Mirrors — plane, concave, convex; mirror equation 1 - v + 1 - u = 1 - f: Foundations

2.5.2 · D1 · Physics › Optics › Mirrors — plane, concave, convex; mirror equation 1 - v + 1

Is page pe kuch bhi assume nahi kiya gaya. Aap the parent topic ki ek bhi line padhne se pehle, aapko ideas ka ek chota sa toolkit chahiye. Hum har ek idea ko ek picture se build karte hain, batate hain ki woh kaisa dikhta hai, aur kyun topic uske bina nahi chal sakta. Upar se neeche padhein — har tool uske upar wale tool pe lean karta hai.

1. Light ka ek ray — woh arrow jise hum track karte hain

Picture: ek seedhi line ek arrow ke saath. Bas itna.

Topic ko yeh kyun chahiye: har mirror argument hai "ek arrow andar aata hai, ek arrow baahir jaata hai." Draw karne ke liye ray ke bina, reflect karne ke liye kuch nahi hai.

Figure — Mirrors — plane, concave, convex; mirror equation 1 - v + 1 - u = 1 - f

2. Normal — "seedha baahir" wali line

Picture: ek dashed line jo hit-point par surface ke saath perfect square-corner banaati hai (agli figure mein dashed line dekhein).

Topic ko yeh kyun chahiye: reflection ka law angles ko normal se measure karta hai, mirror se nahi. Aur curved mirror ke liye kisi bhi point par normal seedha sphere ke centre ki taraf aim karta hai — yeh ek fact $f = R /2$ ki derivation ko power karta hai.

3. Angle of incidence aur angle of reflection

Picture: dashed normal se door khulaai do wedges — ek aane wale arrow ke liye, ek jaane wale arrow ke liye.

Topic ko yeh kyun chahiye: yeh poore chapter mein ek matra physical law hai. Baaki sab $i = r$ ke upar stacked geometry hai. Deeper drill ke liye Reflection of Light — Laws & Normal dekhein.

4. Principal axis, pole, centre aur radius of curvature

Curved mirror ek hollow ball (sphere) se kaata hua ek shiny tukda hai. Iske baare mein baat karne ke liye hum kuch landmarks ke naam rakhte hain.

Picture: ek curved arc (mirror), ek taraf ek dot $C$ , ek seedhi horizontal line jo $C$ ko beech-dot $P$ se jorti hai. $C$ se arc tak har "spoke" ek radius hai, aur — importantly — har spoke ek normal hai (woh arc se seedha milta hai).

Topic ko yeh kyun chahiye: yeh names har ray diagram ki vocabulary hain. $f = R /2$ ka proof literally hai "radius (=normal) kheenchein, $i = r$ apply karein, ek isosceles triangle dhundhein."

5. Focus ( $F$ ) aur focal length ( $f$ )

Picture: kai parallel arrows ek concave mirror se takraate hain aur ek bright dot tak squeeze ho jaate hain — woh dot $F$ hai.

Topic ko yeh kyun chahiye: $F$ wahan hai jahan mirror ki "converging power" rehti hai, aur $f$ woh number hai jo mirror equation mein jaata hai. Parent page prove karta hai $f = R /2$ , yaani focus mirror aur ball ke centre ke beech halfway baith ta hai.

6. Similar triangles — geometry engine

Picture: ek chota triangle aur ek bada triangle jiske identical corner angles hain — ek doosre ka scaled-up photocopy.

$\frac{side _{1}^{small}}{side _{1}^{big}} = \frac{side _{2}^{small}}{side _{2}^{big}}$

7. Signed distances — direction ke saath measure karna

Yeh jo symbols create karta hai:

Symbol	Plain meaning	Picture	Real object ke liye sign
$u$	object distance ( $P$ →object)	mirror ke left arrow	$u < 0$
$v$	image distance ( $P$ →image)	image ki taraf arrow	$-$ agar front, $+$ agar behind
$f$	focal length ( $P$ → $F$ )	$P$ se focus dot	concave $-$ , convex $+$
$R$	radius ( $P$ → $C$ )	$P$ se ball-centre	concave $-$ , convex $+$
$h$	object height	upright arrow	$+$ (upar)
$h^{'}$	image height	image arrow	$-$ agar inverted

Topic ko yeh kyun chahiye: mirror equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ aur magnification $m = - \frac{v}{u}$ sirf signed numbers ke saath sahi hain. Raw magnitudes daalo aur aap aisi images predict karoge jo exist hi nahi karti.

Ek seedha arrow jo light ke travel karne ka path aur direction dikhata hai.

Normal kahan draw kiya jaata hai, aur woh surface se kya angle banata hai?

Hit-point par, surface ke perpendicular (

9 0^{\circ}

Law of reflection state karein.

Angle of incidence angle of reflection ke equal hota hai (

i = r

), dono normal se measure kiye jaate hain.

Spherical mirror par koi bhi point par hamesha normal kaun si line hoti hai?

Radius — us point se centre of curvature

C

tak wapas jaane wali line.

Pole, centre of curvature, aur radius ko ek ek sentence mein naam bataayein.

Pole

P

= surface ka beech; centre

C

= sphere ka centre; radius

R = P C

Focus

F

kya define karta hai?

Woh point jahan principal axis ke parallel rays reflect hone ke baad milti hain (ya se aati lagti hain).

Do triangles "similar" kab hote hain, aur isse kya milta hai?

Jab unke angles match karein; tab matching sides ek common ratio share karti hain.

Sign convention ke under, real object ki distance

u

ka sign kya hoga?

Negative (

u < 0

), kyunki woh incident light ke against hai.

Magnification do tarike se likhein.

m = \frac{h ^{'}}{h} = - \frac{v}{u}

Mirror equation mein

v, u, f

ki jagah

\frac{1}{v}, \frac{1}{u}, \frac{1}{f}

kyun use hota hai?

Derived relation

uv = v f + u f

uv f

se divide karne par reciprocals tidy result ke roop mein milte hain.

Foundations — Mirrors — plane, concave, convex; mirror equation 1 - v + 1 - u = 1 - f

1. Light ka ek ray — woh arrow jise hum track karte hain

2. Normal — "seedha baahir" wali line

3. Angle of incidence aur angle of reflection

4. Principal axis, pole, centre aur radius of curvature

5. Focus ( $F$ ) aur focal length ( $f$ )

6. Similar triangles — geometry engine

7. Signed distances — direction ke saath measure karna

8. Magnification ( $m$ ) — size/orientation report

9. Reciprocals — isliye equation mein $v$ nahi, $\frac{1}{v}$ hai

Prerequisite map

Equipment checklist