Monochromatic green light of wavelength `5 xx 10^(-7) m` illuminates a pair of slits 1 mm apart. The separation of bright lines on the interference pattern formed on a screen 2 m away is

Options

A. `0.25` mm
B. `0.1 mm`
C. `1.0 mm`
D. `0.01mm`

Explanation

To solve the problem of finding the separation of bright lines (fringe width) in an interference pattern created by two slits illuminated by monochromatic green light, we can follow these steps:

### Step 1: Identify the given data
We have the following information:
- Wavelength of light, \( \lambda = 5 \times 10^{-7} \, \text{m} \)
- Distance between the slits, \( d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} \)
- Distance from the slits to the screen, \( D = 2 \, \text{m} \)

### Step 2: Use the formula for fringe width
The formula for fringe width (the separation between two consecutive bright lines) in a double-slit interference pattern is given by:
\[ \beta = \frac{D \lambda}{d} \]
where:
- \( \beta \) is the fringe width,
- \( D \) is the distance from the slits to the screen,
- \( \lambda \) is the wavelength of the light,
- \( d \) is the distance between the slits.

### Step 3: Substitute the values into the formula
Now we will substitute the values into the formula:
\[ \beta = \frac{(2 \, \text{m}) \cdot (5 \times 10^{-7} \, \text{m})}{1 \times 10^{-3} \, \text{m}} \]

### Step 4: Calculate the fringe width
Calculating the above expression:
\[ \beta = \frac{2 \cdot 5 \times 10^{-7}}{1 \times 10^{-3}} \]
\[ = \frac{10 \times 10^{-7}}{1 \times 10^{-3}} \]
\[ = 10 \times 10^{-7 + 3} = 10 \times 10^{-4} \, \text{m} = 1 \times 10^{-3} \, \text{m} = 1 \, \text{mm} \]

### Step 5: Conclusion
The separation of bright lines (fringe width) on the interference pattern is \( 1 \, \text{mm} \).