A beam of light of wavelength 600nm from a distance source falls on a single slit 1mm wide and a resulting diffraction pattern is observed on a screen 2m away. The distance between the first dark frings on either side of central bright fringe is

Options

A. 1.2cm
B. 1.2mm
C. 2.4cm
D. 2.4mm

Explanation

To solve the problem of finding the distance between the first dark fringes on either side of the central bright fringe in a single slit diffraction pattern, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Wavelength of light, \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
- Width of the slit, \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Distance from the slit to the screen, \( D = 2 \, \text{m} \)

2. **Formula for the Position of Dark Fringes**:
The position of the first dark fringe in a single slit diffraction pattern is given by the formula:
\[ y_1 = \frac{\lambda D}{d} \]
where \( y_1 \) is the distance from the central maximum to the first dark fringe.

3. **Substituting the Values**:
Plugging in the values into the formula:
\[ y_1 = \frac{600 \times 10^{-9} \, \text{m} \times 2 \, \text{m}}{1 \times 10^{-3} \, \text{m}} \]

4. **Calculating \( y_1 \)**:
Performing the calculation:
\[ y_1 = \frac{600 \times 10^{-9} \times 2}{1 \times 10^{-3}} = 1200 \times 10^{-6} \, \text{m} = 1.2 \, \text{mm} \]

5. **Finding the Distance Between the First Dark Fringes**:
The distance between the first dark fringes on either side of the central bright fringe is \( 2y_1 \):
\[ \text{Distance between first dark fringes} = 2y_1 = 2 \times 1.2 \, \text{mm} = 2.4 \, \text{mm} \]

6. **Conclusion**:
The distance between the first dark fringes on either side of the central bright fringe is \( 2.4 \, \text{mm} \).

### Final Answer:
The distance between the first dark fringes on either side of the central bright fringe is **2.4 mm**.

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