Young’s double slit experiment is performed with light of wavelength 550 nm . The separation between the slits is `1.10 mm` and screen is placed at distance of 1 m . What is the distance between the consecutive bright or dark fringes

Options

A. `1.5 mm`
B. `1.0 mm`
C. `0.5 mm`
D. None of these

Answer

To solve the problem of finding the distance between consecutive bright or dark fringes in Young's double slit experiment, we can use the formula for fringe width (β):

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

where:
- \( \beta \) = fringe width (distance between consecutive bright or dark fringes)
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = separation between the slits

### Step 1: Convert the given values to appropriate units
- Wavelength \( \lambda = 550 \, \text{nm} = 550 \times 10^{-9} \, \text{m} \)
- Distance to screen \( D = 1 \, \text{m} \)
- Slit separation \( d = 1.10 \, \text{mm} = 1.10 \times 10^{-3} \, \text{m} \)

### Step 2: Substitute the values into the fringe width formula
Now we substitute the values into the formula:

\[ \beta = \frac{(550 \times 10^{-9} \, \text{m}) \times (1 \, \text{m})}{1.10 \times 10^{-3} \, \text{m}} \]

### Step 3: Calculate the fringe width
Calculating the above expression:

\[ \beta = \frac{550 \times 10^{-9}}{1.10 \times 10^{-3}} \]

\[ \beta = \frac{550}{1.10} \times 10^{-6} \]

\[ \beta = 500 \times 10^{-6} \, \text{m} \]

\[ \beta = 0.5 \, \text{mm} \]

### Conclusion
The distance between consecutive bright or dark fringes is \( 0.5 \, \text{mm} \).

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