The Young's double slit experiment the wavelength of light `lamda=4xx10^(-7)m` and separation between the slits is `d=0.1mm`. If the frintge width is `4mm` then the seperation between the slits and the screen will be

Options

A. 100 mm
B. 1m
C. `10^(6)m`
D. `10Å`

Explanation

To solve the problem, we will use the formula for fringe width in the Young's double slit experiment:

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

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

Given:
- Wavelength, \(\lambda = 4 \times 10^{-7} \, m\)
- Separation between the slits, \(d = 0.1 \, mm = 0.1 \times 10^{-3} \, m = 1 \times 10^{-4} \, m\)
- Fringe width, \(\beta = 4 \, mm = 4 \times 10^{-3} \, m\)

We need to find \(D\).

### Step 1: Rearrange the formula to solve for \(D\)

From the formula for fringe width, we can rearrange it to find \(D\):

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

### Step 2: Substitute the known values into the equation

Now we will substitute the known values into the rearranged formula:

\[ D = \frac{(4 \times 10^{-3} \, m)(1 \times 10^{-4} \, m)}{4 \times 10^{-7} \, m} \]

### Step 3: Calculate the numerator

First, calculate the numerator:

\[ 4 \times 10^{-3} \, m \times 1 \times 10^{-4} \, m = 4 \times 10^{-7} \, m^2 \]

### Step 4: Divide the numerator by the wavelength

Now, divide the result by the wavelength:

\[ D = \frac{4 \times 10^{-7} \, m^2}{4 \times 10^{-7} \, m} = 1 \, m \]

### Final Answer

The separation between the slits and the screen is:

\[ D = 1 \, m \]