Draw ray diagrams for convex lenses
Scenario
Camera lens ek pahad (mountain) ko choti si film par fit kar deta hai, par wahi lens cinema hall mein choti reel se badi screen par movie dikhata hai.
Ek hi lens kabhi image choti aur kabhi badi kaise bana deta hai?
Mental model
Convex lens = Concave mirror ka refraction wala bhai.
Jo rules aur cases concave mirror mein light ko bounce karke (reflection) hote the, wahi saare same cases convex lens mein light ko paar kara ke (refraction) hote hain. Paas laoge toh image badi aur door bhagegi.
Explanation
Convex lens ke ray diagrams banana bahut similar hai concave mirror ke. Bas farq yeh hai ki light yahan reflect nahi hoti, balki doosri side paar (refract) nikal jati hai. Isliye lens ke dono taraf Focus (F1, F2) aur Centre of curvature (2F1, 2F2) mark kiye jate hain.
Ray trace karne ke teen main rules hain: 1) Principal axis ke parallel aane wali ray doosri side Focus (F2) se guzarti hai. 2) Optical centre (O) se guzarne wali ray bina mude seedhi nikal jati hai. 3) Focus (F1) se aane wali ray doosri side parallel ho jati hai.
Jaise-jaise aap object ko left side se lens ke paas laate ho (beyond 2F1 se between F1 and O tak), doosri taraf (right side) banne wali real image right ki taraf bhagti hai aur size mein badhti jati hai.
Jab object 2F1 par hota hai, toh image exact 2F2 par banti hai aur same size ki hoti hai. Jab object F1 par hota hai, toh image infinity par banti hai. Agar object F1 aur O ke beech aa jaye, toh real image nahi ban paati; rays diverge ho jati hain. Inhe peeche extend karne par object wali side par hi ek virtual, erect, aur magnified image banti hai (yahi magnifying glass ka case hai).
Worked example
Problem: Where is the image formed if an object is placed between F1 and 2F1 of a convex lens?
- Object paas aa raha hai (2F1 ke aage).
- Image ko aur door jaana chahiye aur size mein bada hona chahiye.
Answer: Beyond 2F2; real, inverted and enlarged.
Problem: To use a convex lens as a reading glass, where should the book be held?
- Reading glass ek virtual, seedhi aur badi image banata hai.
- Convex lens mein aisa sirf last case mein hota hai (F aur O ke beech).
Answer: Between the optical centre and the principal focus (F1).
Key points
- Real vs Virtual: Forms real, inverted images on the opposite side. Forms virtual, erect, magnified image on the same side if object is between F1 and O.
- Optical Centre (O): A ray passing through O goes undeviated.
- Object at 2F1: Image is formed at 2F2, is real, inverted, and of the same size.
Common mistakes
- Confusing F and 2F with C: Lenses mein Centre of Curvature ko C ki jagah 2F (twice the focal length) likhte hain. Dono kaam same karte hain, bas naam alag hai.
Recall questions
- Where does a ray parallel to the principal axis go after refracting through a convex lens?
- What happens to a ray passing through the optical centre of a lens?
- What type of image is formed when an object is at 2F1 of a convex lens?
Questions & answers
A student obtained a sharp image of a candle flame on a screen using a convex lens. If the object is at 2F1, state the characteristics of the image.
Real, inverted, formed at 2F2, and of the same size as the object.
Approach: When object is at 2F (similar to C in mirrors), image is at 2F on the other side, same size.
Where is the image formed when an object is placed between F1 and the optical center of a convex lens?
On the same side as the object (virtual and erect).
Approach: Rays diverge after passing through the lens and appear to meet behind the object.
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