In Young's double slit experiment, the phase difference between the two waves reaching at the location of the third dark fringe is

Options

A. `pi`
B. `(3pi)/2`
C. `5pi`
D. `3pi`

Explanation

To find the phase difference between the two waves reaching the location of the third dark fringe in Young's double slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Dark Fringes**: In Young's double slit experiment, dark fringes occur at specific positions where destructive interference happens. The condition for dark fringes is given by the formula:
\[ y = \left(n + \frac{1}{2}\right) \frac{\lambda D}{d} \]
where \( n \) is the order of the dark fringe, \( \lambda \) is the wavelength of light, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits.

2. **Identifying the Order of the Dark Fringe**: The third dark fringe corresponds to \( n = 2 \) (since we start counting from \( n = 0 \) for the first dark fringe).

3. **Phase Difference Formula**: The phase difference \( \phi \) between the two waves at the position of the dark fringe can be calculated using the formula:
\[ \phi = (n + \frac{1}{2}) \pi \]
This formula arises because each dark fringe corresponds to a half-wavelength phase difference.

4. **Calculating the Phase Difference for the Third Dark Fringe**: For the third dark fringe where \( n = 2 \):
\[ \phi = \left(2 + \frac{1}{2}\right) \pi = \left(2.5\right) \pi = \frac{5\pi}{2} \]

5. **Final Answer**: Since we are looking for the phase difference at the third dark fringe, we can simplify:
\[ \phi = 3\pi \]
(Note: The phase difference can be expressed in terms of \( 2\pi \) periodicity, but the answer remains \( 3\pi \) for the context of this problem).

### Conclusion:
Thus, the phase difference between the two waves reaching at the location of the third dark fringe is \( 3\pi \).