In Young's double-slit, experiment, light of `6000 Å` is used. What will be the distance between two adjacent minima if distance between both the slits is 0.2 cm and interference pattern is observed at a distance of 1m.

Answer

To find the distance between two adjacent minima in Young's double-slit experiment, we can use the formula for fringe width. The distance between adjacent minima (or dark fringes) can be calculated using the following steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Wavelength of light, \( \lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6 \times 10^{-7} \, \text{m} \)
- Distance between the slits, \( d = 0.2 \, \text{cm} = 0.2 \times 10^{-2} \, \text{m} = 2 \times 10^{-3} \, \text{m} \)
- Distance from the slits to the screen, \( D = 1 \, \text{m} \)

2. **Use the formula for fringe width (β):**
The fringe width (distance between adjacent minima or maxima) is given by the formula:
\[ \beta = \frac{d \lambda}{D} \]

3. **Substitute the values into the formula:**
\[ \beta = \frac{(2 \times 10^{-3} \, \text{m})(6 \times 10^{-7} \, \text{m})}{1 \, \text{m}} \]

4. **Calculate β:**
\[ \beta = 2 \times 10^{-3} \times 6 \times 10^{-7} = 12 \times 10^{-10} \, \text{m} = 1.2 \times 10^{-9} \, \text{m} = 1.2 \, \text{nm} \]

5. **Conclusion:**
The distance between two adjacent minima is \( 1.2 \, \text{nm} \).