In a double-slit experiment, the two slits are separated by one milimeter and the screen is placed one meter away. The fringe separation for blue green light of wavelength `500` nm is

Options

A. `10` mm
B. `0.5` mm
C. `20` mm
D. `15`mm

Explanation

To find the fringe separation (also known as fringe width) in a double-slit experiment, we can use the formula:

\[ \beta = \frac{\lambda D}{d} \]

Where:
- \(\beta\) is the fringe separation,
- \(\lambda\) is the wavelength of the light,
- \(D\) is the distance from the slits to the screen,
- \(d\) is the separation between the two slits.

### Given Data:
- Wavelength, \(\lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m}\)
- Distance to the screen, \(D = 1 \, \text{m}\)
- Slit separation, \(d = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m}\)

### Step-by-Step Solution:

1. **Convert all units to meters**:
- Wavelength: \(500 \, \text{nm} = 500 \times 10^{-9} \, \text{m}\)
- Slit separation: \(1 \, \text{mm} = 1 \times 10^{-3} \, \text{m}\)

2. **Substitute the values into the fringe width formula**:
\[ \beta = \frac{(500 \times 10^{-9} \, \text{m}) \times (1 \, \text{m})}{(1 \times 10^{-3} \, \text{m})} \]

3. **Calculate the numerator**:
\[ 500 \times 10^{-9} \times 1 = 500 \times 10^{-9} \, \text{m} \]

4. **Calculate the fringe width**:
\[ \beta = \frac{500 \times 10^{-9}}{1 \times 10^{-3}} = 500 \times 10^{-6} \, \text{m} \]

5. **Convert the result to millimeters**:
\[ 500 \times 10^{-6} \, \text{m} = 0.5 \, \text{mm} \]

### Final Answer:
The fringe separation for blue-green light of wavelength \(500 \, \text{nm}\) is \(0.5 \, \text{mm}\).

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