In a double slit experiment, the distance between the slits is d. The screen is at a distance D from the slits. If a bright fringe is formed opposite to one of the slits, its order is

Options

A. `(d)/(lambda)`
B. `(lambda^(2))/(dD)`
C. `(D^(2))/(2lambda D)`
D. `(d^(2))/(2D lambda)`

Explanation

To solve the problem of finding the order of the bright fringe formed opposite to one of the slits in a double slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a double slit setup with two slits separated by a distance \( d \).
- The screen is placed at a distance \( D \) from the slits.

2. **Identify the Position of the Bright Fringe**:
- A bright fringe is formed directly opposite to one of the slits.
- Since the screen is at distance \( D \), the position of the bright fringe \( X \) opposite to one of the slits is given by \( X = \frac{D}{2} \).

3. **Calculate the Path Difference**:
- The path difference \( \Delta \) for the interference pattern can be calculated using the formula:
\[ \Delta = \frac{d \cdot X}{D} \]
- Substituting \( X = \frac{D}{2} \) into the equation gives:
\[ \Delta = \frac{d \cdot \frac{D}{2}}{D} = \frac{d}{2} \]

4. **Relate Path Difference to Fringe Order**:
- For a bright fringe, the path difference is given by:
\[ \Delta = n \lambda \]
- Where \( n \) is the order of the bright fringe and \( \lambda \) is the wavelength of the light used.

5. **Set Up the Equation**:
- From the previous step, we have:
\[ n \lambda = \frac{d}{2} \]

6. **Solve for the Order \( n \)**:
- Rearranging the equation to find \( n \):
\[ n = \frac{d}{2\lambda} \]

### Final Answer:
The order of the bright fringe formed opposite to one of the slits is:
\[ n = \frac{d}{2\lambda} \]