gen-define-the-double-slit-interference-pattern-and-give-one-sho-d039

Define the double-slit interference pattern and give one short worked example.

# Double-Slit Interference Pattern ## Definition The **double-slit interference pattern** occurs when coherent light passes through two narrow, closely-spaced slits and creates an alternating pattern of bright and dark fringes on a screen. This happens because light waves from each slit overlap and interfere: - **Constructive interference** (bright fringes): waves arrive in phase - **Destructive interference** (dark fringes): waves arrive out of phase **Condition for bright fringes:** $$d \sin\theta = m\lambda$$ where: - *d* = slit separation - *θ* = angle from central axis - *m* = order number (0, ±1, ±2, ...) - *λ* = wavelength of light --- ## Worked Example **Problem:** Red laser light (λ = 650 nm) passes through two slits separated by d = 0.30 mm. A screen is placed L = 2.0 m away. Find the distance between the central bright fringe and the first bright fringe. **Solution:** For small angles: $\sin\theta \approx \tan\theta = \frac{y}{L}$ For first bright fringe (m = 1): $$d \sin\theta = \lambda$$ $$\sin\theta = \frac{\lambda}{d} = \frac{650 \times 10^{-9}}{0.30 \times 10^{-3}} = 2.17 \times 10^{-3}$$ Distance from center: $$y_1 = L\tan\theta \approx L\sin\theta = 2.0 \times 2.17 \times 10^{-3}$$ $$y_1 = 4.3 \text{ mm}$$ The first bright fringe appears **4.3 mm** from the center.