In the Young's double slit experiment, the spacing between two slits is `0.1mm`. If the screen is kept at a distance of `1.0m` from the slits and the wavelength of ligth is `5000Å`, then the fringe width is

Options

A. `1.0 cm`
B. `1.5 cm`
C. `0.5 cm`
D. `2.0 cm`

Answer

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

### Step 1: Identify the given values
- Slit separation (d) = 0.1 mm = \(0.1 \times 10^{-3}\) m = \(1 \times 10^{-4}\) m
- Distance from slits to screen (D) = 1.0 m
- Wavelength of light (λ) = 5000 Å = \(5000 \times 10^{-10}\) m = \(5 \times 10^{-7}\) 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
Substituting the known values into the formula:
\[ \beta = \frac{(5 \times 10^{-7} \text{ m}) \times (1 \text{ m})}{(1 \times 10^{-4} \text{ m})} \]

### Step 4: Calculate the fringe width
Calculating the above expression:
\[ \beta = \frac{5 \times 10^{-7}}{1 \times 10^{-4}} = 5 \times 10^{-3} \text{ m} \]

### Step 5: Convert the fringe width to centimeters
To convert meters to centimeters, we multiply by 100:
\[ \beta = 5 \times 10^{-3} \text{ m} \times 100 = 0.5 \text{ cm} \]

### Final Answer
The fringe width is \(0.5 \text{ cm}\).

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