A narrow slit of width 1 mm is illuminated by monochromatic light of wavelength 600 nm. The distance between the first minima on either side of a screen at a distance of 2 m is

Options

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

Answer

To solve the problem, we need to find the distance between the first minima on either side of a screen when a narrow slit is illuminated by monochromatic light. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

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

2. **Determine the Condition for Minima**:
- The condition for minima in single-slit diffraction is given by:
\[ a \sin \theta = n \lambda \]
- For the first minima (n = 1):
\[ a \sin \theta = \lambda \]

3. **Approximate for Small Angles**:
- For small angles, \(\sin \theta \approx \theta\) (in radians):
\[ a \theta = \lambda \implies \theta = \frac{\lambda}{a} \]

4. **Calculate the Angular Width**:
- The angular width between the first minima on either side is:
\[ 2\theta = 2 \left(\frac{\lambda}{a}\right) \]

5. **Convert Angular Width to Linear Distance**:
- The linear distance (y) between the first minima on either side can be calculated using:
\[ y = 2D \theta \]
- Substitute \(\theta\):
\[ y = 2D \left(\frac{\lambda}{a}\right) \]

6. **Substitute the Values**:
- Now substituting the known values:
\[ y = 2 \times 2 \, \text{m} \times \left(\frac{600 \times 10^{-9} \, \text{m}}{1 \times 10^{-3} \, \text{m}}\right) \]
- Simplifying this:
\[ y = 4 \times \left(\frac{600 \times 10^{-9}}{1 \times 10^{-3}}\right) \]
\[ y = 4 \times 600 \times 10^{-6} \, \text{m} = 2400 \times 10^{-6} \, \text{m} = 2.4 \, \text{mm} \]

7. **Final Answer**:
- The distance between the first minima on either side of the screen is **2.4 mm**.