Wave Interference and Diffraction Guide

Act as an IB Physics tutor. Help me understand this wave interference problem: **Key concepts:** - **Constructive interference**: Path difference = $n\lambda$ (where n = 0, 1, 2, ...) - **Destructive interference**: Path difference = $(n + \frac{1}{2})\lambda$ **Double-slit interference:** $$d \sin(\theta) = n\lambda$$ (for bright fringes) $$d \sin(\theta) = (n + \frac{1}{2})\lambda$$ (for dark fringes) Where: $d$ = slit separation, $\lambda$ = wavelength, $\theta$ = angle **Single-slit diffraction:** $$b \sin(\theta) = n\lambda$$ (for dark fringes) **Problem-solving steps:** 1. Identify the setup (double-slit, single-slit, etc.) 2. Draw a diagram showing path difference 3. Determine if asking for max or min (bright or dark) 4. Apply appropriate formula 5. Solve for unknown (usually θ, λ, or d) 6. Use small angle approximation if needed: $\sin(\theta) \approx \tan(\theta) \approx \theta$ **IB Tip:** Clearly state which formula you're using and why **My problem:** [PASTE WAVE INTERFERENCE PROBLEM]