Wahi Sign Convention, Ek Chhota Farak 🔄
Achhi khabar: lens ke liye sign convention bilkul wahi hai jo mirror (darpan) ke liye tha. Dooriyan ab optical centre (O) se naapi jaati hain, aur u hamesha negative hi rehta hai.
Bas do jagah farak hai — formula mein aur magnification (aavardhan) mein. Aur wo farak ek hi wajah se aata hai: lens mein roshni paar nikal jaati hai, laut'ti nahi.
📘 Teen Formule
📐 Lens formula:
1/v − 1/u = 1/f
📐 Magnification:
m = h′/h = v/u
📐 Power (kshamata):
P = 1 / f (metre mein)
Ikai: dioptre (D)
| Mirror | Lens | |
|---|---|---|
| Formula | 1/v + 1/u = 1/f | 1/v − 1/u = 1/f |
| Magnification | m = −v/u | m = +v/u |
| Jodne wala | Concave (f = −) | Convex (f = +) |
| Failane wala | Convex (f = +) | Concave (f = −) |
| REAL image ke liye | v = negative | v = positive |
| Origin | Pole (P) | Optical centre (O) |
| R = 2f? | Haan | Nahi (sirf f aur 2f) |
🎯 Ek line mein poora antar yaad karo:
"Mirror mein sab kuch ULTA hai lens ke."
Formula mein +/−, magnification mein −/+, f ka chinh, real image ka chinh — chaaron jagah ulta.
Ek baar ye pakad liya toh dono kabhi nahi gadbadenge.
🧮 Hal Kiye Hue Sawaal
Ek convex lens ki focal length 10 cm hai. 4 cm ka object uske
15 cm saamne rakha hai. v, m aur h′ nikaalo.
Step 1 — Diya hua:
f = +10 cm (convex — positive!)
u = −15 cm
h = +4 cm
Step 2 — Lens formula:
1/v − 1/u = 1/f
1/v = 1/f + 1/u = 1/10 + 1/(−15)
1/v = 1/10 − 1/15 = (3 − 2)/30 = 1/30
v = +30 cm
Step 3 — Magnification:
m = v/u = 30/(−15) = −2
Step 4 — Oonchai:
h′ = m × h = −2 × 4 = −8 cm
Jawab: Image lens ke 30 cm doosri taraf, real,
inverted, 2 guna bada, oonchai 8 cm.
✅ Jaanch: f = 10, toh 2F = 20. Object 15 cm par hai — yani
F aur 2F ke beech. Table kehti hai: image 2F se pare, bada, real, inverted. v = 30
sach mein 20 se pare hai. Sahi!
Usi convex lens (f = 10 cm) ke saamne 2 cm ka object sirf
5 cm door rakha hai. Ab kya hoga?
Step 1: f = +10 cm, u = −5 cm, h = +2 cm
Step 2:
1/v = 1/10 + 1/(−5) = 1/10 − 1/5 = (1 − 2)/10 = −1/10
v = −10 cm
Step 3:
m = v/u = (−10)/(−5) = +2
h′ = 2 × 2 = +4 cm
Jawab: Image lens ki usi taraf 10 cm par,
virtual, erect, 2 guna bada.
🔍 Yahi magnifying glass hai! Object F (10 cm) se paas hai, isliye image virtual,
seedha aur bada bana. Isiliye padhte waqt lens ko akshar ke bahut paas rakhte
hain.
✅ Jaanch: v negative aaya → lens mein negative v ka matlab
virtual. Aur m positive → erect. Dono milte hain.
Ek concave lens ki focal length 20 cm hai. 5 cm ka object uske
30 cm saamne hai. Image nikaalo.
Step 1: f = −20 cm (concave — negative!), u = −30 cm,
h = +5 cm
Step 2:
1/v = 1/f + 1/u = 1/(−20) + 1/(−30)
1/v = −1/20 − 1/30 = (−3 − 2)/60 = −5/60 = −1/12
v = −12 cm
Step 3:
m = v/u = (−12)/(−30) = +0.4
h′ = 0.4 × 5 = +2 cm
Jawab: Image 12 cm par usi taraf, virtual,
erect, chhota (0.4 guna), oonchai 2 cm.
✅ Jaanch: concave lens ka jawab hamesha virtual + erect +
diminished hota hai. Aur dhyaan do: |v| = 12 < |f| = 20 — image hamesha O aur F ke beech hi
banta hai. Dono sahi.
(a) Ek convex lens ki focal length 25 cm hai. Uska power kya
hai?
Hal: Pehle cm ko metre mein badlo (ye sabse aam galti hai!)
f = 25 cm = +0.25 m
P = 1/f = 1/0.25 = +4 D
(b) Ek concave lens ki focal length 50 cm hai. Power?
f = −50 cm = −0.50 m
P = 1/(−0.5) = −2 D
(c) Kisi chashme par +2.5 D likha hai. Focal length?
f = 1/P = 1/2.5 = 0.4 m = 40 cm, aur positive matlab
convex lens → yani us vyakti ko hypermetropia hai.
Ek +5.0 D ka convex lens aur ek −3.0 D ka concave lens
saath sata kar (in contact) rakhe hain. Combination (sanyojan) ka power aur focal length kya
hoga?
Niyam: Saath sate hue lens ke power seedhe jud jaate hain:
P = P₁ + P₂
Hal: P = 5.0 + (−3.0) = +2.0 D
f = 1/P = 1/2 = 0.5 m = 50 cm
Jawab: Combination ek +2 D ka convex lens jaisa kaam karega,
jiski focal length 50 cm hai.
💡 Yahi power ki khoobsurati hai: focal length ko jodna mushkil hai (1/f jodna
padta), par power ko seedha jod sakte hain. Isiliye chashme aur camera ke lens
dioptre mein maape jaate hain, cm mein nahi.
✍️ Khud Karo — Practice
Convex lens, f = 15 cm. 4 cm ka object 25 cm door hai. v, m, h′
nikaalo.
Jawab: f = +15, u = −25
1/v = 1/15 − 1/25 = (5 − 3)/75 = 2/75 → v = +37.5 cm
m = 37.5/(−25) = −1.5 • h′ = −1.5 × 4 = −6 cm
Real, inverted, 1.5 guna bada. (Object F aur 2F ke beech tha — sahi baitha!)
Concave lens, f = 10 cm. 6 cm ka object 20 cm door hai.
Jawab: f = −10, u = −20
1/v = −1/10 − 1/20 = (−2 − 1)/20 = −3/20 → v = −6.67 cm
m = (−6.67)/(−20) = +0.33 • h′ = 0.33 × 6 = +2 cm
Virtual, erect, chhota.
Do lens, +2.0 D aur +3.0 D, saath sata kar rakhe hain. Kul power
aur focal length?
Jawab: P = 2 + 3 = +5.0 D
f = 1/5 = 0.2 m = 20 cm (convex)
⚠️ Lens numericals ki 5 aam galtiyan:
1️⃣ Mirror wala formula laga dena — lens mein minus hai (1/v − 1/u)
2️⃣ m mein minus laga dena — lens mein m = +v/u
3️⃣ Convex lens ka f negative likh dena — convex lens = positive
(mirror se ulta!)
4️⃣ Power mein cm hi rehne dena — pehle metre mein badlo
5️⃣ v ka chinh galat padhna — lens mein positive v = real
(mirror se ulta!)
Bharat duniya ka sabse bada chashme ke lens banane wala kendra ban raha hai. Par
isse bhi zaroori kahani hai "Jaipur Foot" wale model ki soch — sasti technology se
aam aadmi tak pahunch.
Aaj bharat mein Aravind Eye Hospital (Madurai) ka model duniya bhar mein padhaya
jaata hai: wahan lakhon logon ka motiyabind (cataract) ka operation hota hai
jisme aankh ka dhundhla lens nikaal kar ek artificial convex lens daala jaata hai.
Jinke paas paise hain wo poora paisa dete hain, aur usi se
garibon ka ilaaj muft ho jaata hai.
Wo artificial lens bharat mein hi Aurolab mein banta hai — jo lens videsh mein
hazaron rupaye ka tha, wo yahan kuch sau rupaye mein ban gaya. Nateeja: karodon logon ki nazar wapas
aayi.
Ek chhota sa P = 1/f, aur usse crore zindagiyon mein roshni.
🧠 Apne Aap Ko Test Karo
🧮 Numerical Trainer mein mirror aur lens dono ke sawaal khud hal karo!
Start Practice →