In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by `5xx10^(-2)` m towards the slits, the change in fringe width is `3xx10^(-5)`. If the distance between the slits is `10^(-3)`m, calculate the wavelength of the light used.

Options

A. 3000 Ã…
B. 4000 Ã…
C. 6000 Ã…
D. 7000 Ã…

Explanation

To solve the problem, we will use the formula for fringe width in a double-slit experiment and analyze the change in fringe width when the screen is moved closer to the slits.

### Step-by-Step Solution:

1. **Understand the Fringe Width Formula**:
The fringe width (β) in a double-slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light,
- \( D \) = distance from the slits to the screen,
- \( d \) = distance between the slits.

2. **Identify the Change in Fringe Width**:
When the screen is moved closer by \( \Delta D = 5 \times 10^{-2} \) m, the change in fringe width (\( \Delta \beta \)) is given as \( 3 \times 10^{-5} \) m.

3. **Set Up the Equation for Change in Fringe Width**:
The change in fringe width can be expressed as:
\[ \Delta \beta = \frac{\lambda \Delta D}{d} \]
Rearranging this gives:
\[ \lambda = \frac{\Delta \beta \cdot d}{\Delta D} \]

4. **Substitute the Given Values**:
- \( \Delta \beta = 3 \times 10^{-5} \) m,
- \( d = 10^{-3} \) m,
- \( \Delta D = 5 \times 10^{-2} \) m.

Plugging these values into the equation:
\[ \lambda = \frac{(3 \times 10^{-5}) \cdot (10^{-3})}{5 \times 10^{-2}} \]

5. **Calculate the Wavelength**:
\[ \lambda = \frac{3 \times 10^{-8}}{5 \times 10^{-2}} = 6 \times 10^{-7} \text{ m} \]
Converting to angstroms (1 m = \( 10^{10} \) angstroms):
\[ \lambda = 6 \times 10^{-7} \text{ m} = 6000 \text{ angstroms} \]

6. **Final Answer**:
The wavelength of the light used is \( 6000 \) angstroms.