In YDSE experiment separation between plane of slits and screen is `1 m`. Separation between slits is `2 mm`. The wavelength of light is `500 nm`. The fringe width is

Options

A. 0.85 mm
B. 0.50 mm
C. 0.75 mm
D. 0.25 mm

Answer

To solve the problem of finding the fringe width in a Young's Double Slit Experiment (YDSE), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Distance between the slits and the screen (D) = 1 m
- Separation between the slits (d) = 2 mm = 2 × 10^-3 m
- Wavelength of light (λ) = 500 nm = 500 × 10^-9 m

2. **Use the Formula for Fringe Width**:
The formula for fringe width (β) in a YDSE is given by:
\[ \beta = \frac{\lambda D}{d} \]

3. **Substitute the Values into the Formula**:
Now, substitute the values we have into the formula:
\[ \beta = \frac{(500 \times 10^{-9} \text{ m})(1 \text{ m})}{2 \times 10^{-3} \text{ m}} \]

4. **Calculate the Fringe Width**:
- First, calculate the numerator:
\[ 500 \times 10^{-9} \text{ m} \times 1 \text{ m} = 500 \times 10^{-9} \text{ m} \]
- Now, divide by the separation between the slits:
\[ \beta = \frac{500 \times 10^{-9}}{2 \times 10^{-3}} = \frac{500}{2} \times 10^{-9 + 3} = 250 \times 10^{-6} \text{ m} \]

5. **Convert to Millimeters**:
- To convert meters to millimeters:
\[ 250 \times 10^{-6} \text{ m} = 0.250 \text{ mm} \]

6. **Final Answer**:
The fringe width (β) is:
\[ \beta = 0.25 \text{ mm} \]