1109 – Lecture 2 Notes

PHY-1109 Physics

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Lecture 2 – Interference of Light

🌊 Young’s Double-Slit Experiment (YDS)

• Setup → Light source → narrow slit → double slits → screen
• Observation → Bright & dark fringes (interference pattern)

➡️ Key Idea: Light behaves like a wave, and when waves overlap, they interfere.

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🔑 Basic Terms in Interference

• Coherent sources → Two waves with constant phase difference.
• Path difference (Δx) → Extra distance one wave travels compared to the other.
• Phase difference (Δϕ) → Difference in oscillation phase due to Δx.
  • Formula:

$$\Delta \varphi =\frac{2\pi }{\lambda }\Delta x$$

• Constructive interference → Waves in phase → Bright fringe.
  • Condition: Δx = mλ (m = 0, 1, 2, …)
• Destructive interference → Waves out of phase → Dark fringe.
  • Condition: Δx = (m + ½)λ

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🧮 Theoretical Treatment of YDS

• Path difference due to slit separation d and screen distance D:

$$\Delta x=\frac{d\cdot y}{D}$$

where y = fringe position on screen.

• Fringe width (Δy):

  $\Delta y=\frac{\lambda D}{d}$

➡️ Larger wavelength (λ) → wider fringes.
➡️ Increasing slit separation (d) → narrower fringes.

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📌 Visual Flow

Light source → Coherent waves from two slits → Overlap on screen
→ Path difference → Constructive/Destructive interference → Bright/Dark fringes

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⚡ Key Takeaways

• Young’s experiment proved wave nature of light.
• Interference needs coherent sources.
• Bright & dark fringes arise from path difference.
• Fringe width depends on λ, D, and d.

📘 Glossary – Lecture 2

• Interference → Phenomenon where two or more waves superpose to form a resultant wave with varying intensity (bright/dark regions).

• Constructive Interference → When waves meet in phase (path difference = integral multiple of λ), producing a bright fringe.

• Destructive Interference → When waves meet out of phase (path difference = odd half multiple of λ), producing a dark fringe.

• Path Difference (Δx) → Difference in distance traveled by two waves from slits to a point on the screen.

• Phase Difference (Δφ) → Difference in phase between two waves due to path difference (Δφ = 2πΔx / λ).

• Coherent Sources → Sources having constant phase difference and same frequency, necessary for stable interference.

• Fringe Width (ω) → The spacing between two consecutive bright (or dark) fringes:

  $\omega =\frac{\lambda D}{d}$

  where λ = wavelength, D = distance between slits and screen, d = slit separation.

• Central Maximum → The bright fringe at the center of the interference pattern (zero path difference).