In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :

<p>In Young's double slit experiment, the fringe width $\beta$ is given by:</p> <p>$\beta = \frac{\lambda D}{d}$</p> <p>where:</p> <p><p>$\lambda$ is the wavelength of light,</p></p> <p><p>$D$ is the distance from the slits to the screen,</p></p> <p><p>$d$ is the separation between the slits.</p></p> <p>Here's how the change affects the fringe width:</p> <p><p><strong>Initial Situation:</strong> </p> <p>When $d = 0.2 \text{ mm}$, the fringe width is: </p> <p>$\beta_{\text{initial}} = \frac{\lambda D}{0.2 \text{ mm}}$</p></p> <p><p><strong>After Increasing Slit Separation:</strong> </p> <p>When $d$ is increased to $0.4 \text{ mm}$: </p> <p>$\beta_{\text{new}} = \frac{\lambda D}{0.4 \text{ mm}}$</p></p> <p><p><strong>Comparing the Two Fringe Widths:</strong> </p> <p>Notice that: </p> <p>$$\beta_{\text{new}} = \frac{1}{2} \times \frac{\lambda D}{0.2 \text{ mm}} = \frac{1}{2} \beta_{\text{initial}}$$ </p> <p>This means the fringe width is halved, which is a reduction of $50\%$.</p></p> <p>Thus, the fringe width decreases by $50\%$ when the slit separation is increased from $0.2 \text{ mm}$ to $0.4 \text{ mm}$.</p> <p>The correct answer is Option B: $50\%$.</p>