In interference and diffraction, the light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. A. As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy. B. Diffraction and interference are characteristics exhibited only by light waves. Choose the correct answer from the options given below:

Related Formula

Core Logic

Where Δ x = λ$\Delta x = \lambda$, the phase difference Δφ = 2π$\Delta\phi = 2\pi$. Intensity I = I₀ ²((2π)/(2)) = I₀ ²(π) = I₀$I = I_0 \cos^2\left(\frac{2\pi}{2}\right) = I_0 \cos^2(\pi) = I_0$. We are given that at this point, Intensity = K$= K$. Thus, I₀ = K$I_0 = K$.

Step 1: Calculate Intensity at new path difference

Now evaluate at Δ x = (λ)/(3)$\Delta x = \frac{\lambda}{3}$. The phase difference is:

Substitute this into the intensity formula:

Since ((π)/(3)) = (1)/(2)$\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$:

Since I₀ = K$I_0 = K$, we get:

Pattern Recognition

In YDSE, phase angle is strictly mapped to path difference λ → 2π$\lambda → 2\pi$. The square of the cosine half-angle dictates the final intensity drop.

Chapter Mix

Class 12 Physics: Wave Optics