Young's Double Slit Experiment: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Young's Double Slit Experiment. Understanding the underlying formula is key to arriving at the correct answer below:

Phase difference $\phi = \frac{2\pi}{\lambda} \times \Delta x$. When $\Delta x = \lambda$, $\phi = 2\pi$, intensity $I = I_{max}\cos^2(\pi) = I_{max} = K$. When $\Delta x = \lambda/4$, $\phi = \pi/2$. The intensity is $I = I_{max}\cos^2(\phi/2) = K\cos^2(\pi/4) = K(1/\sqrt{2})^2 = K/2$.