In Young's experiment, the distance between two slit is 0.8 mm and distance of screen from slit is `1.2` m. If the fringe width is `0.79` mm, then the wave length of light will be

Options

A. 4267 A.U
B. 3267 A.U
C. 5267 A.U.
D. 5537 A.U

Explanation

To find the wavelength of light used in Young's double slit experiment, we can use the formula for fringe width (β):

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

Where:
- \( \beta \) = fringe width
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the two slits

### Step 1: Identify the given values
- Fringe width (\( \beta \)) = 0.79 mm = \( 0.79 \times 10^{-3} \) m
- Distance between the slits (\( d \)) = 0.8 mm = \( 0.8 \times 10^{-3} \) m
- Distance from the slits to the screen (\( D \)) = 1.2 m

### Step 2: Rearrange the formula to solve for wavelength (\( \lambda \))
We can rearrange the formula to find \( \lambda \):

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

### Step 3: Substitute the values into the equation
Now, substitute the known values into the rearranged formula:

\[ \lambda = \frac{(0.79 \times 10^{-3} \, \text{m}) \times (0.8 \times 10^{-3} \, \text{m})}{1.2 \, \text{m}} \]

### Step 4: Perform the calculation
Calculating the numerator:

\[ 0.79 \times 0.8 = 0.632 \]

Now, substituting this back into the equation:

\[ \lambda = \frac{0.632 \times 10^{-6}}{1.2} \]

Calculating the wavelength:

\[ \lambda = 0.5267 \times 10^{-6} \, \text{m} \]

### Step 5: Convert to Angstroms
Since \( 1 \, \text{m} = 10^{10} \, \text{Å} \):

\[ \lambda = 0.5267 \times 10^{-6} \, \text{m} \times 10^{10} \, \text{Å/m} = 5267 \, \text{Å} \]

### Final Answer
The wavelength of the light used is \( 5267 \, \text{Å} \).

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