Apply lens formula
Scenario
Aap ek magnifying glass se chiti (ant) ko dekh rahe ho. Agar glass ko chiti se `5 cm` door rakho, toh image kahan aur kitni door banegi?
Lens ke through banne wali image ki exact location mathematical form mein kaise nikalein?
Mental model
Mirror formula ka judwa bhai, bas ek minus sign ka farq.
Lens formula (`1/v - 1/u = 1/f`) object distance, image distance, aur focal length ko connect karta hai. Mirror formula mein beech mein plus (`+`) hota tha, yahan minus (`-`) hai.
Explanation
Lens formula physics mein light ka sabse important mathematical tool hai. Yeh humein batata hai ki agar humein `f` aur `u` pata hain, toh image kahan (`v`) banegi.
Formula hai: `1/v - 1/u = 1/f`
Yahan:
- `v` = image distance
- `u` = object distance
- `f` = focal length
Is formula ko use karte waqt 2 cheezein bahut carefully karni hoti hain. Pehli: har value ko sign convention ke sath daalna (`+` ya `-`). Agar `u = -10 cm` hai, toh formula ban jata hai `1/v - (1/-10) = 1/f`, jo solve hone par `1/v + 1/10` ban jayega. Yeh minus-minus ki galti sabse aam hai.
Doosri baat: Jab aap solve kar rahe hote ho, toh finally aapko `1/v` ki value milti hai (jaise `1/v = 1/15`). Wahi par answer mat chod dena! Aapko fraction ko palatna (reciprocal) hoga, tab jaa kar `v` ki final value aayegi (`v = 15 cm`).
Signs ka dhyan hamesha rakhein. Agar solve karte waqt `v` positive (`+ve`) aata hai, toh samajh lijiye image lens ke right side mein bani hai (Real and inverted). Agar `v` negative aata hai, toh image left side mein bani hai (Virtual and erect).
Worked example
Problem: An object is placed `15 cm` in front of a concave lens of focal length `30 cm`. Find the image position.
- Values ko signs ke saath likhein. Concave lens ka `f` negative hota hai.
- Lens formula likhein.
- Values ko formula mein daalein.
- Signs ko simplify karein.
- `1/15` ko right side mein shift karein.
- LCM (`30`) le kar solve karein.
- Reciprocal nikaalein.
Answer: Image is formed `10 cm` in front of the lens (virtual).
Problem: A convex lens of focal length `10 cm` forms a real image at `20 cm`. Find the object distance.
- Signs pehchanein: convex ka `f` `+` hota hai, aur real image ka `v` `+`.
- Formula apply karein.
- Values substitute karein.
- `1/u` nikalne ke liye equation rearrange karein.
- LCM (`20`) lein.
- `u` ki value nikalein.
Answer: `u = -20 cm`
Key points
- The Formula: `1/v - 1/u = 1/f`
- Don't Forget the Reciprocal: Always invert the final fraction. If `1/v = 2/30`, then `v = 30/2 = 15 cm`.
Common mistakes
- Using mirror formula by mistake: Exam ke pressure mein bache `1/v + 1/u = 1/f` likh dete hain. Lens mein (`-`) lagta hai, yaad rakhne ka tareeka: LENS mein 'Less' jaisa minus hai.
Recall questions
- What is the lens formula?
- If solving gives `1/v = -1/5`, what is the value of `v`?
- What is the lens formula relating object distance, image distance, and focal length?
Questions & answers
A concave lens of focal length `15 cm` forms an image `10 cm` from the lens. How far is the object placed from the lens?
`30 cm` (`-30 cm` in coordinate form)
Approach: `f = -15 cm`, `v = -10 cm` (since concave lens always forms virtual image on the same side). `1/u = 1/v - 1/f`.
A convex lens forms a real image at `40 cm`. If `f = 20 cm`, find the object distance.
`u = -40 cm`
Approach: Use lens formula `1/v - 1/u = 1/f`, put `v = +40` and `f = +20`.
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