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

Answer

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 Concept
The separation between two adjacent minima in a double slit experiment is given by the fringe width (β). The formula for fringe width is:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) is the wavelength of light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

### Step 2: Gather Given Data
From the problem statement, we have:
- Wavelength \( \lambda = 12000 \) Å (angstroms),
- Distance between slits \( d = 0.1 \) cm,
- Distance to the screen \( D = 1 \) m.

### Step 3: Convert Units
We need to convert all measurements to meters:
- Convert \( \lambda \) from angstroms to meters:
\[ \lambda = 12000 \, \text{Å} = 12000 \times 10^{-10} \, \text{m} = 12 \times 10^{-7} \, \text{m} \]
- Convert \( d \) from centimeters to meters:
\[ d = 0.1 \, \text{cm} = 0.1 \times 10^{-2} \, \text{m} = 1 \times 10^{-3} \, \text{m} \]

### Step 4: Substitute Values into the Formula
Now we can substitute the values into the fringe width formula:
\[ \beta = \frac{(12 \times 10^{-7} \, \text{m}) \times (1 \, \text{m})}{(1 \times 10^{-3} \, \text{m})} \]

### Step 5: Calculate the Fringe Width
Calculating the above expression:
\[ \beta = \frac{12 \times 10^{-7}}{1 \times 10^{-3}} = 12 \times 10^{-4} \, \text{m} \]

### Step 6: Convert to Millimeters
To convert the result into millimeters:
\[ \beta = 12 \times 10^{-4} \, \text{m} = 1.2 \, \text{mm} \]

### Final Answer
The separation between two adjacent minima is \( 1.2 \, \text{mm} \).

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