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. 1.5mm
B. 1m
C. 0.5mm
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 follow these steps:

### Step 1: Understand the formula for fringe width
The distance between consecutive bright or dark fringes (fringe width, β) is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = separation between the slits

### Step 2: Convert the given values into appropriate units
1. **Wavelength (λ)**: Given as 550 nm, we convert it to meters:
\[ \lambda = 550 \text{ nm} = 550 \times 10^{-9} \text{ m} \]

2. **Distance to the screen (D)**: Given as 1 m, we keep it as is:
\[ D = 1 \text{ m} \]

3. **Separation between the slits (d)**: Given as 1.10 mm, we convert it to meters:
\[ d = 1.10 \text{ mm} = 1.10 \times 10^{-3} \text{ m} \]

### Step 3: Substitute the values into the formula
Now, we substitute the values into the formula for fringe width:
\[ \beta = \frac{(550 \times 10^{-9} \text{ m}) \times (1 \text{ m})}{(1.10 \times 10^{-3} \text{ m})} \]

### Step 4: Calculate the fringe width
Perform the calculation:
\[ \beta = \frac{550 \times 10^{-9}}{1.10 \times 10^{-3}} = \frac{550}{1.10} \times 10^{-6} \]
Calculating \( \frac{550}{1.10} \):
\[ \frac{550}{1.10} = 500 \]
So,
\[ \beta = 500 \times 10^{-6} \text{ m} = 5.0 \times 10^{-4} \text{ m} \]

### Step 5: Convert the result to mm
To express the fringe width in millimeters:
\[ \beta = 5.0 \times 10^{-4} \text{ m} = 0.5 \text{ mm} \]

### Final Answer
The distance between consecutive bright or dark fringes is:
\[ \beta = 0.5 \text{ mm} \]

---