Two slits, 4 mm apart, are illuminated by light of wavelength `6000 Å`. What will be the fringe width on a screen placed 2 m from the slits

Options

A. 0.12 mm
B. 0.3 mm
C. 3.0mm
D. 4.0mm

Answer

To solve the problem of finding the fringe width on a screen placed 2 m from two slits that are 4 mm apart and illuminated by light of wavelength 6000 Å, we can follow these steps:

### Step 1: Identify the given values
- Distance between the slits (d) = 4 mm = 4 x 10^-3 m
- Wavelength of light (λ) = 6000 Å = 6000 x 10^-10 m
- Distance from the slits to the screen (D) = 2 m

### Step 2: Write the formula for fringe width
The formula for fringe width (β) in a double-slit experiment is given by:

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

### Step 3: Substitute the values into the formula
Now, we can substitute the values we have into the formula:

\[ \beta = \frac{(6000 \times 10^{-10} \text{ m}) \cdot (2 \text{ m})}{(4 \times 10^{-3} \text{ m})} \]

### Step 4: Calculate the fringe width
Now, we will perform the calculation:

\[ \beta = \frac{6000 \times 10^{-10} \cdot 2}{4 \times 10^{-3}} \]

Calculating the numerator:

\[ 6000 \times 10^{-10} \cdot 2 = 12000 \times 10^{-10} = 1.2 \times 10^{-6} \text{ m} \]

Now, calculating the denominator:

\[ 4 \times 10^{-3} \text{ m} = 4 \times 10^{-3} \text{ m} \]

Now, substituting back into the equation:

\[ \beta = \frac{1.2 \times 10^{-6}}{4 \times 10^{-3}} = 0.3 \times 10^{-3} \text{ m} \]

### Step 5: Convert the fringe width to millimeters
Since we need the answer in millimeters:

\[ \beta = 0.3 \times 10^{-3} \text{ m} = 0.3 \text{ mm} \]

### Final Answer
The fringe width on the screen is **0.3 mm**.

---