Class 12 Physics · Chapter 9
Short answer:
Is chapter me NCERT ke exercise me karib 20 questions hain — sabse zyada numerical-heavy chapter hai poore Class 12 syllabus me. Coverage: mirror formula aur sign convention, Snell's law + refractive index, critical angle aur total internal reflection (TIR), refraction at spherical surfaces, thin lens formula, lensmaker's formula, power of lens aur lens combinations, prism me angle of deviation, aur optical instruments (simple microscope, compound microscope, astronomical telescope) ki magnifying power. Har numerical me Cartesian sign convention follow karna compulsory hai — yahi sabse zyada marks katta hai.
Ray optics me light ko straight-line rays maan kar mirrors, lenses aur prisms se uska behaviour predict karte hain — aur poora chapter formulas ke sahi sign convention se apply karne pe tika hai. Class 10 me jo basic reflection-refraction padha tha, yahan wahi concepts advanced level pe aate hain: spherical surfaces pe refraction, lens combinations, prism deviation, aur microscope-telescope jaise real optical instruments ka design. Ek cheez hamesha yaad rakhna — Cartesian sign convention (object hamesha left se aata hai, distances usi direction se positive/negative measure hoti hain) pura chapter control karta hai. Agar sign convention galat lagaya, formula sahi hone ke bawajood answer galat aayega.
Chapter 9 Summary — 5 Minute Revision
1. Reflection at Spherical Mirrors
Mirror formula: 1/v + 1/u = 1/f, jahan f = R/2 (R = radius of curvature). Concave mirror ka f negative hota hai (Cartesian convention me, pole se principal focus object ki taraf), convex mirror ka f positive.
- Magnification: m = −v/u = h′/h
- Concave mirror: object focus ke andar ho to virtual, magnified, erect image; focus se bahar ho to real, inverted image.
- Convex mirror: hamesha virtual, erect, diminished image — isliye vehicle mirrors me use hota hai (wide field of view).
2. Refraction — Snell's Law aur Refractive Index
Snell's law: n1 sinθ1 = n2 sinθ2. Refractive index n2 medium 1 ke respect me = sinθ1/sinθ2 = speed of light in medium 1 / speed in medium 2.
Real depth aur apparent depth se bhi refractive index nikalta hai: n = real depth / apparent depth (jab observer denser medium ko rarer medium se dekh raha ho, jaise pool ke andar sikka).
3. Total Internal Reflection (TIR)
Total internal reflection tabhi hoti hai jab light denser medium se rarer medium me jaaye AND angle of incidence critical angle se zyada ho — dono conditions zaroori hain, sirf ek nahi. Critical angle: sinθc = 1/n (denser medium ke refractive index n ke against, jahan light travel kar raha hai).
- Optical fibres TIR pe kaam karte hain — core ka refractive index cladding se zyada rakha jata hai.
- Totally reflecting prisms (45°-90°-45°) periscope aur binoculars me mirror ki jagah use hote hain kyunki TIR me energy loss nahi hota, jabki silvered mirror me thoda hota hai.
4. Refraction at Spherical Surfaces aur Thin Lenses
Single spherical surface: n2/v − n1/u = (n2 − n1)/R
Thin lens formula: 1/v − 1/u = 1/f — yahan mirror formula se sign different hai (plus ki jagah minus), isliye lens aur mirror formula ko kabhi mix mat karo.
Lensmaker's formula: 1/f = (n − 1)(1/R1 − 1/R2) — lens ke material (n) aur dono surfaces ki curvature se focal length design karne ke liye.
5. Power of Lens aur Combination
Power P = 1/f (f metre me), unit = dioptre (D). Convex/converging lens ka P positive, concave/diverging ka P negative.
Lenses contact me ho to: P = P1 + P2 + P3 + ... aur 1/f = 1/f1 + 1/f2 + ...
Do lenses jab d distance pe separated hon: P = P1 + P2 − d·P1·P2 (d metre me).
6. Refraction through a Prism
Angle of deviation: δ = i + e − A (A = prism angle, i = angle of incidence, e = angle of emergence). Minimum deviation δm par prism symmetric position me hota hai (i = e), aur us waqt: n = sin[(A + δm)/2] / sin(A/2).
7. Optical Instruments — Magnifying Power
- Simple microscope (magnifying glass): image near point pe ho to m = 1 + D/f; image infinity pe (normal adjustment) ho to m = D/f. (D = least distance of distinct vision, standard 25 cm)
- Compound microscope: objective (short focal length fo) real magnified image banata hai, eyepiece (fe) usko further magnify karta hai. M = mo × me, approx M ≈ (L/fo) × (D/fe), jahan L tube length hai.
- Astronomical telescope (normal adjustment): m = fo/fe, tube length L = fo + fe. Objective ka focal length bada aur eyepiece ka chota rakha jata hai taaki magnification zyada mile.
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–Q20)
Q1. Ek concave mirror ka focal length 15 cm hai. Ek object mirror se 10 cm door rakha gaya hai. Image ki position, nature aur magnification nikalo.
Concave mirror hai, object focus ke andar hai (10 cm < 15 cm), isliye virtual, magnified, erect image expect karte hain.
Given: f = −15 cm, u = −10 cm (Cartesian convention)
Mirror formula: 1/v + 1/u = 1/f
1/v = 1/f − 1/u = (−1/15) − (−1/10) = −1/15 + 1/10 = (−2+3)/30 = 1/30
v = +30 cm
Magnification: m = −v/u = −(30)/(−10) = +3
Answer: Image virtual hai, mirror ke peeche 30 cm pe banta hai, 3× magnified aur erect (m positive).
Q2. Ek convex mirror (car ka side mirror) ka focal length 20 cm hai. Object mirror se 30 cm door hai. Image position aur nature batao.
Convex mirror ka f hamesha positive hota hai.
Given: f = +20 cm, u = −30 cm
1/v = 1/f − 1/u = 1/20 − (−1/30) = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12
v = +12 cm
m = −v/u = −(12)/(−30) = +0.4
Answer: Image virtual hai, mirror ke peeche 12 cm pe banta hai, erect aur diminished (0.4× size) — isliye convex mirror me wide field of view milta hai.
Q3. Ek pond ki real depth 12 cm hai, lekin upar se seedha dekhne par woh 9 cm gehra dikhta hai. Water ka refractive index nikalo.
Formula: n = real depth / apparent depth
n = 12/9 = 1.33
Answer: Water ka refractive index ≈ 1.33 (standard value).
Q4. Light air se glass (n = 1.5) me 45° angle of incidence pe enter karti hai. Angle of refraction nikalo.
Snell's law: n1 sinθ1 = n2 sinθ2
(1) sin45° = (1.5) sinθ2
sinθ2 = 0.7071/1.5 = 0.4714
θ2 = sin⁻¹(0.4714) ≈ 28.1°
Answer: Angle of refraction ≈ 28.1° — glass me jaate hi ray normal ki taraf mudti hai (denser medium).
Q5. Water (n = 1.33) ke liye critical angle nikalo.
sinθc = 1/n = 1/1.33 = 0.7519
θc = sin⁻¹(0.7519) ≈ 48.8°
Answer: Critical angle ≈ 48.8° — is angle se zyada pe pani ke andar se light TIR karegi (agar water se air me jaa rahi ho).
Q6. Glass (n = 1.5) ke andar light 50° angle of incidence pe glass-air surface pe girti hai. Check karo TIR hogi ya nahi.
Critical angle: sinθc = 1/n = 1/1.5 = 0.667
θc = sin⁻¹(0.667) ≈ 41.8°
Given angle of incidence = 50°, jo θc (41.8°) se zyada hai
Answer: Haan, TIR hogi kyunki light denser (glass) se rarer (air) me ja rahi hai AND angle of incidence critical angle se zyada hai — dono conditions satisfy ho rahi hain.
Q7. Ek convex lens ka focal length 20 cm hai. Object lens se 30 cm door rakha hai. Image position, nature aur magnification nikalo.
Given: f = +20 cm, u = −30 cm
Lens formula: 1/v − 1/u = 1/f
1/v = 1/f + 1/u = 1/20 + (−1/30) = (3−2)/60 = 1/60
v = +60 cm
m = v/u = 60/(−30) = −2
Answer: Image real hai, lens ke doosri taraf 60 cm pe banta hai, inverted aur 2× magnified (m negative = inverted).
Q8. Ek concave (diverging) lens ka focal length 15 cm hai. Object lens se 20 cm door hai. Image position aur nature batao.
Given: f = −15 cm, u = −20 cm
1/v = 1/f + 1/u = (−1/15) + (−1/20) = (−4−3)/60 = −7/60
v = −60/7 ≈ −8.57 cm
m = v/u = (−8.57)/(−20) ≈ +0.43
Answer: Image virtual hai, object ki hi taraf 8.57 cm pe banta hai, erect aur diminished — diverging lens hamesha aisi hi image banata hai chahe object kahin bhi ho.
Q9. Ek biconvex lens ke dono surfaces ki radii 20 cm hain aur material ka refractive index 1.5 hai. Focal length nikalo (lensmaker's formula se).
Biconvex lens: R1 positive, R2 negative (Cartesian convention).
Given: n = 1.5, R1 = +20 cm, R2 = −20 cm
Lensmaker's formula: 1/f = (n−1)(1/R1 − 1/R2)
1/f = (1.5−1)(1/20 − 1/(−20)) = (0.5)(1/20 + 1/20) = (0.5)(2/20) = 0.05
f = 1/0.05 = 20 cm
Answer: Focal length = 20 cm.
Q10. Ek myopic (short-sighted) person ke liye concave lens ka focal length 50 cm hai. Lens ki power nikalo.
Given: f = −50 cm = −0.5 m
Power: P = 1/f (f metre me)
P = 1/(−0.5) = −2 D
Answer: Power = −2 D (negative kyunki concave/diverging lens hai — myopia correction ke liye).
Q11. Do lenses contact me rakhe hain — convex lens f1 = +10 cm aur concave lens f2 = −15 cm. Combination ki power aur equivalent focal length nikalo.
P1 = 1/f1 = 1/0.10 = +10 D
P2 = 1/f2 = 1/(−0.15) = −6.67 D
Combination: P = P1 + P2 = 10 + (−6.67) = +3.33 D
f = 1/P = 1/3.33 = 0.30 m = 30 cm
Answer: Combined power = +3.33 D, equivalent focal length = 30 cm (converging combination, kyunki convex lens ka effect zyada strong hai).
Q12. Ek prism ka angle A = 60° hai aur minimum deviation δm = 40° observe hua. Prism material ka refractive index nikalo.
Formula: n = sin[(A + δm)/2] / sin(A/2)
n = sin[(60°+40°)/2] / sin(30°) = sin(50°)/sin(30°)
n = 0.766/0.5 = 1.53
Answer: Refractive index ≈ 1.53.
Q13. Ek simple microscope (magnifying glass) ka focal length 5 cm hai. Near point D = 25 cm liya jaata hai. Magnifying power nikalo jab (a) image near point pe bane, (b) image infinity pe bane.
(a) Image near point pe: m = 1 + D/f = 1 + 25/5 = 1 + 5 = 6
(b) Image infinity pe (normal adjustment): m = D/f = 25/5 = 5
Answer: (a) m = 6, (b) m = 5 — near point pe rakhne se magnification thoda zyada milta hai, lekin eye strain bhi zyada hota hai.
Q14. Ek compound microscope me objective ka focal length fo = 1 cm, eyepiece ka fe = 5 cm hai. Dono lenses ke beech tube length L ≈ 20 cm hai. D = 25 cm lekar approximate magnifying power nikalo.
Approx formula use karte hain jab final image near point pe banti hai.
mo ≈ L/fo = 20/1 = 20
me = 1 + D/fe = 1 + 25/5 = 6
M = mo × me = 20 × 6 = 120
Answer: Magnifying power ≈ 120 (approx formula, tube length ko object distance ke approx equal maan kar).
Q15. Ek astronomical telescope normal adjustment me kaam kar raha hai — objective ka focal length fo = 100 cm, eyepiece ka fe = 5 cm hai. Magnifying power aur tube length nikalo.
Magnifying power (normal adjustment): m = fo/fe = 100/5 = 20
Tube length: L = fo + fe = 100 + 5 = 105 cm
Answer: m = 20×, tube length = 105 cm — objective ka focal length jitna zyada bada aur eyepiece jitna chota, magnification utni zyada.
Q16. Ek convex spherical surface (R = +20 cm) air-glass boundary hai (n1 = 1, n2 = 1.5). Object air me surface se 30 cm door hai. Image position nikalo.
Formula: n2/v − n1/u = (n2 − n1)/R
Given: n1 = 1, n2 = 1.5, R = +20 cm, u = −30 cm
1.5/v − 1/(−30) = (1.5−1)/20 = 0.5/20 = 0.025
1.5/v = 0.025 − 1/30 = 0.025 − 0.0333 = −0.0083
v = 1.5/(−0.0083) ≈ −180 cm
Answer: v ≈ −180 cm — image virtual hai aur object ki hi taraf (air side) 180 cm pe banta hai, kyunki object surface ke bahut paas (30 cm) rakha gaya hai R (20 cm) ke comparable distance pe.
Q17. Do thin lenses f1 = 10 cm aur f2 = 15 cm ek doosre se d = 5 cm door rakhe hain. Combination ki power nikalo.
P1 = 1/0.10 = 10 D, P2 = 1/0.15 = 6.67 D, d = 0.05 m
Formula: P = P1 + P2 − d·P1·P2
P = 10 + 6.67 − (0.05 × 10 × 6.67) = 16.67 − 3.33 = 13.33 D
f = 1/P = 1/13.33 ≈ 0.075 m = 7.5 cm
Answer: Combined power ≈ 13.33 D, equivalent focal length ≈ 7.5 cm.
Q18. Ek converging light beam ke path me 6 cm mota glass slab (n = 1.5) rakha jaata hai. Convergence point kitna shift hoga?
Formula: apparent shift = t(1 − 1/n)
shift = 6 × (1 − 1/1.5) = 6 × (1 − 0.667) = 6 × 0.333
shift = 2 cm
Answer: Convergence point 2 cm door shift ho jayega (slab ki taraf, image ki farther direction me), jo slab ki thickness se kam hai.
Q19. Ek prism ka angle A = 60° hai. Ek ray 45° angle of incidence pe girti hai aur 50° angle of emergence pe nikalti hai. Angle of deviation nikalo.
Formula: δ = i + e − A
δ = 45° + 50° − 60°
δ = 35°
Answer: Angle of deviation = 35°.
Q20. Ek optical fibre ke core ka refractive index 1.5 hai aur cladding ka 1.4 hai. Fibre kaam karne ke liye critical angle nikalo aur bताओ light guiding ke liye kya condition chahiye.
Critical angle formula (core-cladding boundary): sinθc = n2/n1 = 1.4/1.5 = 0.9333
θc = sin⁻¹(0.9333) ≈ 69°
Answer: Critical angle ≈ 69°. Light ko core ke andar guide hone ke liye har baar core-cladding interface pe angle of incidence 69° se zyada hona chahiye, taaki TIR ho aur light bina energy loss ke fibre ke through travel kare.
Important Equations — Ek Nazar Me
| Concept | Formula |
|---|---|
| Mirror formula | 1/v + 1/u = 1/f (f = R/2) |
| Mirror magnification | m = −v/u = h′/h |
| Snell's law | n1 sinθ1 = n2 sinθ2 |
| Refractive index (real/apparent depth) | n = real depth / apparent depth |
| Critical angle | sinθc = 1/n (denser to rarer) |
| Refraction at spherical surface | n2/v − n1/u = (n2 − n1)/R |
| Thin lens formula | 1/v − 1/u = 1/f |
| Lensmaker's formula | 1/f = (n − 1)(1/R1 − 1/R2) |
| Power of lens | P = 1/f (f in metres, unit: dioptre D) |
| Lenses in contact | P = P1 + P2 + ... ; 1/f = 1/f1 + 1/f2 + ... |
| Lenses separated by distance d | P = P1 + P2 − d·P1·P2 (d in metres) |
| Prism angle of deviation | δ = i + e − A |
| Prism refractive index (min. deviation) | n = sin[(A + δm)/2] / sin(A/2) |
| Simple microscope (image at near point) | m = 1 + D/f |
| Simple microscope (image at infinity) | m = D/f |
| Compound microscope (approx) | M = mo × me ≈ (L/fo)(D/fe) |
| Astronomical telescope (normal adjustment) | m = fo/fe ; tube length L = fo + fe |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Sign convention mix-up. Cartesian convention me object distance u hamesha negative hota hai (object left se aata hai), lekin students isse positive le lete hain — poora answer galat aa jaata hai chahe formula sahi ho.
- Mirror formula lens pe ya lens formula mirror pe laga dena. Mirror formula me plus hota hai (1/v + 1/u = 1/f), lens formula me minus (1/v − 1/u = 1/f) — dono ko interchange karna common mistake hai exam me.
- TIR ke liye sirf ek condition check karna. 'Total internal reflection tabhi hoti hai jab light denser medium se rarer medium me jaaye AND angle of incidence critical angle se zyada ho' — dono conditions zaroori hain. Sirf angle bada hone se TIR nahi hoti agar light rarer se denser me jaa rahi ho.
- Snell's law me refractive index ratio ulta laga dena. n1 sinθ1 = n2 sinθ2 me n1 aur n2 ko swap kar dena, jisse angle of refraction galat side pe chala jaata hai (denser me angle bada aa jaata hai jabki chota aana chahiye).
- Magnification ka sign misinterpret karna. m negative ka matlab image inverted hai, m positive ka matlab erect — students magnitude sahi nikaal lete hain lekin sign dekhkar image ki nature (real/virtual, erect/inverted) galat bata dete hain.
- Lensmaker's formula me R1, R2 ka sign galat lena. Biconvex lens me R1 positive aur R2 negative hota hai (Cartesian convention se), lekin students dono ko positive maan lete hain jisse focal length ka sign hi galat aa jaata hai.
Board-Style Important Questions
- 1 mark: Total internal reflection hone ke liye do zaroori conditions likho.
- 2 marks: Mirror formula aur lens formula likho aur unke sign me difference batao.
- 2 marks: Critical angle ki definition do aur uska formula likho.
- 3 marks: Ek convex lens ke saamne object rakha gaya hai jiska u aur f diya gaya ho — image position, nature aur magnification nikalne ka numerical solve karo (poori working steps ke saath).
- 3 marks: Prism ke angle of minimum deviation se refractive index nikalne ka formula derive karo (ya diya gaya numerical solve karo).
- 5 marks: Astronomical telescope ka ray diagram banao (normal adjustment me) aur uski magnifying power ka formula derive karo.
Aksar Poochhe Jaane Wale Sawaal
Mirror formula aur lens formula me kya difference hai?
Mirror formula me plus sign hota hai — 1/v + 1/u = 1/f. Lens formula me minus sign hota hai — 1/v − 1/u = 1/f. Ye dono formulas alag hain kyunki inki sign convention derivation different hoti hai, isliye inhe kabhi interchange mat karo.
Total internal reflection kab hoti hai?
TIR tabhi hoti hai jab do conditions ek saath satisfy hon: (1) light denser medium se rarer medium me travel kar rahi ho, aur (2) angle of incidence critical angle se zyada ho. Dono me se ek bhi condition miss ho to TIR nahi hogi.
Concave mirror hamesha real image banata hai kya?
Nahi. Agar object focus ke andar (f se kam distance pe) rakha jaaye to concave mirror virtual, magnified, erect image banata hai — jaise shaving/makeup mirror me hota hai. Object focus se bahar ho tabhi real image banti hai.
Power of lens negative kyun hoti hai concave lens ke liye?
Power P = 1/f hoti hai. Concave (diverging) lens ka focal length Cartesian convention me negative hota hai, isliye uski power bhi automatically negative aati hai. Convex (converging) lens ka f positive hota hai isliye power positive hoti hai.
Compound microscope me eyepiece aur objective ka focal length kaisa hona chahiye?
Objective ka focal length chota rakha jaata hai taaki real, magnified image jaldi bane. Eyepiece ka focal length bhi chota hota hai (objective se thoda zyada) taaki woh us image ko further magnify kar sake — dono ka combined effect high total magnification deta hai.
Telescope ki magnifying power badhane ke liye kya karna chahiye?
Normal adjustment me magnifying power m = fo/fe hoti hai. Isse badhane ke liye objective ka focal length (fo) bada aur eyepiece ka focal length (fe) chota rakhna chahiye — isi wajah se astronomical telescopes ki objective lens bahut lambi focal length ki hoti hai.
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