Diagram Se Number Tak 📏
Pichhle lesson mein humne ray (kiran) diagram se pata kiya ki image kahan banega. Par diagram se ye nahi pata chalta ki image theek kitni doori par hai, ya kitne guna bada hai.
Iske liye do formula hain — aur dono itne chhote hain ki ek minute mein yaad ho jaate hain. Par ek shart hai: sign convention pehle samajhna padega. Warna formula sahi hoga aur jawab galat.
⚠️ New Cartesian Sign Convention — Sabse Zaroori Hissa
Ye 4 niyam hain. Inhe ratt maar kar nahi, samajh kar yaad karo — poora chapter inhi par tika hai.
📌 Chaar niyam:
1️⃣ Object hamesha baayen rakha jaata hai — roshni baayen se daayen chalti hai.
2️⃣ Saari dooriyan pole (P) se naapi jaati hain.
3️⃣ Aati hui roshni ki disha mein = positive, ulti disha mein =
negative.
4️⃣ Axis ke upar ki lambai = positive, neeche ki = negative.
| Raashi | Chinh (sign) | Matlab |
|---|---|---|
| u (object distance) | Hamesha − | Object hamesha mirror ke saamne |
| f concave (avatal) mirror | − | Focus mirror ke saamne |
| f convex (uttal) mirror | + | Focus mirror ke peeche |
| v negative | − | Image saamne → REAL, inverted |
| v positive | + | Image peeche → VIRTUAL, erect |
| h (object height) | Hamesha + | Object seedha rakha jaata hai |
| h′ negative | − | Image ULTA (inverted) |
🎯 Jaanch ka sabse aasaan tareeka: jawab nikalne ke baad
v ka chinh dekho.
v negative → image mirror ke saamne → real aur inverted
v positive → image mirror ke peeche → virtual aur erect
Bas isi se aap bina diagram banaye bata sakte ho ki image kaisa hai!
📘 Do Formule
📐 Mirror formula:
1/v + 1/u = 1/f
📐 Magnification (aavardhan):
m = h′/h = −v/u
Aur yaad rakho: f = R/2
Ye sabse aam confusion hai. Yaad rakhne ka tareeka:
Mirror mein roshni wapas laut'ti hai → do dooriyan
ek hi taraf → formula mein +
Lens mein roshni paar nikal jaati hai → dooriyan
ulti taraf → formula mein −
Aur magnification mein bhi ulta: mirror m = −v/u, par
lens m = +v/u. Minus sign wahin lagta hai jahan formula mein plus tha!
🧮 Hal Kiye Hue Sawaal
Ek concave mirror ki focal length 15 cm hai. Ek 5 cm ooncha object uske
10 cm saamne rakha hai. Image ki doori, magnification aur oonchai nikaalo.
Step 1 — Diya hua likho (chinh ke saath):
f = −15 cm (concave)
u = −10 cm (object hamesha −)
h = +5 cm
Step 2 — Mirror formula:
1/v + 1/u = 1/f
1/v = 1/f − 1/u = 1/(−15) − 1/(−10)
1/v = −1/15 + 1/10 = (−2 + 3)/30 = 1/30
v = +30 cm
Step 3 — Magnification:
m = −v/u = −(+30)/(−10) = +3
Step 4 — Image ki oonchai:
h′ = m × h = 3 × 5 = +15 cm
Jawab: Image mirror ke 30 cm peeche banega, 3 guna
bada, 15 cm ooncha.
Nature: v positive hai → virtual; m positive hai →
erect; |m| > 1 → enlarged.
✅ Jaanch: u = 10, f = 15 — yani object F aur P ke beech hai. Table ke hisaab se
yahi ek case virtual, erect aur bada deta hai. Sahi hai! Isiliye daadhi banate waqt mirror
paas rakha jaata hai.
Usi concave mirror (R = 30 cm) ke saamne 3 cm ka object 20 cm door
rakha hai. Image ka poora vivaran do.
Step 1:
R = −30 cm → f = R/2 = −15 cm
u = −20 cm, h = +3 cm
Step 2:
1/v = 1/f − 1/u = 1/(−15) − 1/(−20)
1/v = −1/15 + 1/20 = (−4 + 3)/60 = −1/60
v = −60 cm
Step 3:
m = −v/u = −(−60)/(−20) = −60/20 = −3
h′ = −3 × 3 = −9 cm
Jawab: Image mirror ke 60 cm saamne, real,
inverted, 3 guna bada, oonchai 9 cm (ulta).
✅ Jaanch: f = 15, C = 30. Object 20 cm par hai — yani F aur C ke
beech. Table kehti hai: image C se pare, bada, real, inverted. v = 60 sach mein C (30)
se pare hai. Sahi!
Gaur karo: wahi mirror, wahi object — sirf doori badal di, aur image virtual se
real ho gaya aur seedha se ulta. Chammach wala experiment yahi
tha.
Ek convex mirror ki focal length 15 cm hai. 4 cm ka object uske
10 cm saamne hai. Image nikaalo.
Step 1: f = +15 cm (convex — dhyaan do, positive!),
u = −10 cm, h = +4 cm
Step 2:
1/v = 1/f − 1/u = 1/15 − 1/(−10) = 1/15 + 1/10
1/v = (2 + 3)/30 = 5/30 = 1/6
v = +6 cm
Step 3:
m = −v/u = −(6)/(−10) = +0.6
h′ = 0.6 × 4 = +2.4 cm
Jawab: Image 6 cm peeche, virtual,
erect, chhota (0.6 guna), oonchai 2.4 cm.
✅ Jaanch: convex mirror ka jawab hamesha virtual + erect +
diminished hota hai — aur yahi mila. Agar aapko convex mirror ka jawab kabhi real ya bada mile, toh
zaroor kahin sign ki galti hai.
Ek gaadi ke convex rear-view mirror ki radius of curvature (R) 3.00 m hai. Peeche aa rahi
ek bus 5.00 m door hai. Image kahan aur kitne guna banega?
Step 1: R = +3.00 m → f = R/2 = +1.50 m (convex),
u = −5.00 m
Step 2:
1/v = 1/1.5 − 1/(−5) = 0.6667 + 0.2 = 0.8667
v = +1.15 m (lagbhag)
Step 3:
m = −v/u = −(1.15)/(−5) = +0.23
Jawab: Image mirror ke 1.15 m peeche, virtual, erect, aur asli bus
se sirf 0.23 guna (yani chauthai se bhi chhota).
🚗 Isi wajah se warning likhi hoti hai: bus itni chhoti dikhti hai ki dimaag use
door samajh leta hai — jabki wo sirf 5 m par hai! Isiliye mirror par
"Objects in mirror are closer than they appear" likha rehta hai.
✍️ Khud Karo — Practice
Ek concave mirror ki focal length 12 cm hai. 6 cm ka object
18 cm door rakha hai. v, m aur h′ nikaalo.
Jawab: f = −12, u = −18
1/v = −1/12 + 1/18 = (−3 + 2)/36 = −1/36 → v = −36 cm
m = −(−36)/(−18) = −2 • h′ = −2 × 6 = −12 cm
Real, inverted, 2 guna bada, 36 cm saamne.
Ek convex mirror ki focal length 20 cm hai. 5 cm ka object
30 cm door hai. v, m aur h′ nikaalo.
Jawab: f = +20, u = −30
1/v = 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12 → v = +12 cm
m = −(12)/(−30) = +0.4 • h′ = 0.4 × 5 = +2 cm
Virtual, erect, chhota (0.4 guna), 12 cm peeche.
⚠️ Numericals mein sabse aam 4 galtiyan:
1️⃣ u ko positive likh dena — u hamesha negative hai, koi apwaad nahi
2️⃣ Concave ka f positive likh dena — concave = −, convex = +
3️⃣ R aur f ko mila dena — sawaal mein R diya ho toh pehle 2 se bhaag do
4️⃣ 1/v nikaalkar wahin rok dena — aakhir mein ulta (reciprocal)
karna mat bhoolo!
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