In Young's double slit experiement when wavelength used is `6000Å` and the screen is `40cm` from the slits, the fringes are `0.012cm` wide. What is the distance between the slits?

Options

A. `0.24 cm`
B. `0.2 cm`
C. `2.4 cm`
D. `0.024 cm`

Explanation

To find the distance between the slits in Young's double slit experiment, we can use the formula for fringe width (β):

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

Where:
- \( \beta \) is the fringe width,
- \( D \) is the distance from the slits to the screen,
- \( \lambda \) is the wavelength of light used,
- \( d \) is the distance between the slits.

### Step 1: Convert the given values into appropriate units
- Wavelength \( \lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6 \times 10^{-7} \, \text{m} \)
- Distance from slits to screen \( D = 40 \, \text{cm} = 0.4 \, \text{m} \)
- Fringe width \( \beta = 0.012 \, \text{cm} = 0.012 \times 10^{-2} \, \text{m} = 1.2 \times 10^{-4} \, \text{m} \)

### Step 2: Rearrange the formula to solve for \( d \)
From the formula \( \beta = \frac{D \cdot \lambda}{d} \), we can rearrange it to find \( d \):

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

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

\[ d = \frac{0.4 \, \text{m} \cdot 6 \times 10^{-7} \, \text{m}}{1.2 \times 10^{-4} \, \text{m}} \]

### Step 4: Calculate the value of \( d \)
Calculating the numerator:

\[ 0.4 \cdot 6 \times 10^{-7} = 2.4 \times 10^{-7} \, \text{m} \]

Now, divide by the fringe width:

\[ d = \frac{2.4 \times 10^{-7}}{1.2 \times 10^{-4}} = 2 \times 10^{-3} \, \text{m} \]

### Step 5: Convert \( d \) into centimeters
Since \( 1 \, \text{m} = 100 \, \text{cm} \):

\[ d = 2 \times 10^{-3} \, \text{m} = 0.2 \, \text{cm} \]

### Final Answer
The distance between the slits \( d \) is \( 0.2 \, \text{cm} \).

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