🌈 Interference of Light Waves & Young’s Double-Slit Experiment

1 • Why do we need coherent sources? 💡

  • Two independent lamps change phase randomly in about 10-10 s, so their waves never stay “in step.” Their brightnesses just add; no fringes appear :contentReference[oaicite:0]{index=0}.
  • A pair of sources is called coherent when their phase gap stays fixed. Only then can the waves combine to give stable bright and dark regions :contentReference[oaicite:1]{index=1}.

2 • Young’s clever trick 🧑‍🔬

  • Thomas Young let a single bright source S light two tiny, closely spaced pinholes S1 and S2 on an opaque slide :contentReference[oaicite:2]{index=2}.
  • Because S1 and S2 both come from the same parent wave, any sudden phase jump at S reaches them together. The two pinholes therefore act as phase-locked (coherent) sources :contentReference[oaicite:3]{index=3}.
  • Spherical waves from S1 and S2 overlap on a distant screen and paint a regular pattern of bright and dark bands called fringes :contentReference[oaicite:4]{index=4}.

3 • Maths of the fringes 📐

Let

  • d = distance between pinholes
  • D = distance from pinholes to the screen (≳ a few cm)
  • λ = wavelength of the light
  • x = distance of a point on the screen from the central line

Then:

  • Bright (constructive) band 🎉
    \[ \frac{xd}{D}=n\lambda \quad\Rightarrow\quad x_n = \frac{n\,\lambda D}{d}, \; n = 0,\pm1,\pm2,\ldots \] :contentReference[oaicite:5]{index=5}
  • Dark (destructive) band 🌑
    \[ \frac{xd}{D}=\Bigl(n+\frac12\Bigr)\lambda \quad\Rightarrow\quad x_n = \Bigl(n+\tfrac12\Bigr)\frac{\lambda D}{d} \] :contentReference[oaicite:6]{index=6}
  • The spacing between neighbouring bright (or dark) fringes is constant: \[ \beta = x_{n+1}-x_n = \frac{\lambda D}{d} \] (equal-spacing fact stated just after the formulas) :contentReference[oaicite:7]{index=7}.

4 • What the pattern looks like 👀

  • Bands are equally spaced parallel stripes—alternating bright and dark all across the screen :contentReference[oaicite:8]{index=8}.
  • The central band ( n = 0 ) is brightest. Moving sideways, brightness rises and falls periodically as the waves switch between in-step and out-of-step.
  • A computer-generated view (similar to Young’s original sketch) shows the neat, barcode-like look of the fringes :contentReference[oaicite:9]{index=9}.

🚀 Quick NEET boosters (must-know gems!)

  1. Condition for bright and dark fringes: \( \displaystyle \frac{xd}{D}= n\lambda \) and \( \displaystyle \frac{xd}{D}= (n+\tfrac12)\lambda \) respectively.
  2. Fringe width formula \( \beta=\lambda D/d \) — tells how λ, slit gap, and screen distance shape the pattern.
  3. Creating coherence: use one source and two pinholes instead of two separate lamps.
  4. Ordinary light sources are incoherent because their phases jitter in ≈ 10-10 s.
  5. Equal spacing of fringes is a fingerprint of wave interference, validating the wave nature of light.

✨ Keep experimenting & keep shining! ✨