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NEB Class 12 Physics Interference Note Handwritten in PDF
What is Interference?
Interference is the phenomenon where two or more coherent waves superpose to produce a resultant wave of greater, lesser, or equal amplitude.
Constructive interference: Waves in phase → amplitudes add → bright fringe
- Condition: Path difference = nλ (n = 0, ±1, ±2…)
Destructive interference: Waves out of phase (180°) → amplitudes cancel → dark fringe
- Condition: Path difference = (2n−1)λ/2 = (n + ½)λ
Coherent Sources — Why They Are Essential
For sustained, observable interference fringes to form, sources must be coherent:
- Same frequency (or wavelength)
- Constant phase difference (not changing randomly)
Two separate light bulbs CANNOT produce interference because:
- Their phases change randomly millions of times per second
- Any fringe pattern forms and disappears so fast it’s invisible
How to create coherent sources in practice:
- Split a single source into two using two narrow slits (Young’s experiment)
- Partial reflection from two surfaces (thin film interference)
Young’s Double Slit Experiment — Setup and Theory
Setup:
- Monochromatic light source S
- Single slit → double slit (S₁ and S₂, separation = d)
- Screen at distance D from double slit
Path difference for point P at height y from center: Δ = yd/D (for D >> d, which is always true in the experiment)
Bright fringe condition: yd/D = nλ → y_n = nλD/d
Dark fringe condition: yd/D = (n+½)λ → y_n = (2n+1)λD/2d
Fringe Width Formula
Fringe width (β): Distance between two consecutive bright (or dark) fringes
β = λD/d
This is the most important formula in this chapter.
Effect of changing each parameter:
- Increase λ (use red light instead of blue) → fringe width increases
- Increase D (move screen farther) → fringe width increases
- Increase d (slits farther apart) → fringe width decreases
NEB exam numerical type: “In Young’s experiment, λ = 600 nm, d = 0.5 mm, D = 1.5 m. Find fringe width.” Answer: β = (600 × 10⁻⁹ × 1.5) / (0.5 × 10⁻³) = 1.8 mm
White Light Interference
With white light:
- Central fringe is white (all wavelengths have zero path difference at center)
- Outer fringes are coloured — violet (shortest λ, narrowest β) is innermost, red (longest λ, widest β) is outermost
- After a few fringes, colours overlap and the pattern becomes unclear
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Frequently Asked Questions
What is interference of light in Class 12 Physics
Interference occurs when two coherent light waves superpose. Constructive interference (path difference = nλ) gives bright fringes. Destructive interference (path difference = (n+½)λ) gives dark fringes. Interference proves wave nature of light. Young’s double slit experiment (1801) was the first demonstration.
What is fringe width formula in Young’s double slit experiment?
Fringe width β = λD/d. Where λ is wavelength, D is distance from slits to screen, d is slit separation. Fringe width increases with longer wavelength (red gives wider fringes than blue) and greater D. Fringe width decreases with larger slit separation d. This is the most important formula in this chapter.
What are coherent sources in Class 12 Physics?
Coherent sources emit light of same frequency and maintain constant phase difference. Two separate bulbs cannot produce interference because their phases change randomly millions of times per second. In Young’s experiment a single source illuminates both slits — making them coherent. Lasers are naturally coherent sources.
What is the condition for constructive and destructive interference?
Constructive interference (bright fringe): path difference Δ = nλ where n = 0, ±1, ±2. Waves arrive in phase and amplitudes add. Destructive interference (dark fringe): path difference Δ = (n+½)λ. Waves arrive in anti-phase and cancel out. The central fringe (n=0) is always bright for any wavelength.
What happens to fringe width with red light instead of blue?
Since β = λD/d, fringe width is directly proportional to wavelength. Red light (λ ≈ 700 nm) gives wider fringes than blue light (λ ≈ 450 nm) for same setup. With white light, central fringe is white but outer fringes are coloured — violet innermost (smallest λ) and red outermost (largest λ).
What is the significance of Young’s double slit experiment?
Young’s experiment (1801) definitively proved wave nature of light through interference — a wave phenomenon impossible for particles. It provided the first method to measure wavelength of light. In modern quantum mechanics, the same experiment with single photons demonstrates wave-particle duality at the quantum level.
How to calculate fringe width NEB numerical problems?
Formula: β = λD/d. Convert λ from nm to m (multiply by 10⁻⁹), D and d must be in metres. Example: λ=600 nm, D=1.5 m, d=0.5 mm. β = (600×10⁻⁹ × 1.5)/(0.5×10⁻³) = 1.8×10⁻³ m = 1.8 mm. Always convert all units to SI before calculating to avoid errors in NEB board exam.
Which interference topics are most important for Exam?
Most important: Young’s double slit experiment setup and derivation (4 marks), fringe width formula with numericals (4 marks), coherent sources explanation (2 marks), constructive and destructive conditions (2 marks). Fringe width numerical problems appear in almost every NEB Class 12 Physics board examination.
