Class 12 Physics · Chapter 10
Short answer:
Is chapter me hum 13 exercise-style questions cover karte hain — Huygens' principle ke conceptual questions, constructive/destructive interference ki conditions, YDSE ka fringe width aur path difference calculation, aur single-slit diffraction ka qualitative pattern. Rationalised syllabus (2026-27) me full YDSE mathematical derivation, Doppler effect for light, resolving power aur polarization hata diye gaye hain — is spec me bhi inhe touch nahi kiya gaya, sirf final formulas aur unki application cover hoti hai.
Wave optics light ko ek wave ki tarah treat karta hai, particle ki tarah nahi — aur yahi wave nature interference aur diffraction jaise phenomena explain karti hai jo particle model se explain nahi hote. Is chapter me Huygens' principle se shuru karke hum dekhte hain ki wavefront kaise propagate karta hai, phir Young's double slit experiment (YDSE) ke through interference samajhte hain, aur akhir me single slit diffraction ka qualitative pattern dekhte hain. Rationalised syllabus me sirf final results use karne hain — lambi derivations ab syllabus me nahi hain.
Chapter 10 Summary — 5 Minute Revision
1. Huygens' Principle
Huygens' principle kehta hai ki wavefront ka har point khud ek naya secondary wavelet source ban jaata hai — inn sab wavelets ka common tangent (envelope) hi agla wavefront banata hai. Ye principle wave propagation, reflection aur refraction ko geometrically explain karne ke liye use hota hai.
- Wavefront — ek surface jispe saare points same phase pe hote hain.
- Point source se nikalne wala wavefront spherical hota hai; door se dekhne pe (jaise sunlight) ye practically plane wavefront ban jaata hai.
- Wavefront hamesha propagation direction ke perpendicular hota hai.
2. Interference — Constructive aur Destructive
Jab do coherent light sources (same frequency, constant phase difference) overlap karte hain, to unki resultant intensity redistribute ho jaati hai — kahin bright fringes (constructive interference), kahin dark fringes (destructive interference).
| Type | Path difference condition | Result |
|---|---|---|
| Constructive (bright fringe) | Δx = nλ (n = 0, 1, 2, ...) | Maximum intensity |
| Destructive (dark fringe) | Δx = (n + ½)λ (n = 0, 1, 2, ...) | Minimum (zero) intensity |
↔ Table ko side me swipe karein
Coherent sources zaroori hain — do independent light sources (jaise do bulbs) interference pattern nahi dete kyunki unka phase relation random hota hai. YDSE me single source se do slits banake coherence ensure ki jaati hai.
3. Young's Double Slit Experiment (YDSE) — Final Results
Rationalised syllabus me full derivation nahi karni — sirf ye final results use karne hain:
- Fringe width: β = λD/d — jahan λ = wavelength, D = slits se screen ki distance, d = slits ke beech separation.
- Fringe width saare bright aur saare dark fringes ke liye same hota hai (equally spaced pattern).
- β directly λ aur D ke proportional hai, aur d ke inversely proportional hai.
Fringe pattern par parameters ka effect
| Change | Fringe width β pe effect |
|---|---|
| λ (wavelength) badhaye — e.g. red light use karein | β badhta hai |
| d (slit separation) badhaye | β ghatta hai |
| D (screen distance) badhaye | β badhta hai |
| Poora setup water me daal dein (medium refractive index n) | wavelength λ/n ho jaati hai → β ghat jaata hai |
↔ Table ko side me swipe karein
4. Diffraction — Qualitative Treatment
Diffraction light ka wave nature hai jisme light apni straight-line path se bend karke obstacle ya slit ke geometric shadow region me bhi pahunch jaati hai — khaaskar jab obstacle/slit ka size wavelength ke comparable ho.
- Single slit diffraction pattern: ek central bright band (central maximum) jo sabse zyada intense hota hai, uske dono taraf alternate dark aur kam-intense bright bands (secondary maxima) hote hain jinki intensity gradually kam hoti jaati hai.
- Central maximum ki width, secondary maxima ki width se double hoti hai.
5. Interference vs Diffraction — Qualitative Comparison
| Feature | Interference (YDSE) | Diffraction (single slit) |
|---|---|---|
| Source | Do coherent sources (do slits) | Single slit ke different points secondary wavelets ka source ban jaate hain |
| Fringe/band width | Saari fringes equal width ki hoti hain | Central maximum baaki maxima se zyada chaura hota hai |
| Intensity pattern | Sabhi bright fringes lagbhag same intensity ki hoti hain | Intensity center se bahar jaate hue rapidly kam hoti hai |
↔ Table ko side me swipe karein
Poore Class 12 Physics ke handwritten colour notes
IITian & district toppers ke banaye short notes — revision-ready, diagram ke saath. Board se pehle poora syllabus 3 din me revise.
Exercise Questions — Solutions (Q1–Q13)
Q1. Huygens' principle kya kehta hai? Isse wavefront ka propagation kaise explain hota hai?
Huygens' principle ke anusaar, wavefront ka har point ek naya secondary wavelet source ban jaata hai jo sabhi directions me spherical wavelets emit karta hai. In sab secondary wavelets ka common tangent (envelope) agle instant ka naya wavefront banata hai. Isi principle se reflection aur refraction bhi geometrically construct kiye ja sakte hain.
Q2. Wavefront kya hota hai aur propagation direction ke saath iska kya relation hai?
Wavefront ek aisi imaginary surface hai jispe wave source se same time me nikle saare points same phase me hote hain. Wavefront hamesha wave ki propagation direction ke perpendicular hota hai — jaise plane wavefront ke liye rays parallel straight lines hoti hain, spherical wavefront ke liye rays radially outward hoti hain.
Q3. Interference hone ke liye do sources ka coherent hona kyun zaroori hai?
Coherent sources ka matlab hai constant phase difference aur same frequency wale sources. Agar phase difference random ho (jaise do independent bulbs), to constructive aur destructive interference points continuously shift karte rehte hain aur time-averaged pattern uniform illumination ban jaata hai — koi stable bright-dark fringe pattern dikhayi nahi deta. Isliye YDSE me single source se do slits banake coherence ensure ki jaati hai.
Q4. Constructive aur destructive interference ke liye path difference conditions likhiye.
Constructive interference (bright fringe) ke liye path difference Δx = nλ hota hai, jahan n = 0, 1, 2, 3... Destructive interference (dark fringe) ke liye path difference Δx = (n + ½)λ hota hai.
Q5. YDSE me do slits ke beech separation 0.5 mm hai, screen 1.5 m door hai, aur light ki wavelength 600 nm hai. Fringe width nikaliye.
Fringe width β = λD/d.
β = (600 × 10⁻⁹ × 1.5) / (0.5 × 10⁻³)
β = (9 × 10⁻⁷) / (5 × 10⁻⁴)
β = 1.8 × 10⁻³ m = 1.8 mm
Q6. Ek YDSE setup me fringe width 2 mm hai. Agar screen ki distance double kar di jaaye (baaki sab constant rahe), to naya fringe width kya hoga?
β = λD/d hai, isliye β directly D ke proportional hai.
β₂ = β₁ × (D₂/D₁) = 2 mm × 2 = 4 mm
Naya fringe width 4 mm ho jayega.
Q7. YDSE me agar slit separation d ko half kar diya jaaye, fringe width par kya effect padega?
β = λD/d, aur β, d ke inversely proportional hai.
β₂ = β₁ × (d₁/d₂) = β₁ × 2
d ko half karne se fringe width double ho jayega.
Q8. Do coherent sources se ek point par path difference 450 nm hai. Agar light ki wavelength 600 nm hai, to us point par bright fringe banegi ya dark?
Path difference / wavelength ka ratio check karte hain.
Δx/λ = 450/600 = 0.75 = ¾
Ye n + ½ ke form me nahi aata seedha, lekin check karte hain: ¾λ = (0 + ¾)λ jo (n+½)λ pattern se match nahi karta seedha n=0 ke liye (0.5λ hona chahiye). Isliye ye point na pure bright hai na pure dark — partial intensity milegi. (Note: exact bright ke liye Δx = nλ, exact dark ke liye Δx = (n+½)λ hona chahiye; 0.75λ inme se koi bhi nahi hai.)
Q9. YDSE me red light (λ ≈ 700 nm) se violet light (λ ≈ 400 nm) pe switch karne se fringe pattern par kya effect padega?
β = λD/d, aur β directly λ ke proportional hai. Violet light ki wavelength kam hai (400 nm red ke 700 nm se), isliye fringe width kam ho jayegi — fringes ek dusre ke zyada paas aa jayengi.
Q10. Single slit diffraction pattern ka qualitative description dijiye.
Single slit se guzarne ke baad light ek central bright band (central maximum) banati hai jo sabse zyada intense hota hai. Iske dono taraf alternate dark aur kam-intensity bright bands (secondary maxima) dikhayi dete hain, aur inki intensity center se door jaate hue gradually kam hoti jaati hai. Central maximum secondary maxima se zyada chaura (double width) hota hai.
Q11. Interference pattern aur diffraction pattern me do main differences batayiye.
(1) Interference pattern (YDSE) me saari bright fringes lagbhag equal width aur equal intensity ki hoti hain, jabki diffraction pattern me central maximum sabse chaura aur sabse intense hota hai, aur baaki maxima ki intensity rapidly kam hoti jaati hai. (2) Interference do alag coherent sources (slits) ke wavelets ke superposition se hota hai, jabki diffraction single slit ke andar hi different points se aane wale secondary wavelets ke superposition se hota hai.
Q12. Kya diffraction sirf light ke saath hi hota hai? Kis condition me diffraction prominent hota hai?
Nahi, diffraction sabhi waves (sound, water waves, light) ke saath hota hai — ye wave nature ki universal property hai. Diffraction tab prominent hota hai jab obstacle ya slit ka size wave ki wavelength ke comparable ho. Light ki wavelength bahut chhoti hoti hai (~500 nm), isliye rozmarra ki bade obstacles ke saath diffraction easily observe nahi hoti — sirf narrow slits ya small obstacles ke saath dikhti hai.
Q13. YDSE me agar poora apparatus hawa se paani (refractive index n = 4/3) me daal diya jaaye, to fringe width par kya effect padega?
Medium me light ki wavelength ghat jaati hai: λ_medium = λ_air/n.
β_medium = λ_medium × D/d = (λ_air/n) × D/d = β_air/n
Fringe width n = 4/3 factor se ghat jayega, yaani β_medium = (3/4) × β_air.
Important Equations — Ek Nazar Me
| Quantity | Formula | Notes |
|---|---|---|
| Fringe width (YDSE) | β = λD/d | λ = wavelength, D = slit-to-screen distance, d = slit separation |
| Path difference (constructive/bright fringe) | Δx = nλ | n = 0, 1, 2, ... |
| Path difference (destructive/dark fringe) | Δx = (n + ½)λ | n = 0, 1, 2, ... |
| Wavelength in medium | λ_medium = λ_air / n | n = refractive index of medium; fringe width scales down by same factor |
| Condition: β vs λ | β ∝ λ | directly proportional |
| Condition: β vs d | β ∝ 1/d | inversely proportional |
| Condition: β vs D | β ∝ D | directly proportional |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Interference aur diffraction pattern ko confuse karna. Interference (YDSE) me saari fringes equal width ki hoti hain; diffraction me central maximum sabse chaura aur sabse intense hota hai — ye do alag phenomena hain, mix mat karo.
- Constructive aur destructive condition ulta likhna. Bright fringe ke liye Δx = nλ hota hai (integer multiple), dark fringe ke liye Δx = (n+½)λ hota hai (half-integer multiple) — inhe swap mat karo.
- Fringe width ka d ke saath relation galat samajhna. β, d ke inversely proportional hai — d badhane se fringe width ghatta hai, badhta nahi. Bahut students isse directly proportional maan lete hain.
- Removed topics (Doppler effect for light, polarization, resolving power) se formula ya concept apply karna. Ye sections ab syllabus se poori tarah hata diye gaye hain — exam me inse related koi bhi question ya formula expect mat karo, aur galti se inhe answer me mat likho.
- Full YDSE derivation likhne ki koshish karna. Rationalised syllabus me sirf final results (β = λD/d aur path difference conditions) use karne hain — lambi geometric derivation ab syllabus me nahi hai, isliye exam me use likhne ki zaroorat nahi.
- Single slit diffraction ke central maximum ki width galat samajhna. Central maximum, secondary maxima se double width ka hota hai — ye qualitative fact yaad rakhna zaroori hai, formula misapply mat karo jahan syllabus me sirf qualitative treatment expected hai.
Board-Style Important Questions
- 1 mark: Huygens' principle ke anusaar wavefront ka definition kya hai?
- 2 marks: YDSE me fringe width ki formula likhiye aur ismein har term define kijiye.
- 2 marks: Constructive aur destructive interference ke liye path difference conditions likhiye.
- 3 marks: YDSE me slit separation aur screen distance diye jaane par fringe width calculate kijiye (numerical).
- 3 marks: Single slit diffraction pattern ka qualitative description dijiye aur ise interference pattern se compare kijiye.
Aksar Poochhe Jaane Wale Sawaal
Wave Optics me Doppler effect for light padhna hai kya?
Nahi, Doppler effect for light current rationalised NCERT syllabus se poori tarah hata diya gaya hai. Isse related koi bhi question ab exam me nahi aayega.
Kya YDSE ki full mathematical derivation yaad karni padegi?
Nahi, ab sirf final results — fringe width β = λD/d aur path difference conditions — use karne hain. Lambi geometric derivation syllabus se hata di gayi hai.
Polarization is chapter me hai kya?
Nahi, polarization by scattering aur by reflection dono current syllabus se hata diye gaye hain. Is chapter ka focus sirf Huygens' principle, interference, aur diffraction (qualitative) tak limited hai.
Resolving power of optical instruments padhna zaroori hai?
Nahi, resolving power topic bhi rationalised syllabus se poori tarah drop kar diya gaya hai. Isse related koi formula ya question expect na karein.
Fringe width kis-kis cheez par depend karta hai?
Fringe width β = λD/d ke according wavelength (λ) aur screen distance (D) ke directly proportional hai, aur slit separation (d) ke inversely proportional hai.
Diffraction pattern interference pattern se kaise different hai?
Interference pattern (YDSE) me saari bright fringes equal width aur lagbhag equal intensity ki hoti hain. Diffraction pattern me central maximum sabse chaura aur sabse zyada intense hota hai, aur baaki maxima ki intensity rapidly kam hoti jaati hai.
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