Apply lens sign convention
Scenario
Aapne mirror wale saare sign conventions yaad kar liye the. Ab achanak lens aa gaya.
Kya lens ke formulas aur signs mirror se bilkul alag hain?
Mental model
Mirror wala hi graph paper, bas 'v' ka logic palat gaya.
Origin abhi bhi center (Optical Centre) hai. Object left mein (u negative), aur Convex ka Focus (f positive). Lekin kyunki lens mein light paar (right) jati hai, Real image ab right side (+v) banti hai, jabki mirror mein wo left (-v) banti thi.
Explanation
Lens ke sign convention (New Cartesian Convention) lagbhag mirror jaise hi hain. Sabse bada farq sirf Origin point ka hai; yahan origin Pole (P) ki jagah Optical Centre (O) hota hai.
Object ko humesha lens ke left mein rakhte hain, isliye Object distance (u) hamesha negative (-ve) hi rahegi.
Focal length (f) ke rule mein bhi koi badlaav nahi. Convex lens hamesha right side wale focus ko use karta hai (main focus), isliye iski f positive (+ve) hoti hai. Concave lens light ko aise failata hai ki wo left focus se aati lagti hai, isliye iski f negative (-ve) hoti hai.
Sabse bada twist Image distance (v) mein aata hai. Mirrors ke case mein, Real image ussi taraf (left) banti thi, isliye 'v' negative hota tha. Lekin Lenses mein, light material ke aar-paar nikal jati hai. Isliye, lens mein Real images right side par banti hain, jiska matlab unki distance (v) positive (+ve) hoti hai. Aur agar image lens ke samne hi reh jaye (left side), toh wo Virtual hoti hai, yani virtual image ke liye 'v' negative hoga.
Worked example
Problem: A convex lens forms a real image 30 cm from the lens. What is the sign of the image distance (v)?
- Image ka nature pehchanein.
- Lenses mein real images doosri taraf (right side) banti hain.
Answer: v = +30 cm
Problem: A concave lens has a focal length of 15 cm. Write its value with the correct sign.
- Concave lenses light ko diverge karte hain, jo left focus se aati hui lagti hai.
Answer: f = -15 cm
Key points
- Object Distance (u): Always negative (u = -).
- Focal Length (f): Convex = positive (+ve). Concave = negative (-ve).
- Image Distance (v) twist: In lenses, Real images are on the right (v is +ve). Virtual images are on the left (v is -ve).
Common mistakes
- Using mirror logic for 'v' directly: Bache ratte marte hain ki 'Real image = -v'. Yeh sirf mirrors ke liye sach hai! Lens mein light paar hoti hai, toh Real image = +v.
Recall questions
- What is the sign of the focal length for a convex lens?
- If a lens forms a virtual image, what is the sign of image distance (v)?
- What is the sign of the object distance u for any lens?
Questions & answers
An object is placed 10 cm from a converging lens. State the signs for u and f.
u is negative (-10 cm), f is positive.
Approach: Object is always on left (-). Converging lens is convex (+).
A concave lens has a focal length of 15 cm. What sign should be used for f in calculations?
Negative (f = -15 cm).
Approach: Concave lenses always have a negative focal length.
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