In Young's double slit experiment, the slits are 3 mm apart. The wavelength of light used is 5000 Å and the distance between the slits and the screen is 90 cm. The fringe width in mm is

Options

A. 1.5
B. 0.015
C. `2.0`
D. 0.15

Explanation

To solve the problem of finding the fringe width in Young's double slit experiment, we will follow these steps:

### Step 1: Understand the given values
- Distance between the slits (d) = 3 mm = 3 x 10^-3 m
- Wavelength of light (λ) = 5000 Å = 5000 x 10^-10 m = 5 x 10^-7 m
- Distance from the slits to the screen (D) = 90 cm = 90 x 10^-2 m = 0.90 m

### Step 2: Use the formula for fringe width
The formula for fringe width (β) in Young's double slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]

### Step 3: Substitute the values into the formula
Now we will substitute the known values into the formula:
\[ \beta = \frac{(5 \times 10^{-7} \text{ m}) \times (0.90 \text{ m})}{(3 \times 10^{-3} \text{ m})} \]

### Step 4: Calculate the numerator
First, calculate the numerator:
\[ 5 \times 10^{-7} \text{ m} \times 0.90 \text{ m} = 4.5 \times 10^{-7} \text{ m}^2 \]

### Step 5: Calculate the fringe width
Now, divide the result by the distance between the slits:
\[ \beta = \frac{4.5 \times 10^{-7} \text{ m}^2}{3 \times 10^{-3} \text{ m}} = 1.5 \times 10^{-4} \text{ m} \]

### Step 6: Convert to mm
To convert the fringe width from meters to millimeters, multiply by 1000:
\[ \beta = 1.5 \times 10^{-4} \text{ m} \times 1000 = 0.15 \text{ mm} \]

### Conclusion
The fringe width is \(0.15 \text{ mm}\).

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