Class 10 Science · Chapter 9
Short answer:
Is chapter me NCERT ke 14 in-text questions (chaaron page-wise sets — spherical mirrors, mirror formula & magnification, refraction & refractive index, aur lens power) plus 17 exercise questions — total 31 questions — step-by-step solve kiye gaye hain. Har numerical me given values, formula, sign convention ke saath substitution, aur final answer sahi sign aur unit ke saath diya gaya hai. Iske alaawa: complete summary (reflection ke laws, concave/convex mirror ke image formation tables, refraction, Snell's law, lens formula, power), ek formula reference table, 6 sabse common exam mistakes, board-style practice questions marks-wise, aur 6 FAQs.
Poora chapter sirf do cheezon par tika hai — sign convention aur do formulas: mirror ka 1/v + 1/u = 1/f aur lens ka 1/v - 1/u = 1/f. Light ek straight line me chalti hai, lekin jab woh kisi polished surface se takraati hai to reflect hoti hai, aur jab ek medium se doosre medium me jaati hai to apna raasta mod leti hai — yahi refraction hai. Class 10 me hum spherical mirrors (concave aur convex) aur spherical lenses (convex aur concave) padhte hain: inme image kahan banegi, kaisi banegi (real/virtual, erect/inverted), aur kitni badi banegi — ye sab formula se nikaalna aata hona chahiye. Sabse zyada marks numericals me katte hain, aur wajah hamesha ek hi hoti hai — sign galat lag gaya. Isliye is chapter me sign convention ko rat'ta nahi, samajh kar yaad karna hai.
Chapter 9 Summary — 5 Minute Revision
1. Light aur Reflection
- Light ek prakaar ki energy hai jo straight line me travel karti hai (rectilinear propagation).
- Jab light kisi smooth, polished surface par girti hai to wapas laut aati hai — ise reflection kehte hain.
Reflection ke do niyam (Laws of Reflection)
- Law 1: Angle of incidence (∠i) = Angle of reflection (∠r)
- Law 2: Incident ray, reflected ray, aur point of incidence par khiche gaye normal — teeno ek hi plane me hote hain.
- Ye niyam har reflecting surface par lagte hain — plane mirror ho ya spherical.
Plane mirror ka image
- Hamesha virtual aur erect
- Size object ke barabar (m = +1)
- Mirror ke peeche utni hi doori par jitni object aage hai
- Laterally inverted (left-right ulta)
2. Spherical Mirrors — basic terms
| Term | Matlab |
|---|---|
| Pole (P) | Mirror ke reflecting surface ka centre point |
| Centre of curvature (C) | Us sphere ka centre jiska mirror ek hissa hai |
| Radius of curvature (R) | P se C tak ki doori |
| Principal focus (F) | Wo point jahan principal axis ke parallel aane wali rays reflect hokar milti hain (concave) ya jahan se aati hui lagti hain (convex) |
| Focal length (f) | P se F tak ki doori; f = R/2 |
| Aperture | Mirror ke reflecting surface ka diameter |
↔ Table ko side me swipe karein
Concave mirror (converging)
Reflecting surface andar ki taraf dhansa hua. Parallel rays ko ek point par converge karta hai. Uses: shaving mirror, dentist ka mirror, torch/headlight ka reflector, solar furnace.
Convex mirror (diverging)
Reflecting surface bahar ki taraf uthaa hua. Parallel rays ko diverge karta hai. Image hamesha virtual, erect aur diminished — isliye rear-view mirror me use hota hai (wide field of view).
3. Concave mirror — image formation table
| Object ki position | Image ki position | Size | Nature |
|---|---|---|---|
| Infinity par | F par | Bahut chhota (point) | Real, inverted |
| C se pare (beyond C) | F aur C ke beech | Diminished | Real, inverted |
| C par | C par | Same size | Real, inverted |
| F aur C ke beech | C se pare | Enlarged | Real, inverted |
| F par | Infinity par | Bahut bada | Real, inverted |
| P aur F ke beech | Mirror ke peeche | Enlarged | Virtual, erect |
↔ Table ko side me swipe karein
4. Convex mirror — image formation table
| Object ki position | Image ki position | Size | Nature |
|---|---|---|---|
| Infinity par | F par (mirror ke peeche) | Bahut chhota | Virtual, erect |
| Infinity aur P ke beech (kahin bhi) | P aur F ke beech (peeche) | Diminished | Virtual, erect |
↔ Table ko side me swipe karein
5. New Cartesian Sign Convention (mirrors)
- Object hamesha mirror ke baayin taraf rakha jaata hai — isliye u hamesha negative.
- Saari distances pole (P) se naapi jaati hain.
- Incident light ki direction me (right) naapi gayi distance = positive; ulti direction (left) = negative.
- Principal axis ke upar ki height = positive; neeche ki height = negative.
- Concave mirror: f aur R negative. Convex mirror: f aur R positive.
6. Refraction of Light
- Jab light ek transparent medium se doosre me obliquely jaati hai to uska path mud jaata hai — ye refraction hai. Wajah: alag-alag medium me light ki speed alag hoti hai.
- Rarer → Denser (jaise air se glass): ray normal ki taraf mudti hai (r < i).
- Denser → Rarer (glass se air): ray normal se door mudti hai (r > i).
- Normal ke saath (i = 0°) aane wali ray bilkul nahi mudti.
- Rectangular glass slab me emergent ray incident ray ke parallel nikalti hai, bas thoda lateral displacement ho jaata hai.
Laws of Refraction
- Law 1: Incident ray, refracted ray aur normal — ek hi plane me.
- Law 2 (Snell's Law): sin i / sin r ek constant hota hai (do given media ke liye).
7. Refractive Index
- Medium 2 ka medium 1 ke sapeksh refractive index: n21 = v1/v2 = sin i / sin r
- Absolute refractive index: n = c/v, jahan c = 3 × 108 m/s (vacuum me light ki speed).
- n jitna zyada, medium utna optically denser, aur usme light utni slow.
- Optical density ≠ mass density. Kerosene ki mass density paani se kam hai, par optical density zyada.
| Medium | Refractive index (approx.) |
|---|---|
| Air | 1.0003 |
| Water | 1.33 |
| Kerosene | 1.44 |
| Turpentine oil | 1.47 |
| Crown glass | 1.52 |
| Diamond | 2.42 |
↔ Table ko side me swipe karein
8. Spherical Lenses
- Convex lens (converging): beech me mota, kinaare par patla. Parallel rays ko F par converge karta hai. f positive.
- Concave lens (diverging): beech me patla, kinaare par mota. Rays ko diverge karta hai. f negative. Image hamesha virtual, erect, diminished.
- Optical centre (O): lens ka central point — isse guzarne wali ray bina muday nikal jaati hai. Saari distances O se naapte hain.
Convex lens — image formation table
| Object ki position | Image ki position | Size | Nature |
|---|---|---|---|
| Infinity par | F2 par | Bahut chhota | Real, inverted |
| 2F1 se pare | F2 aur 2F2 ke beech | Diminished | Real, inverted |
| 2F1 par | 2F2 par | Same size | Real, inverted |
| F1 aur 2F1 ke beech | 2F2 se pare | Enlarged | Real, inverted |
| F1 par | Infinity par | Bahut bada | Real, inverted |
| O aur F1 ke beech | Object ki hi side | Enlarged | Virtual, erect |
↔ Table ko side me swipe karein
Concave lens — image formation table
| Object ki position | Image ki position | Size | Nature |
|---|---|---|---|
| Infinity par | F1 par | Bahut chhota | Virtual, erect |
| Infinity aur O ke beech | F1 aur O ke beech | Diminished | Virtual, erect |
↔ Table ko side me swipe karein
9. Power of a Lens
- Power = lens ki light ko mod'ne ki kshamata. P = 1/f (f meters me).
- SI unit = dioptre (D). 1 D = 1 m-1.
- Convex lens ka power positive, concave lens ka negative.
- Lenses contact me rakhe jaayein to: P = P1 + P2 + P3 + ...
In-Text Questions — Solutions
Q1. Concave mirror ke principal focus ko define kijiye.
Concave mirror par jab principal axis ke parallel kai rays girti hain, to reflection ke baad wo saari rays principal axis par ek hi point par aakar milti hain. Us point ko concave mirror ka principal focus (F) kehte hain.
Yaani concave mirror rays ko converge karke jis point par ikattha karta hai, wahi uska principal focus hai. Pole se is point tak ki doori focal length (f) kehlaati hai, aur f = R/2.
f = R / 2
Q2. Ek spherical mirror ka radius of curvature 20 cm hai. Uski focal length kya hogi?
Given: R = 20 cm
Formula: focal length radius of curvature ki aadhi hoti hai.
f = R / 2
f = 20 / 2 = 10 cm
Answer: Focal length = 10 cm.
Note: Yahan mirror concave hai ya convex ye bataya nahi gaya, isliye magnitude 10 cm likhna hi kaafi hai. Agar concave hota to f = -10 cm, aur convex hota to f = +10 cm.
Q3. Aisa mirror bataiye jo object ka erect aur enlarged image bana sake.
Concave mirror.
Kab? Jab object mirror ke pole (P) aur principal focus (F) ke beech rakha jaaye, tab concave mirror mirror ke peeche ek virtual, erect aur enlarged image banata hai.
Isi wajah se shaving mirror aur dentist ke mirror concave hote hain — chehra ya daant bada dikhta hai. Convex mirror kabhi enlarged image nahi bana sakta, uska image hamesha diminished hi hota hai.
Q4. Vehicles me rear-view mirror ke roop me convex mirror hi kyun pasand kiya jaata hai?
Do wajah hain:
- Image hamesha erect aur virtual banta hai — chahe object kitni bhi doori par ho. Driver ko peeche ka traffic seedha dikhta hai, ulta nahi.
- Field of view bahut wide hota hai — kyunki image diminished banta hai, isliye ek chhote mirror me bhi peeche ka bada area dikh jaata hai.
Plane mirror ka field of view kam hota hai aur concave mirror kabhi-kabhi real, inverted image bana deta — dono hi driving ke liye khatarnaak hote. Isliye convex hi safe choice hai.
Q5. Ek convex mirror ka radius of curvature 32 cm hai. Uski focal length nikaaliye.
Given: Convex mirror, R = +32 cm (convex mirror ke liye R positive hota hai)
f = R / 2
f = 32 / 2 = 16 cm
Answer: Focal length = +16 cm (mirror ke peeche, isliye positive).
Q6. Ek concave mirror, apne saamne 10 cm par rakhe object ka teen guna badaa (magnified) real image banata hai. Image kahan bana hai?
Given: u = -10 cm (object hamesha mirror ke saamne, isliye negative), image real aur 3 guna enlarged.
Step 1 — magnification ka sign: Real image hamesha inverted hota hai, aur inverted image ke liye magnification negative hoti hai. Isliye m = -3 (m = +3 nahi).
m = - v / u
-3 = - v / (-10)
-3 = v / 10
v = -30 cm
Answer: Image mirror ke saamne 30 cm ki doori par banta hai (v ka negative sign yahi bata raha hai). Image real, inverted aur 3 guna enlarged hai.
Q7. Hawa me chal rahi ek light ray paani me tirchhi (obliquely) prayesh karti hai. Kya ray normal ki taraf mudegi ya normal se door? Kyun?
Ray normal ki taraf mudegi.
Kaaran: Paani hawa ke mukable optically denser medium hai (paani ka n = 1.33, hawa ka n ≈ 1.0003). Jab light rarer medium se denser medium me jaati hai to uski speed kam ho jaati hai, aur speed kam hone par ray normal ki taraf mud jaati hai.
Yaani yahan angle of refraction, angle of incidence se chhota hoga: r < i.
Q8. Light hawa se glass me prayesh karti hai jiska refractive index 1.50 hai. Glass me light ki speed kya hogi? Vacuum me light ki speed 3 × 10⁸ m/s hai.
Given: n = 1.50, c = 3 × 108 m/s
n = c / v
v = c / n
v = (3 × 108) / 1.50
v = 2 × 108 m/s
Answer: Glass me light ki speed = 2 × 108 m/s.
Dhyaan dijiye — ye vacuum ki speed se kam hai, jo hona hi chahiye kyunki glass optically denser hai.
Q9. Table 9.3 se pata kijiye ki kis medium ki optical density sabse zyada hai aur kiski sabse kam.
Sabse zyada optical density: Diamond — iska refractive index 2.42 hai, table me sabse ooncha.
Sabse kam optical density: Air (hawa) — iska refractive index 1.0003 hai, table me sabse kam.
Rule yaad rakhiye: jis medium ka refractive index zyada, uski optical density zyada, aur usme light utni hi dheere chalti hai.
Q10. Aapko kerosene, turpentine aur paani diya gaya hai. In teeno me se kisme light sabse tez chalti hai? Table 9.3 ki jaankari ka istemaal kijiye.
Refractive index:
- Water — 1.33
- Kerosene — 1.44
- Turpentine — 1.47
v = c / n
Is formula me n aur v ek doosre ke inversely proportional hain — n jitna kam, v utna zyada. Teeno me water ka n sabse kam (1.33) hai.
Answer: Light paani (water) me sabse tez chalti hai.
Q11. Heere (diamond) ka refractive index 2.42 hai. Is kathan ka kya matlab hai?
Iska matlab hai ki vacuum me light ki speed, diamond me light ki speed se 2.42 guna zyada hai.
n = c / v = 2.42
v = c / 2.42 ≈ 1.24 × 108 m/s
Yaani diamond ke andar light ki speed lagbhag 1.24 × 108 m/s reh jaati hai. Diamond ka refractive index sabse zyada hone ki wajah se hi usme light bahut zyada mudti hai aur andar hi andar baar-baar reflect hoti hai — isi se heera itna chamakta hai.
Q12. Lens ke power ke 1 dioptre ko define kijiye.
1 dioptre us lens ka power hai jiski focal length 1 metre ho.
P = 1 / f (f in metres)
Dioptre power ka SI unit hai, symbol D. Convex (converging) lens ka power positive hota hai aur concave (diverging) lens ka negative.
Q13. Ek convex lens, ek needle ka real aur inverted image apne se 50 cm ki doori par banata hai. Agar image object ke barabar size ka hai, to needle lens ke saamne kahan rakhi gayi hai? Lens ka power bhi nikaaliye.
Given: v = +50 cm (real image lens ke doosri taraf banta hai, isliye positive), image object ke barabar size ka.
Step 1 — object ki position: Convex lens same-size real image tabhi banata hai jab object 2F1 par ho, aur tab image 2F2 par banta hai. Isliye |u| = |v| = 50 cm, aur object baayin taraf hai to u = -50 cm.
Step 2 — focal length:
1/v - 1/u = 1/f
1/50 - 1/(-50) = 1/f
1/50 + 1/50 = 2/50 = 1/25
f = +25 cm = +0.25 m
Step 3 — power:
P = 1 / f = 1 / 0.25
P = +4 D
Answer: Needle lens se 50 cm saamne rakhi gayi hai, aur lens ka power +4 D hai (positive, kyunki convex lens hai).
Q14. 2 m focal length wale concave lens ka power nikaaliye.
Given: Concave lens, f = -2 m (concave lens ki focal length hamesha negative hoti hai — ye sign lagana mat bhooliye).
P = 1 / f
P = 1 / (-2)
P = -0.5 D
Answer: Power = -0.5 D. Negative sign confirm karta hai ki lens diverging (concave) hai.
Poore Class 10 Science 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–Q17)
Q1. Inme se kis material se lens nahi banaya ja sakta? (a) Paani (b) Kaanch (c) Plastic (d) Mitti
Answer: (d) Mitti (Clay)
Lens banane ke liye material ka transparent hona zaroori hai, taaki light usme se guzar sake aur refract ho. Paani, kaanch aur plastic — teeno transparent hain, teeno se lens ban sakta hai. Mitti opaque hai, light usme se guzarti hi nahi, isliye usse lens nahi ban sakta.
Q2. Ek concave mirror dwaara bana image virtual, erect aur object se bada dikhai deta hai. Object ki position kya honi chahiye? (a) Principal focus aur centre of curvature ke beech (b) Centre of curvature par (c) Centre of curvature se pare (d) Mirror ke pole aur principal focus ke beech
Answer: (d) Mirror ke pole aur principal focus ke beech
Concave mirror sirf ek hi position me virtual aur erect image banata hai — jab object P aur F ke beech ho. Tab image mirror ke peeche, virtual, erect aur enlarged banta hai. Baaki teeno positions (F–C ke beech, C par, C se pare) me image hamesha real aur inverted banta hai.
Yahi principle shaving mirror me use hota hai.
Q3. Convex lens se object ke barabar size ka real image paane ke liye object kahan rakhna chahiye? (a) Lens ke principal focus par (b) Focal length se do guni doori par (c) Anant (infinity) par (d) Lens ke optical centre aur principal focus ke beech
Answer: (b) Focal length se do guni doori par (yaani 2F1 par)
Convex lens ka niyam hai: object 2F1 par ho to image 2F2 par banta hai — real, inverted aur object ke barabar size ka.
F par rakhne se image infinity par jaata hai, infinity par rakhne se image F par point jaisa banta hai, aur O–F ke beech rakhne se image virtual ho jaata hai.
Q4. Ek spherical mirror aur ek patla spherical lens — dono ki focal length -15 cm hai. Ye sambhavatah hain: (a) dono concave (b) dono convex (c) mirror concave par lens convex (d) mirror convex par lens concave
Answer: (a) Dono concave
Sign convention yaad kijiye:
- Mirror: concave ka f negative, convex ka f positive → f = -15 cm matlab concave mirror.
- Lens: convex ka f positive, concave ka f negative → f = -15 cm matlab concave lens.
Isliye dono hi concave hain.
Q5. Aap mirror se chahe kitni bhi doori par khade ho jaayein, aapka image hamesha erect hi dikhta hai. Mirror ho sakta hai: (a) plane (b) concave (c) convex (d) ya to plane ya convex
Answer: (d) Ya to plane ya convex
Plane mirror hamesha virtual aur erect image banata hai (m = +1). Convex mirror bhi hamesha virtual aur erect image banata hai (chhota, par erect). Dono me object ki doori chahe kuch bhi ho, image erect hi rehta hai.
Concave mirror sirf tabhi erect image deta hai jab object P aur F ke beech ho — doori badhte hi image inverted ho jaata hai. Isliye concave answer nahi ho sakta.
Q6. Dictionary me chhote akshar padhne ke liye aap kaun sa lens pasand karenge? (a) 50 cm focal length ka convex lens (b) 50 cm focal length ka concave lens (c) 5 cm focal length ka convex lens (d) 5 cm focal length ka concave lens
Answer: (c) 5 cm focal length ka convex lens
Do baatein:
- Magnifying glass ke liye convex lens hi chahiye — concave lens hamesha diminished image banata hai, akshar aur chhote dikhenge.
- Convex lens me focal length jitni kam hogi, power (P = 1/f) utni zyada aur magnification utni zyada hogi. 5 cm < 50 cm, isliye 5 cm wala behtar hai.
Object ko lens ke optical centre aur focus ke beech rakhne par virtual, erect, enlarged image milega.
Q7. Hume 15 cm focal length wale concave mirror se ek object ka erect image chahiye. Object ki mirror se doori ki range kya honi chahiye? Image ka nature kya hoga? Image object se bada hoga ya chhota? Ray diagram bhi banaiye.
Given: Concave mirror, f = -15 cm
Range: Concave mirror erect image tabhi banata hai jab object pole aur principal focus ke beech ho. Isliye object ki doori 0 se 15 cm ke beech honi chahiye (15 cm se kam).
0 < |u| < 15 cm
Nature of image: Virtual aur erect (mirror ke peeche banta hai, screen par nahi aata).
Size: Object se bada (enlarged).
Ray diagram: Object AB ko P aur F ke beech rakhiye. Do rays lijiye — (i) A se principal axis ke parallel ek ray jo reflect hokar F se guzarti hui lagti hai, (ii) A se ek ray jo C ki taraf jaati hui direction me hai aur usi raaste wapas aati hai. Reflected rays aage jaakar milti nahi, isliye unhe peeche extend kijiye — mirror ke peeche milkar virtual, erect, enlarged image A'B' banega.
Example: Shaving mirror me chehra isi tarah bada dikhta hai.
Q8. Nimn sthitiyon me istemaal hone wale mirror ka prakaar bataiye — (a) Car ki headlight (b) Vehicle ka side/rear-view mirror (c) Solar furnace. Apne uttar ka kaaran bhi dijiye.
(a) Car ki headlight — Concave mirror
Bulb ko concave mirror ke focus par rakha jaata hai. Focus se nikli rays reflect hokar principal axis ke parallel ho jaati hain, jisse ek shaktishaali, door tak jaane wala parallel beam milta hai.
(b) Side/rear-view mirror — Convex mirror
Convex mirror hamesha virtual, erect aur diminished image banata hai, aur uska field of view bahut wide hota hai. Driver ko peeche ka bada area ek chhote mirror me hi seedha dikh jaata hai.
(c) Solar furnace — Concave mirror (bada concave/parabolic reflector)
Suraj se aane wali parallel rays concave mirror par girkar focus par converge ho jaati hain. Us ek point par bahut zyada heat ikattha ho jaati hai, jisse bahut ooncha temperature milta hai.
Q9. Ek convex lens ka aadha hissa kaale kaagaz se dhak diya gaya. Kya ye lens object ka poora image banayega? Prayog karke jaanchiye. Apne observations samjhaiye.
Haan, lens object ka poora (complete) image banayega.
Kaaran: Object ke har point se light rays lens ke poore surface par girti hain — sirf ek hisse par nahi. Agar aadha hissa dhak bhi diya jaaye, to baaki khule aadhe hisse se guzarne wali rays ab bhi refract hokar ussi jagah milengi jahan pehle milti thi. Isliye image ka shape aur position bilkul waise hi rahenge, poora image banega.
Farak kya aayega: Lens se guzarne wali rays ki sankhya aadhi reh jaati hai, isliye image ki brightness (intensity) kam ho jaayegi — image dhundhla dikhega. Size, shape ya position par koi asar nahi.
Yahi baat lens ke upar wala aadha ya neeche wala aadha — dono case me lagu hoti hai.
Q10. 5 cm lambi ek vastu ko 10 cm focal length wale converging lens se 25 cm door rakha gaya hai. Ray diagram banaiye aur bane image ki position, size aur nature nikaaliye.
Given: h = +5 cm, u = -25 cm, f = +10 cm (converging = convex lens)
Step 1 — image ki position (lens formula):
1/v - 1/u = 1/f
1/v = 1/f + 1/u
1/v = 1/10 + 1/(-25) = 1/10 - 1/25
1/v = (5 - 2)/50 = 3/50
v = 50/3 = +16.7 cm
Step 2 — magnification:
m = v / u = 16.7 / (-25) = -0.67
Step 3 — image ka size:
m = h' / h ⟹ h' = m × h
h' = (-0.67) × 5 = -3.3 cm
Answer:
- Position: Lens ke doosri taraf, 16.7 cm par (v positive hai isliye)
- Size: 3.3 cm (minus sign sirf inverted hone ka sanket hai)
- Nature: Real, inverted aur diminished
Ray diagram: Object 2F1 (20 cm) se pare hai, isliye image F2 (10 cm) aur 2F2 (20 cm) ke beech banega — 16.7 cm bilkul isi range me hai, jo hamare answer ko verify karta hai.
Q11. 15 cm focal length wala ek concave lens, lens se 10 cm par image banata hai. Object lens se kitni doori par rakha hai? Ray diagram banaiye.
Given: Concave lens, f = -15 cm (concave lens ka f negative). Concave lens ka image hamesha virtual aur object ki hi side banta hai, isliye v = -10 cm.
1/v - 1/u = 1/f
1/u = 1/v - 1/f
1/u = 1/(-10) - 1/(-15)
1/u = -1/10 + 1/15
1/u = (-3 + 2)/30 = -1/30
u = -30 cm
Answer: Object lens se 30 cm ki doori par rakha hai (negative sign bata raha hai ki lens ke baayin taraf, yaani incident light wali side par hai).
Ray diagram: Object 30 cm par, image 10 cm par usi side — virtual, erect aur diminished. Do rays lijiye: (i) parallel ray jo refract hokar F1 se aati hui lagti hai, (ii) optical centre se seedhi guzarne wali ray. Inhe peeche extend karke virtual image milega.
Q12. Ek object 15 cm focal length wale convex mirror se 10 cm ki doori par rakha hai. Image ki position aur nature nikaaliye.
Given: Convex mirror, f = +15 cm (convex mirror ka f positive), u = -10 cm
1/v + 1/u = 1/f
1/v = 1/f - 1/u
1/v = 1/15 - 1/(-10) = 1/15 + 1/10
1/v = (2 + 3)/30 = 5/30 = 1/6
v = +6 cm
Magnification:
m = - v / u = - (6) / (-10) = +0.6
Answer:
- Position: Image mirror ke peeche 6 cm par (v ka positive sign yahi bata raha hai)
- Nature: Virtual aur erect (m positive hai)
- Size: Diminished — object ka 0.6 guna (m < 1)
Q13. Plane mirror dwaara utpann magnification +1 hoti hai. Iska kya matlab hai?
Magnification ka formula hai m = h'/h. Yahan do baatein nikalti hain:
- Magnitude 1 ka matlab: h' = h, yaani image ka size object ke bilkul barabar hai — na bada, na chhota.
- Plus sign ka matlab: Image erect (seedha) hai aur virtual hai. (Negative m hota to image inverted aur real hota.)
m = h' / h = +1 ⟹ h' = h, image erect aur virtual
Isiliye aaina dekhte waqt hum apne hi barabar size ka, seedha image dekhte hain.
Q14. 5.0 cm lambi ek vastu ko 30 cm radius of curvature wale convex mirror ke saamne 20 cm ki doori par rakha gaya hai. Image ki position, nature aur size nikaaliye.
Given: h = +5.0 cm, u = -20 cm, R = +30 cm (convex mirror)
Step 1 — focal length:
f = R / 2 = 30 / 2 = +15 cm
Step 2 — image ki position:
1/v + 1/u = 1/f
1/v = 1/15 - 1/(-20) = 1/15 + 1/20
1/v = (4 + 3)/60 = 7/60
v = 60/7 = +8.6 cm
Step 3 — magnification aur size:
m = - v / u = - (8.57) / (-20) = +0.43
h' = m × h = 0.43 × 5.0 = +2.2 cm
Answer:
- Position: Mirror ke peeche 8.6 cm par
- Nature: Virtual aur erect (v positive, m positive)
- Size: 2.2 cm — diminished (object 5.0 cm tha)
Q15. 7.0 cm size ki ek vastu ko 18 cm focal length wale concave mirror ke saamne 27 cm par rakha gaya hai. Screen ko mirror se kitni doori par rakhein ki tez (sharp focussed) image mile? Image ka size aur nature bhi nikaaliye.
Given: h = +7.0 cm, u = -27 cm, f = -18 cm (concave mirror ka f negative)
Step 1 — image ki position:
1/v + 1/u = 1/f
1/v = 1/f - 1/u
1/v = 1/(-18) - 1/(-27) = -1/18 + 1/27
1/v = (-3 + 2)/54 = -1/54
v = -54 cm
Step 2 — magnification aur size:
m = - v / u = - (-54) / (-27) = -2
h' = m × h = (-2) × 7.0 = -14 cm
Answer:
- Screen ki position: Mirror ke saamne 54 cm par (v negative hai matlab image object wali side par banta hai — real image, isliye screen par mil sakta hai)
- Size: 14 cm (negative sign inverted hone ka sanket)
- Nature: Real, inverted aur enlarged (2 guna bada)
Check: f = 18 cm to C = 36 cm. Object 27 cm par hai — yaani F(18) aur C(36) ke beech. Table ke hisaab se image C se pare, real, inverted aur enlarged hona chahiye — 54 cm > 36 cm, bilkul sahi.
Q16. -2.0 D power wale lens ki focal length nikaaliye. Ye kis prakaar ka lens hai?
Given: P = -2.0 D
P = 1 / f ⟹ f = 1 / P
f = 1 / (-2.0) = -0.5 m
f = -50 cm
Answer: Focal length = -0.5 m (yaani -50 cm).
Power aur focal length dono negative hain, isliye ye ek concave (diverging) lens hai.
Q17. Ek doctor ne +1.5 D power ka corrective lens likha hai. Lens ki focal length nikaaliye. Ye lens diverging hai ya converging?
Given: P = +1.5 D
P = 1 / f ⟹ f = 1 / P
f = 1 / 1.5 = +0.67 m
f = +66.7 cm (lagbhag)
Answer: Focal length = +0.67 m (≈ 66.7 cm).
Power positive hai, isliye ye converging (convex) lens hai. Aise lens hypermetropia (door-drishti dosh) theek karne ke liye diye jaate hain.
Important Equations — Ek Nazar Me
| Quantity / Relation | Formula | Sign convention note | Unit |
|---|---|---|---|
| Mirror formula | 1/v + 1/u = 1/f | Saari distances pole (P) se. u hamesha negative. Concave: f, R negative. Convex: f, R positive. | cm ya m |
| Focal length & radius of curvature | f = R/2 (R = 2f) | f aur R ka sign hamesha same hota hai (dono mirror ki type par depend karte hain). | cm ya m |
| Magnification (mirror) | m = -v/u = h'/h | m negative ⟹ real + inverted. m positive ⟹ virtual + erect. |m| > 1 enlarged, |m| < 1 diminished. | koi unit nahi |
| Lens formula | 1/v - 1/u = 1/f | Distances optical centre (O) se. Convex lens: f positive. Concave lens: f negative. u negative. | cm ya m |
| Magnification (lens) | m = v/u = h'/h | Mirror wale formula se alag — yahan minus sign nahi lagta. m negative ⟹ real, inverted. | koi unit nahi |
| Power of a lens | P = 1/f | f metres me daalna zaroori hai. Convex: P positive. Concave: P negative. | dioptre (D) = m-1 |
| Lenses in contact | P = P1 + P2 + P3 + ... | Har lens ka apna sign lagakar jodna hai (convex +, concave -). | dioptre (D) |
| Absolute refractive index | n = c/v | c = 3 × 108 m/s. n hamesha 1 se bada. n zyada ⟹ optically denser ⟹ light slow. | koi unit nahi |
| Relative refractive index | n21 = v1/v2 = n2/n1 | Medium 2 ka medium 1 ke sapeksh. n12 = 1/n21. | koi unit nahi |
| Snell's law (2nd law of refraction) | n21 = sin i / sin r | i = angle of incidence, r = angle of refraction — dono normal se naape jaate hain, surface se nahi. | koi unit nahi |
| Angle of incidence & reflection | ∠i = ∠r | Dono angles normal se naape jaate hain; incident ray, reflected ray aur normal ek hi plane me. | degree |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Sign convention lagana bhool jaana (sabse bada marks-killer). Bahut se students formula me seedha u = 25, f = 18 daal dete hain. Object hamesha mirror/lens ke baayin taraf hota hai, isliye u hamesha negative hai. Concave mirror ka f negative, convex mirror ka positive; convex lens ka f positive, concave lens ka negative. Numerical shuru karne se pehle given values ko sign ke saath alag likh lijiye — 'u = -27 cm, f = -18 cm' — phir hi formula me daaliye.
- Mirror ka formula lens par (ya lens ka mirror par) laga dena. Mirror me 1/v + 1/u = 1/f (plus) hai aur lens me 1/v - 1/u = 1/f (minus). Isi tarah magnification: mirror me m = -v/u (minus ke saath) aur lens me m = v/u (bina minus). Ye chaar cheezein aapas me mix ho jaayein to poora numerical galat ho jaata hai. Question padhte hi upar likh lijiye — 'MIRROR' ya 'LENS'.
- Concave lens ka f positive lagana. Question me 'concave lens of focal length 15 cm' likha ho to bhi formula me f = -15 cm hi jaayega — 'minus' likha nahi hota, aapko lagana padta hai. Yahi galti concave mirror ke 'focal length 18 cm' me hoti hai (f = -18 cm). Rule: concave = negative, convex = positive — lens aur mirror dono me nahi, dhyaan se — mirror me concave negative, convex positive; lens me convex positive, concave negative.
- Magnification ke sign ka matlab na samajhna. m ka sign size nahi, nature batata hai: m negative = image real aur inverted; m positive = image virtual aur erect. Size to |m| se pata chalta hai — |m| > 1 enlarged, |m| < 1 diminished. 'm = -2' ka matlab image chhota nahi, balki 2 guna bada aur ulta hai. Aur agar question kahe 'real image, 3 times magnified' to aapko khud m = -3 lena hai, +3 nahi.
- Power nikaalte waqt focal length centimetre me daal dena. P = 1/f me f hamesha metres me hona chahiye. f = 25 cm hai to pehle 0.25 m banaiye, phir P = 1/0.25 = +4 D. Seedha 1/25 kar diya to answer 0.04 aa jaayega — poora galat. Aur f ka sign bhi saath le jaana hai: f = -2 m ⟹ P = -0.5 D.
- Answer me sign aur unit chhod dena, aur nature likhna bhool jaana. 'v = 54' likhna adhoora hai — sahi hai 'v = -54 cm, yaani image mirror ke saamne 54 cm par'. v ka sign hi batata hai image mirror ke saamne (real) hai ya peeche (virtual). Numerical me poore marks tabhi milte hain jab aap position + size (unit ke saath) + nature (real/virtual, erect/inverted, enlarged/diminished) — teeno likhein.
Board-Style Important Questions
- 1 mark: Ek concave lens ki focal length 25 cm hai. Uska power dioptre me nikaaliye.
- 1 mark: Vehicles ke rear-view mirror me convex mirror hi kyun lagaya jaata hai? Ek kaaran likhiye.
- 2 marks: New Cartesian sign convention ke koi chaar niyam likhiye jo spherical mirrors ke liye use hote hain.
- 3 marks: 12 cm focal length wale convex mirror ke saamne 18 cm par ek object rakha hai. Image ki position, magnification aur nature nikaaliye.
- 5 marks: (a) Lens formula aur magnification formula likhiye. (b) 4 cm ka object 20 cm focal length wale convex lens se 30 cm door rakha hai — image ki position, size aur nature nikaaliye. (c) Ray diagram banaiye.
Quick Quiz — Score Check Karein
Q1. Laws of reflection ke anusar, agar angle of incidence 35° hai, to angle of reflection kitna hoga?
Q2. Ek concave mirror ka radius of curvature R = 30 cm hai. Uski focal length f kitni hogi?
Q3. Object concave mirror ke pole (P) aur focus (F) ke beech rakha hai. Image ki nature kya hogi?
Q4. Convex mirror hamesha kis type ki image banata hai, chahe object kahin bhi ho?
Q5. New Cartesian sign convention me concave mirror ki focal length (f) ka sign kya hota hai?
Q6. Light rarer medium (air) se denser medium (glass) me obliquely jaati hai. Refraction ke baad ray kis taraf mudti hai?
Q7. Kisi medium ka absolute refractive index n = c/v formula se nikala jaata hai, jahan c = 3 × 10^8 m/s. Agar ek medium me light ki speed v = 2 × 10^8 m/s hai, to uska refractive index kya hoga?
Q8. Diamond ka refractive index approx 2.42 hai aur water ka approx 1.33 hai. Inme se konsa medium 'optically denser' hai aur kyun?
Q9. Ek rectangular glass slab me light jab enter aur exit karti hai, to emergent ray incident ray ke sapeksh kaisi hoti hai?
Q10. Convex lens (converging lens) ke liye sign convention me focal length (f) ka sign kya hota hai?
Aksar Poochhe Jaane Wale Sawaal
Mirror formula aur lens formula me sign ka farak kyun hai?
Mirror me light reflect hokar wapas ussi taraf jaati hai jahan se aayi thi, jabki lens me light paar nikal jaati hai. Isi geometry ke kaaran derivation me sign badal jaata hai. Practical trick: mirror me plus (1/v + 1/u = 1/f) aur magnification me minus (m = -v/u); lens me minus (1/v - 1/u = 1/f) aur magnification me plus (m = v/u). Yaani dono me ek plus aur ek minus hota hai, bas jagah badal jaati hai.
Real aur virtual image me kaise pehchaanein ki kaun sa bana hai?
Sabse aasan tareeka answer ke sign se hai. Mirror me v negative aaye to image mirror ke saamne bana hai — real. v positive aaye to peeche bana hai — virtual. Lens me ulta hai: v positive matlab image doosri taraf bana — real; v negative matlab object wali hi side bana — virtual. Real image screen par pakda ja sakta hai aur hamesha inverted hota hai; virtual image screen par nahi aata aur hamesha erect hota hai.
Concave mirror kabhi virtual image banata hai kya?
Haan, sirf ek hi case me — jab object mirror ke pole aur principal focus ke beech ho. Tab image mirror ke peeche virtual, erect aur enlarged banta hai. Baaki har position me (F par, F–C ke beech, C par, C se pare) image real aur inverted hi banta hai. Isi ek exception ki wajah se shaving mirror aur dentist ka mirror concave hote hain.
Optical density aur mass density ek hi cheez hai kya?
Nahi, ye do alag cheezein hain. Optical density refractive index se tay hoti hai — matlab us medium me light kitni dheere chalti hai. Mass density matlab per unit volume mass. Sabse achha example kerosene hai: uski mass density paani se kam hai (isliye paani par tairta hai), lekin uska refractive index 1.44 hai jo paani ke 1.33 se zyada hai — yaani kerosene optically denser hai.
Sign convention me distance kahan se naapte hain, aur positive-negative kaise decide hota hai?
Mirror me saari distances pole (P) se naapi jaati hain aur lens me optical centre (O) se. Incident light ki direction (aam taur par baayin se daayin) me naapi gayi distance positive hoti hai, aur uske ulti direction me negative. Isi wajah se object, jo hamesha baayin taraf rakha jaata hai, uska u hamesha negative aata hai. Principal axis ke upar ki height positive, neeche ki negative.
Convex lens ka aadha hissa dhak dein to aadha image banega kya?
Nahi, poora image hi banega. Object ke har point se rays lens ke poore surface par girti hain, isliye khule aadhe hisse se guzarne wali rays bhi ussi jagah milkar poora image bana deti hain. Farak sirf itna hai ki rays ki sankhya aadhi rehne se image ki brightness kam ho jaayegi — image thoda dhundhla dikhega, par uska size, shape aur position bilkul nahi badlega.
Class 10 Science — Saare Chapters
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