Reflecting surface light ko wapas left ki taraf bhejti hai. Toh ek concave mirror ka focus aur centre of curvature object ke saath wali side (left) par hote hain → incident light ke against → negative.
Concave mirror: f<0, R<0.
Convex mirror: focus mirror ke peeche hota hai (right side) → incident-light direction ke saath → positive: f>0, R>0.
Real image aage (left) banta hai → v<0; virtual image peeche → v>0.
Light through jaati hai, left→right chalti rehti hai. Ek convex (converging) lens ke liye, second focus jahan rays converge hoti hain woh right par hai → light ke saath → positive: f>0. Ek concave (diverging) lens ke liye: f<0.
Convex lens: f>0. Concave lens: f<0.
Real image right par banta hai → v>0; virtual image left par (object ki same side) → v<0.
Paraxial geometry use karke (small angles), magnitudes a=∣u∣,b=∣v∣,F=∣f∣ ke saath ek concave mirror ke liye:
a1+b1=F1
Ab signs lagao: object left ⇒u=−a, real image left ⇒v=−b, concave focus left ⇒f=−F. Substitute karo:
−v1+−u1?
Magnitude relation ko −1 se multiply karo:
−a1−b1=−F1⟹v1+u1=f1
kyunki −a=u,−b=v,−F=f. Toh signed mirror formula hai:
v1+u1=f1Yeh step kyun? Humne har magnitude ko uske signed coordinate se replace kiya taaki yeh ek equation ab kisi bhi configuration ke liye bina dobara draw kiye kaam kare.
New Cartesian convention mein chosen positive direction kya hai?
Incident light ki direction (left → right).
Normal real object ke liye object distance u ka sign?
Negative (u<0), kyunki object incident light ke opposite side par hota hai.
Concave mirror ka focal length sign?
Negative (f<0).
Convex mirror ka focal length sign?
Positive (f>0), focus mirror ke peeche hota hai.
Convex lens ka focal length sign?
Positive (f>0).
Concave lens ka focal length sign?
Negative (f<0).
Mirror equation (signed)?
v1+u1=f1.
Lens equation (signed)?
v1−u1=f1.
Mirror ke liye magnification?
m=−v/u.
Lens ke liye magnification?
m=+v/u.
Negative magnification kya batata hai?
Image inverted hai.
Mirror ke liye v<0 ka physically matlab kya hai?
Real image mirror ke saamne (object ki side par) ban rahi hai.
Lens formula "minus" kyun hai jabki mirror ka "plus" hai?
Light lens se transmit hoti hai (object aur image opposite sides par) vs mirror se reflect hoti hai (same side).
Recall Feynman: explain it to a 12-year-old
Socho tum aur light ek hallway mein chal rahe ho. Jahan light ja rahi hai — seedha aage — hum use "plus" kehte hain. Jahan se woh aayi — tumhare peeche — hum use "minus" kehte hain. Ek toy jo tumne peeche rakhi hai (object) ko minus number milta hai. Ek mirror light ko wapas bounce karta hai, toh mirror ka special "focus" point kabhi mirror ke peeche jaata hai (plus) ya saamne (minus). Ek magnifying glass light ko aage chalte rehne deta hai, toh uska focus aage hai — plus. Hum bas sab cheez par yeh plus/minus tags lagaate hain, aur phir ek chhota sa formula batata hai ki picture kahan appear hogi aur kya woh ulti hai. Tags hi poora trick hain!
