Wave Nature of Light

Light exhibits a dual nature — it behaves both as:

1. Particle (photon)
2. Wave (electromagnetic wave)

When light interacts with obstacles or openings comparable to its wavelength (λ), it bends around the edges. This phenomenon is known as diffraction.

Phenomena explained through the wave nature of light:

• Reflection
• Refraction
• Dispersion
• Diffraction
• Interference
• Polarization

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1. Single-Slit Diffraction

When monochromatic light passes through a narrow slit of width a, it spreads out and forms a diffraction pattern on the screen.

(i) Condition for Minima (Dark Fringes)

a · sinθ = mλ    (m = ±1, ±2, ±3, …)     — (1)

Where:

• a → slit width
• λ → wavelength of light
• θ → angular position of minima
• m → diffraction order

(ii) Linear Fringe Position on Screen

If the screen is at distance D from the slit:

y = mλD / a     — (2)

(iii) Key Observations

• Central maximum: Brightest and twice as wide as other maxima.
• Side maxima: Much weaker and decrease in intensity.
• Higher-order maxima: Spread further apart as m increases.
• Effect of Slit/Wavelength:
  • Narrower slit → wider diffraction pattern.
  • Longer wavelength → greater spreading.

Note: This experiment demonstrates the wave nature of light.

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2. Double-Slit Interference (Young's Experiment)

When coherent light passes through two slits separated by distance d, the waves overlap and interfere.

1. Fringe Width

β = λx / d     — (3)

Where:

• β → fringe width
• λ → wavelength
• x → screen distance
• d → distance between slits

2. Interference Pattern

Bright Fringes (Constructive Interference)

Δ (Path difference) = nλ     — (4)

Dark Fringes (Destructive Interference)

Δ (Path difference) = (2n + 1) · λ/2     — (5)

3. Significance

1. Confirms the wave nature of light.
2. Supports Huygens' Principle.
3. Demonstrates superposition of waves.

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3. Electron Double-Slit Experiment (Quantum Theory)

This modern experiment shows that matter also behaves like waves (matter waves or de Broglie waves).

1. Key Observations

• Electrons fired one at a time still produce an interference pattern, which shows electrons behave like probability waves.
• If we measure which slit the electron passes through (with detector):
  • The interference pattern disappears.
  • Only two humps remain (each corresponding to one slit-classically expected).
  • The electron behaves like a classical particle.
  • Measurement collapses the wave function.

Wave–Particle Duality:

• Electrons behave like particles when detected.
• But behave like waves when propagating.

2. Implications

• Supports de Broglie hypothesis.
• Demonstrates quantum superposition.
• Shows observer effect / wave function collapse.
• Reveals that nature at the microscopic level is probabilistic, not deterministic.