A double slit is illuminated by light of wavelength 12000 A .the slits are 0.1 cm apart and the screen is placed one metre away .find the sepration between the two adjacent minima?

Explanation

To solve the problem of finding the separation between two adjacent minima in a double slit experiment, we can follow these steps:

### Step 1: Understand the given parameters
- Wavelength of light (λ) = 12000 Å (Angstroms)
- Distance between the slits (d) = 0.1 cm
- Distance from the slits to the screen (D) = 1 m

### Step 2: Convert the units
- Convert the wavelength from Angstroms to meters:
\[ 1 \text{ Å} = 10^{-10} \text{ m} \]
Therefore,
\[ \lambda = 12000 \text{ Å} = 12000 \times 10^{-10} \text{ m} = 1.2 \times 10^{-6} \text{ m} \]

- Convert the distance between the slits from cm to meters:
\[ d = 0.1 \text{ cm} = 0.1 \times 10^{-2} \text{ m} = 1 \times 10^{-3} \text{ m} \]

### Step 3: Use the formula for fringe width (β)
The formula for fringe width (β) in a double slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
Where:
- λ = wavelength of light
- D = distance from the slits to the screen
- d = distance between the slits

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ \beta = \frac{(1.2 \times 10^{-6} \text{ m})(1 \text{ m})}{1 \times 10^{-3} \text{ m}} \]

### Step 5: Calculate the fringe width
Calculating the above expression:
\[ \beta = \frac{1.2 \times 10^{-6}}{1 \times 10^{-3}} = 1.2 \times 10^{-3} \text{ m} \]
This can also be expressed in millimeters:
\[ \beta = 1.2 \text{ mm} \]

### Step 6: Find the separation between two adjacent minima
The separation between two adjacent minima is equal to the fringe width (β). Thus, the separation between the two adjacent minima is:
\[ \text{Separation} = 1.2 \text{ mm} \]

### Final Answer
The separation between the two adjacent minima is **1.2 mm**.

---