2.5.7 · D1Power of a lens, combination of lenses
Ek lens light rays ko modta hai , aur poora topic ek single number tak reduce ho jaata hai — power — jo batata hai ki yeh kitni zor se modta hai. Jab ek baar aap woh ek number padhna seekh lo, lenses ko stack karna seedhi addition ban jaati hai, scary fraction arithmetic nahi.
Is page par assume kiya gaya hai ki aapne parent note ki notation mein se kuch bhi nahi dekha. Hum har letter, har ratio, har sign ek picture se build karte hain, ek aisi order mein jahan har idea sirf pichle waale par lean karta hai. Jab aap finish karo, Power of a lens, combination of lenses dobara padho aur woh obvious lagni chahiye.
Kisi bhi symbol se pehle, woh scene dekho jisme sab kuch rehta hai.
Definition Principal axisPrincipal axis woh seedhi horizontal line hai jo lens ke exact centre se hoke guzarti hai, uske perpendicular. Yeh hamari "ground line" hai — har distance aur height isi se measure hoti hai.
Picture: upar lens ke beech mein se left-to-right jaati dashed gray line.Isko kyun chahiye: bina ek reference line ke hum yeh nahi keh sakte ki ek ray "kitni uchi" hai ya ek point "kitni door" hai. Yeh hamare poore coordinate world ka origin hai.
Ek ray ek patli seedhi arrow hai jo light ke travel karne ka path dikhati hai. Light left se aati hai, lens se takrati hai, aur jaise hi pass hoti hai bend ho jaati hai (direction change karti hai).
Picture: left se enter karti blue arrow, axis ki taraf bend hoti orange arrow.Isko kyun chahiye: "rays ko modnaa" literally ek lens ka kaam hai, isliye ray woh cheez hai jise hum track karte hain.
h h principal axis ke kitna upar takraati hai, seedha upar measure kiya gaya.
Picture: neeche diye figure mein green vertical segment, axis se le kar jahan ray lens se milti hai wahan tak.Isko kyun chahiye: ek lens ray ko zyada modta hai jitni door woh hit karti hai. Toh bending h
Definition Focus aur focal lengthf axis ke parallel bhejon. Lens ke usse modne ke baad, woh axis ko ek special point par cross karti hai jise focus F focal length f
Picture: upar waale figure mein, orange bent ray red dot F f Isko kyun chahiye: f Chota f lamba f
f f f f power ban jaata hai.
δ δ delta ) woh angle hai jitna lens ray ko turn karta hai — incoming direction aur outgoing direction ke beech ka angle.
Picture: neeche waale figure mein, flat blue "seedha jaata" line aur orange "actually-bent" line ke beech shaded wedge.Isko kyun chahiye: "lens kitni zor se modta hai" exactly yahi angle hai. Yeh woh physical quantity hai jise power measure karegi.
Parent note likhta hai tan δ ≈ δ = h / f
Figure s03 dekho. Bent ray, axis, aur vertical height h right triangle banate hain:
opposite side (angle δ h adjacent side (δ f right angle wahan baithta hai jahan h
tan tan ( angle ) = adjacent side opposite side
Picture: s03 mein, tan δ = f h YEH tool kyun, koi aur kyun nahi? Hum ek angle (δ lengths (h f tan opposite over adjacent se bana hai — aur wahi do sides hain jo haara triangle hamare haath deta hai. Sine ya cosine ko slanted hypotenuse chahiye hoga, jis ki hume parwah nahi.
Recall Small-angle ka matlabtan δ ≈ δ tan
Parent mein lensmaker's relation R 1 R 2 actually .
R radius of curvature R Flatter surface ⇒ bada R zyada sharply curved ⇒ chota R
Picture: imagine karo ki lens face ke peeche ek balloon phula rahe ho; R R 1 pehli surface ke liye hai jise light milti hai, R 2 doosri ke liye. Subscripts 1 , 2 Isko kyun chahiye: parent ka formula P = ( n − 1 ) ( R 1 1 − R 2 1 ) power banata hai. Teekhay curves (R R 1
n n glass light ko air ke comparison mein kitna slow aur bend karta hai . Ordinary glass ka n ≈ 1.5
( n − 1 ) air ke identical hota (n = 1 ( n − 1 ) zaroor multiply hona chahiye.
Ab upar sab kuch ek number mein collapse ho jaata hai.
P Power unit height per bending strength hai, aur yeh focal length ke reciprocal ke barabar hai:
P = f 1 ( f metres mein )
Section 4 se: unit height per bending = h δ = f 1 hi P Reciprocal kyun? Chota f bada P f Unit: dioptre (D 1 D = 1 m − 1 f metres mein hona chahiye — unit defined hai per metre.
f f = 20 cm P = 1/20 nahi hai. Pehle convert karo: 20 cm = 0.2 m P = 1/0.2 = 5 D
Behaviour ka har quadrant cover hona chahiye — yahan "cases" do lens shapes aur unke signs hain.
Definition Lenses ke liye sign convention
Lens
Shape
Parallel rays ke saath kya karta hai
f P
Convex (converging) fat middle
unhe saath ek real focus par kheenchta hai
f > 0 P > 0
Concave (diverging) thin middle
unhe alag failata hai (woh ek focus se peeche se aate lagte hain)
f < 0 P < 0
Picture: convex = ")(" ulta, arrow-heads milte hue; concave = "()", arrows bahar fan karti huin.Minus kyun matter karta hai: ek negative power ek positive ko cancel kar sakti hai. Jab hum combination ki powers add karte hain, sign woh cheez hai jo ek concave lens ko convex lens ka part undo karne deti hai. Sign drop karo aur physics toot jaati hai.
Parent mein combination derivation u v v 1 F
u v
u object tak distance (woh cheez jo aap dekh rahe ho).v image tak distance (jahan lens light ko ek point par bheajta hai).Yeh thin-lens equation v 1 − u 1 = f 1 Thin Lens Equation mein poori tarah banai gayi hai.
Isko kyun chahiye: "powers add hoti hain" ka proof ek object ko u v 1 lenses ke beech track karta hai, phir final image ko v
v 1 F
v 1 sirf lens 1 dwara banaya gaya image; yeh lens 2 ke liye object ban jaata hai. Subscript 1 Capital F poore stack ki combined focal length (focus point F f P = 1/ F
Principal axis - reference line
tan delta approx delta equals h over f
P equals 1 over f - the core number
Lensmaker P equals n minus 1 times curvature
Convex positive - Concave negative
Combination 1 over F equals sum
Power and Combination of Lenses
Parent note mein jaane se pehle har ek ka jawab do; agar koi atka le, woh section dobara padho.
Principal axis kya hai, aur isko kyun chahiye? Lens ke through centre line; yeh woh reference hai jisse saari heights aur distances measure hoti hain.
h Axis ke upar woh height jahan ek ray lens se takraati hai.
f chota f Lens-to-focus distance; chota f
Deviation angle δ Woh angle jitna lens ek ray ko uski original direction se turn karta hai.
tan Haara triangle opposite side (h f tan
tan δ ≈ δ Chote (paraxial) angles ke liye tangent aur radian angle almost coincide karte hain.
R 1 R 2 Pehli aur doosri lens surfaces ki radii of curvature; chota R
Lensmaker relation mein factor ( n − 1 ) Agar glass air se match karta (n = 1 ( n − 1 )
Power P P = 1/ f f 1 D = 1 m − 1
Convex aur concave lenses ke liye P Convex P > 0 P < 0
Lowercase f F f F
Power of a lens, combination of lenses — woh parent jiske liye yeh page taiyaar karta hai.Thin Lens Equation — jahan u v 1/ v − 1/ u = 1/ f Lensmaker's Equation — yahan built n R 1 R 2 Magnification of Lenses — distances ke baad agla quantity.Defects of Vision — dioptres mein spectacle powers.