What is the path difference of destructive interference

Options

A. `n lambda `
B. ` ((n+1) lambda )/(2) `
C. `n ( lambda +1)`
D. `((2n + 1 ) lambda )/(2)`

Explanation

To determine the path difference for destructive interference, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Interference**: Interference occurs when two waves meet. There are two types of interference: constructive and destructive.

2. **Define Path Difference**: The path difference (\( \Delta x \)) is the difference in the distance traveled by two waves from their respective sources to a common point.

3. **Condition for Destructive Interference**: For destructive interference to occur, the waves must be out of phase. This happens when the path difference is an odd multiple of half the wavelength.

4. **Mathematical Representation**: The path difference for destructive interference can be expressed mathematically as:
\[ \Delta x = (2n + 1) \frac{\lambda}{2} \]
where \( n \) is an integer (0, 1, 2, ...), and \( \lambda \) is the wavelength of the waves.

5. **Conclusion**: Thus, the path difference for destructive interference is given by:
\[ \Delta x = \frac{(2n + 1) \lambda}{2} \]