#coherence

Optical Phenomena and Applications

What is the condition for coherence in a double-slit experiment?

**Polarization requires transverse waves** because only transverse can have orientation perpendicular to propagation, longitudinal cannot be polarized, wave theory requires light transverse to explain polarization, polaroids transmit only component along pass-axis, unpolarized has random transverse orientations, after polaroid polarized. Coherence requires a constant phase difference between the two sources, ensuring a stable interference pattern. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives Constant phase diffe

Ref: NCERT > Physics Book > Wave Optics > Optical Phenomena and Applications

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Wavefront and Huygens Principle

Why does the interference pattern from two slits require light to originate from a single source?

**Wavefront types** point source spherical, distant point source plane, after convex lens plane wave focuses to point because lens adds phase delay proportional to thickness, converging spherical wavefront, after concave mirror plane wave becomes spherical converging to focus, illustrating Huygens construction. A single source ensures coherence, maintaining a constant phase relationship between the waves from the slits, essential for a stable interference pattern. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives To

Ref: NCERT > Physics Book > Wave Optics > Wavefront and Huygens Principle

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Wavefront and Huygens Principle

What property of light waves enables the formation of a stable interference pattern when split from a single source?

**Wavefront** is locus of points in same phase, spherical from point source, plane at large distance because radius large, Huygens principle every point on wavefront acts as secondary source of wavelets, new wavefront envelope of secondary wavelets, allows prediction of new wavefront shape from known wavefront, explains reflection and refraction. Coherence, or a fixed phase relationship, is maintained when light from one source is split, allowing constructive and destructive interference to form a stable pattern. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ

Ref: NCERT > Physics Book > Wave Optics > Wavefront and Huygens Principle

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Superposition, Resultant Amplitude and Intensity

Why can’t two ordinary light sources, like sodium lamps, produce a stable interference pattern when illuminating two sli

**Intensity at point** in double-slit I = I_max cos²(φ/2), φ = (2π/λ)Δ, for Δ=λ/4 φ=π/2 I= I_max cos²(π/4)= I_max/2 =2I₀, for Δ=λ/3 φ=2π/3 I= I_max cos²(π/3)= I_max×0.25= I₀, for Δ=5λ/8 φ=5π/4? Actually φ=2π×5/8=5π/4, cos²(5π/8)=?, path difference for destructive φ=(2n+1)π, constructive 2nπ. Ordinary sources emit light with rapidly changing phase differences, making them incoherent and unable to maintain a stable interference pattern. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives They are incoherent due to random

Ref: NCERT > Physics Book > Wave Optics > Superposition, Resultant Amplitude and Intensity

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Interference - Double-Slit and Coherence

What is the nature of the interference pattern formed by incoherent sources?

**Interference** occurs when two coherent waves superpose, path difference Δ = d sinθ, bright fringe when Δ = n λ, n integer, seventh bright Δ=7λ, dark fringe Δ = (2n-1)λ/2, second dark Δ=3λ/2, third dark 5λ/2, sixth dark 11λ/2, distance of bright fringe from central y = n λ D/d, D screen distance, d slit separation, for λ=650 nm d=0.5 mm D=1.0 m fifth dark? Actually dark y=(2n-1)λ D/(2d). Incoherent sources produce no stable interference pattern; intensities simply add up, resulting in uniform illumination. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n =

Ref: NCERT > Physics Book > Wave Optics > Interference - Double-Slit and Coherence

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Interference - Double-Slit and Coherence

What prevents the formation of an interference pattern when two independent light sources are used?

**Coherence** requires constant phase difference, two independent sources not coherent because phase random, prevents interference pattern, laser coherent, visibility of fringes determined by coherence, intensity and phase difference, coherent sources produce stable interference, incoherent intensity adds I = I₁+I₂ no interference, interference pattern distinguishes from diffraction. Independent sources lack a fixed phase relationship (incoherence), causing rapid phase fluctuations that average out interference effects. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC =

Ref: NCERT > Physics Book > Wave Optics > Interference - Double-Slit and Coherence

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Superposition, Resultant Amplitude and Intensity

What determines the visibility of interference fringes when light passes through two slits?

**Superposition principle** resultant displacement sum of individual, for two coherent waves amplitude a each, resultant amplitude A = √(a² + a² +2a² cosφ)=2a|cos(φ/2)|, phase difference φ, path difference Δ = (φ/2π)λ, for φ=π/2 A=√2 a, for φ=6π cos3π=-1? Actually φ=6π cos3π? A=2a|cos3π|=2a, for φ=4π A=2a, intensity I ∝ A², maximum I_max=4I₀ when φ=0, I=2I₀(1+cosφ)=4I₀ cos²(φ/2). Coherence, or a constant phase difference between the waves from the slits, is essential for a visible, stable interference pattern. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' =

Ref: NCERT > Physics Book > Wave Optics > Superposition, Resultant Amplitude and Intensity

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Displacement Current and Ampere-Maxwell Law

In electromagnetic theory, what explains the ability of waves to exhibit coherence?

**Displacement current** I_d = ε₀ dΦ_E/dt, Φ_E = ∫ E·dA electric flux (V·m), ε₀=8.85×10⁻¹² F/m, ensures continuity of current in charging capacitor where conduction current stops between plates, I_d equals conduction current in wires, 3 A conduction ⇒ 3 A displacement, maintaining Ampere's law ∮ B·dl = μ₀(I_c+I_d). Coherence arises from the wave-like nature of electromagnetic waves, where consistent phase relationships between oscillations allow phenomena like interference to occur. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Wave-like natu

Ref: NCERT > Physics Book > Electromagnetic Waves > Displacement Current and Ampere-Maxwell Law

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