In an interference experiment, the spacing between successive maxima or minima is
(Where the symbols have their usual meanings)

Options

A. `lambda d//D`
B. `lambda D//d`
C. `dD//lambda`
D. `lambdad//4D`

Answer

To find the spacing between successive maxima or minima in an interference experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Fringe Width**:
In an interference experiment, such as Young's double-slit experiment, the spacing between successive maxima (bright fringes) or minima (dark fringes) is referred to as the fringe width.

2. **Using the Formula for Fringe Width**:
The formula for the position of the nth maximum (or minimum) on the screen is given by:
\[ y_n = \frac{n \lambda D}{d} \]
where:
- \( y_n \) is the distance of the nth fringe from the central maximum,
- \( n \) is the order of the fringe (n = 0, 1, 2, ...),
- \( \lambda \) is the wavelength of the light used,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

3. **Finding the Difference Between Successive Maxima**:
To find the spacing (fringe width) between two successive maxima, we can calculate the difference between the positions of the nth and (n-1)th maxima:
\[ \Delta y = y_n - y_{n-1} \]
Substituting the formula for \( y_n \):
\[ \Delta y = \frac{n \lambda D}{d} - \frac{(n-1) \lambda D}{d} \]

4. **Simplifying the Expression**:
Simplifying the above expression gives:
\[ \Delta y = \frac{n \lambda D}{d} - \frac{(n-1) \lambda D}{d} = \frac{\lambda D}{d} \]
This result shows that the spacing between successive maxima (or minima) is constant and is equal to the fringe width.

5. **Conclusion**:
Therefore, the spacing between successive maxima or minima in an interference experiment is given by:
\[ \text{Fringe Width} = \frac{\lambda D}{d} \]

### Final Answer:
The spacing between successive maxima or minima is \( \frac{\lambda D}{d} \).

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