead of green light
C. Using red light instead of green light
D. Moving the light source further away from the slits

Answer

To determine which change would cause the observed fringes in a Young's double-slit experiment to be more closely spaced, we need to analyze the formula for fringe width (β):

### Step-by-Step Solution:

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

2. **Identify the relationship between fringe width and wavelength**:
From the formula, we can see that fringe width (β) is directly proportional to the wavelength (λ). This means that if the wavelength decreases, the fringe width will also decrease, resulting in more closely spaced fringes.

3. **Analyze the options provided**:
- **Option 1**: Reducing the separation between the slits (d). If we reduce \( d \), β will increase, leading to wider fringes. This option is incorrect.
- **Option 2**: Using blue light instead of green light. Blue light has a shorter wavelength than green light, which means β will decrease, leading to more closely spaced fringes. This option is correct.
- **Option 3**: Using red light instead of green light. Red light has a longer wavelength than green light, which means β will increase, leading to wider fringes. This option is incorrect.
- **Option 4**: Moving the light source further away from the slits. This does not affect the fringe width as it only changes the intensity of the light. This option is incorrect.

4. **Conclusion**:
The only change that would cause the observed fringes to be more closely spaced is **Option 2: Using blue light instead of green light**.

### Final Answer:
Using blue light instead of green light would cause the observed fringes to be more closely spaced.