Two slits are made one millimeter apart and the screen is placed one metre away. When blue-green light of wavelength 500 nm is used, the fringe separation is

Options

A. `5xx10^(-4)m`
B. `2.5xx10^(-3)m`
C. `2xx10^(-4)m`
D. `10xx10^(-4)m`

Explanation

To find the fringe separation (β) in a double-slit experiment, we can use the formula:

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

where:
- \( \lambda \) is the wavelength of the light,
- \( D \) is the distance from the slits to the screen,
- \( d \) is the distance between the slits.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Distance between the slits, \( d = 1 \text{ mm} = 1 \times 10^{-3} \text{ m} \)
- Distance from the slits to the screen, \( D = 1 \text{ m} \)
- Wavelength of light, \( \lambda = 500 \text{ nm} = 500 \times 10^{-9} \text{ m} \)

2. **Substitute the Values into the Formula:**
\[ \beta = \frac{\lambda D}{d} = \frac{(500 \times 10^{-9} \text{ m})(1 \text{ m})}{1 \times 10^{-3} \text{ m}} \]

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

4. **Convert to Millimeters:**
\[ \beta = 500 \times 10^{-6} \text{ m} = 0.5 \text{ mm} \]

### Final Answer:
The fringe separation is \( 0.5 \text{ mm} \).

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