In Young.s double slit experiment, blue-green light of wavelength 500nm is used. The slits are `1.20mm` apart, and the viewing screen is `5.40 m` away from the slits. What is the fringe width.

Options

A. `6.2mm`
B. `4.2 mm`
C. `2.25 mm`
D. `1.25 mm`

Answer

To find the fringe width in Young's double slit experiment, we can use the formula:

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

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

### Step 1: Convert the given values to standard units
1. **Wavelength (\( \lambda \))**: Given as \( 500 \) nm.
\[ \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \]

2. **Distance between the slits (\( d \))**: Given as \( 1.20 \) mm.
\[ d = 1.20 \, \text{mm} = 1.20 \times 10^{-3} \, \text{m} \]

3. **Distance to the screen (\( D \))**: Given as \( 5.40 \) m.
\[ D = 5.40 \, \text{m} \]

### Step 2: Substitute the values into the formula
Now, substituting the values into the fringe width formula:
\[ x = \frac{(500 \times 10^{-9}) \times 5.40}{1.20 \times 10^{-3}} \]

### Step 3: Calculate the fringe width
1. Calculate the numerator:
\[ 500 \times 10^{-9} \times 5.40 = 2.7 \times 10^{-6} \, \text{m} \]

2. Now, divide by \( d \):
\[ x = \frac{2.7 \times 10^{-6}}{1.20 \times 10^{-3}} = 2.25 \times 10^{-3} \, \text{m} \]

### Step 4: Convert to millimeters
To convert meters to millimeters:
\[ x = 2.25 \times 10^{-3} \, \text{m} = 2.25 \, \text{mm} \]

### Conclusion
Thus, the fringe width \( x \) is:
\[ \boxed{2.25 \, \text{mm}} \]