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

True — plane mirror mein $R=\infty$ hota hai isliye $f=\infty$; mirror equation se $v=-u$ milta hai, matlab $m=+1$, toh image erect hai, same size hai, aur object jitna saamne hai utna hi peeche hai.

False — sirf tab jab object $F$ se aage ho. Agar object focus ke andar ho ($|u|<|f|$) toh concave mirror virtual, erect, magnified image deta hai (shaving-mirror mode).

False — $f>0$ aur kisi bhi real object $u<0$ ke saath, equation hamesha $v>0$ force karti hai, isliye image invariably virtual, erect, aur diminished hoti hai.

False — sign geometry se aata hai, behaviour se nahi. Focus mirror ke saamne hota hai (left mein, incident light ke against), isliye concave ke liye $f<0$ hota hai chahe woh kitna bhi strongly converge kare.

True — $m>0$ matlab erect, aur ek single mirror sirf virtual side par erect image bana sakta hai, toh image virtual aur diminished hai (yeh convex-mirror ki pehchaan hai).

False — magnitude $|f|=|R|/2$ match karti hai, lekin concave wala $f<0$ deta hai aur convex wala $f=+|R|/2$; sign alag hota hai, aur wahi sign sari image behaviour control karta hai.

False — plane-mirror magnification hamesha exactly $+1$ hoti hai; image sirf paas aati hai (phir bhi utni hi door peeche), size kabhi nahi badlta.

Limiting sense mein True — jab object $F$ ki taraf jaata hai, $v\to \infty$, toh $|m|\to \infty$; "image" infinity par chali jaati hai aur real se virtual mein flip hone se theek pehle effectively unboundedly badi hoti hai.

Error: unhone sign chhod diya. Saamne ka real object matlab pole-to-object distance incident light ke against measure hoti hai, isliye $u=-30\text{ cm}$; $+30$ use karne se image galat jagah predict hogi aur ek non-existent virtual image dikha sakta hai.

Error: $f=R/2$ ek paraxial approximation hai. Axis se door ki rays thodi mirror ke paas focus hoti hain, jisse spherical aberration hota hai; clean halfway result sirf axis ke paas hold karta hai.

Error: kisi bhi surface point $M$ par normal centre of curvature $C$ ki taraf radius $R=PC$ ke along chalta hai; sirf pole $P$ par woh radius principal axis ke saath coincide karti hai.

Error: $v>0$ matlab image mirror ke peeche hai, toh yeh virtual hai, real nahi. Mirrors ke liye, real images ka $v<0$ hota hai (saamne) — is student ne lenses wali convention swap kar di.

Error: andar signed values rakhni padti hain. Jaise $v=-15,u=-30$ se $m=-(-15)/(-30)=-0.5$ aata hai; bare magnitudes use karne se orientation galat report hogi.

Error: $C$ par image bhi $C$ par hi banti hai $m=-1$ ke saath — same size, inverted, real. Koi magnification nahi hai; object aur image size mein coincide karte hain.

Partly wrong: equation symmetric hai, isliye object aur image positions swap karna geometrically valid hai (light ki reversibility), lekin unki heights $h,h^{\prime }$ aur magnification symmetric nahi hain — $m=-v/u$ swap hone par $-u/v$ ban jaata hai.

Object top (height $h$) se pole $P$ tak ki ray axis ke baare mein equal angles se reflect hoti hai (axis $P$ par normal hai), do similar right triangles bante hain jinke side ratios $|h^{\prime }/h|=|v/u|$ dete hain; sign negative hota hai kyunki image (height $h^{\prime }$) axis ke neeche girta hai.

Yeh hamesha diminished, erect virtual image banata hai, toh ek wide scene ko ek chhote mirror mein squeeze karta hai — large field of view, is cost par ki cheezein unse hain us se zyada door lagti hain.

Yeh signed similar-triangle lengths compare karke derive kiya gaya tha; consistent signs ke bina wahi formula pole ke alag-alag sides par objects aur images ke liye contradictory answers deta.

Concave surface parallel rays ko actually saamne cross karne par mod deti hai, toh $F$ ek real point hai ($f<0$); convex surface unhe spread karta hai toh woh sirf peeche ek point se diverge hoti lagti hain, $F$ ko virtual banate hue ($f>0$).

Isosceles-triangle argument assume karta hai ki strike point $M$, $P$ ke itna paas hai ki $FM\approx FP$; wide rays ke liye woh approximation toot jaati hai, aur exact focus mirror ki taraf creep karta hai — spherical aberration ki wajah.

$f=\infty$ ke saath equation $v=-u$ deta hai, saamne wale object ke liye hamesha positive-behind, toh image hamesha virtual rahegi — reflected rays sirf glass ke peeche ek point se diverge hoti hain jaise, kabhi converge nahi hoti.

Mirror us axis ko flip karta hai jo uske andar jaati hai (front-back), jise hamara brain left-right swap padhta hai; mirror plane mein vertical aur horizontal directions preserve hote hain, toh image erect rehti hai.

Equation deta hai $\frac{1}{v}=\frac{1}{f}-\frac{1}{f}=0$, toh $v\to \infty$ — reflected rays parallel nikalti hain aur image "infinity par" banti hai, yahi wajah hai ki $F$ par bulb rakhne se searchlight beam banti hai.

Jab $u\to 0^{-}$, $\frac{1}{v}\to -\frac{1}{u}\to +\infty$ toh $v\to 0^{-}$ (pole ke theek saamne), aur $m=-v/u\to +1$: mirror ko chhune wala ek tiny object apni image surface par hi dekhta hai, same size aur erect, locally flat mirror ki tarah behave karta hai.

$\frac{1}{v}=\frac{1}{f}-0=\frac{1}{f}$, toh $v=f$; kyunki concave mirror mein $f<0$ hota hai, yeh $v$ negative hai — mirror ke saamne focus par ek real image, tiny aur inverted (isi tarah concave mirror sharp Sun image banata hai).

Kyunki $v=-u$, hume milta hai $m=-v/u=-(-u)/u=+1$ har object distance ke liye — ek formal proof ki plane mirrors kabhi enlarge ya shrink nahi karte.

$v=f>0$, toh image (virtual) focus par mirror ke peeche hoti hai, ek point-sized erect virtual image — sabse chhoti, sabse peeche wali image jo convex mirror bana sakta hai.

$F$ ke theek bahar image real aur saamne hugely badi hai; exactly $F$ par infinity par chali jaati hai; $F$ ke theek andar mirror ke peeche virtual, erect aur magnified reappear hoti hai — $v$ ka sign flip hota hai jab object focus se guzarta hai.