The position of minima in the diffraction pattern due to a single slite are expressed by the formula

Options

A. ` a sin theta = nlambda`
B. `a sin theta =(2n +1) (lambda)/(2)`
C. `a sin theta=(n lambda)/(2)`
D. `a sin theta =(2n-1)xx(lambda)/(2)`

Answer

To find the position of minima in the diffraction pattern due to a single slit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a single slit of width \(d\).
- A monochromatic light of wavelength \(\lambda\) is incident on the slit.
- The light passing through the slit diffracts and creates a pattern on a screen.

2. **Condition for Minima**:
- The minima in the diffraction pattern occur due to destructive interference of light waves emanating from different parts of the slit.
- The condition for destructive interference is given by the path difference between light waves from two points in the slit.

3. **Path Difference Calculation**:
- For the first minima, consider two points at the edges of the slit. The path difference for light coming from these two points to a point on the screen at an angle \(\theta\) is given by:
\[ \text{Path Difference} = d \sin \theta \]

4. **Setting the Condition for Minima**:
- For destructive interference (minima), the path difference must be equal to an odd multiple of half the wavelength:
\[ d \sin \theta = n \lambda \quad \text{(where \(n\) is an integer)} \]
- For the first minima, we set \(n = 1\):
\[ d \sin \theta = \lambda \]

5. **Generalizing for Higher Minima**:
- For higher orders of minima, we can generalize the condition:
\[ d \sin \theta = n \lambda \quad (n = 1, 2, 3, \ldots) \]

6. **Conclusion**:
- The formula for the position of minima in the diffraction pattern due to a single slit is:
\[ d \sin \theta = n \lambda \]