Apply the Mirror Formula
Scenario
Doctor ke paas jo chhota concave mirror hota hai (ENT wala), woh aapke kaan ke andar ka bada, seedha image dikhata hai. Wahi mirror door se ulta aur chhota image banata hai.
Ek hi mirror do alag-alag image kaise banata hai — aur hum bina diagram banaye image ki exact position kaise nikaalein?
Mental model
Mirror formula ek calculator hai: object kitni door hai (`u`) aur mirror kitna 'strong' hai (`f`) daalo, image kahaan banega (`v`) woh nikaal do.
Ray diagram se aap image dekh sakte ho, par exact number nikaalna mushkil hai. Formula `1/v + 1/u = 1/f` teen quantities ko jodta hai — koi bhi do pata ho toh teesri nikaal lo. Bas sign convention pehle sahi lagana hoga, warna answer galat aayega.
Explanation
Mirror formula concave aur convex dono spherical mirrors ke liye chalta hai:
1/v + 1/u = 1/f
Yahaan `u =` object distance, `v =` image distance, aur `f =` focal length — teeno mirror ke pole (`P`) se naapein jaate hain.
Sabse pehla aur sabse important step: SIGN CONVENTION. Cartesian convention mein incident light left se right jaati hai. Pole origin hai. Object hamesha mirror ke saamne rakha jaata hai, isliye object distance `u` ALWAYS negative hota hai. Concave mirror ka focus saamne hota hai, so `f` is negative; convex mirror ka focus peeche, so `f` is positive.
Ab formula rearrange karo:
v = (u f) / (u - f)
Values daalne se pehle unke sign lagao, phir calculate karo. Agar `v` negative aaya, image mirror ke saamne banta hai — matlab REAL image (screen pe pakad sakte ho). Agar `v` positive aaya, image peeche banta hai — VIRTUAL image (sirf mirror mein dikhta hai).
Ek common trap: log magnitude daal dete hain aur sign bhool jaate hain. Tab formula galat answer deta hai. Rule simple hai — pehle har quantity ko uske sign ke saath likho, tabhi substitute karo.
Takeaway: formula ek switch hai jo aapko batata hai image REAL hai ya VIRTUAL — bina graph paper ke. Ray diagram intuition ke liye, formula exact answer ke liye.
Worked example
Problem: An object is placed `30 cm` in front of a concave mirror of focal length `20 cm`. Find the image distance.
- Pehle sign convention lagao — object saamne hai, so `u` negative; concave mirror, so `f` negative.
- Formula ko `v` ke liye rearrange karo.
- Sign ke saath values daalo.
- Solve karo. `v` negative aaya, matlab image saamne — real image.
Answer: `v = -60 cm` — a real, inverted image forms `60 cm` in front of the mirror.
Problem: A dentist holds a small concave mirror (focal length `4 cm`) `2 cm` from a tooth. Where is the image, and is it real or virtual?
- Object mirror ke bahut paas hai (`F` ke andar). Sign lagao.
- Same formula, values daalo.
- `v` positive aaya — image mirror ke PEECHE banega, virtual.
Answer: `v = +4 cm` — a virtual, erect, magnified image behind the mirror (why dentists use it).
Key points
- The formula: `1/v + 1/u = 1/f` → `v = (u f) / (u - f)`.
- Object distance `u`: Always negative (object is in front of the mirror).
- Focal length `f`: Concave: `f` is negative. Convex: `f` is positive.
- Reading `v`: `v` negative → real image (in front). `v` positive → virtual image (behind).
Common mistakes
- Sign convention bhoolna: `u` aur concave `f` ko positive daal dena. Tab `v` ka sign galat aata hai aur real/virtual ulta ho jaata hai. Hamesha pehle sign likho, phir substitute karo.
- `v` ke sign ko ignore karna: Answer sirf `60 cm` likhna galat hai. Sign hi batata hai image real (`v < 0`) hai ya virtual (`v > 0`) — woh answer ka part hai.
Recall questions
- State the mirror formula and what each symbol means.
- For a concave mirror, an object gives `v = +8 cm`. Is the image real or virtual?
- What is the sign of the focal length for a concave mirror, and why?
Questions & answers
An object is placed `10 cm` from a concave mirror of focal length `15 cm`. Find the position and nature of the image.
`v = +30 cm`: virtual, erect, magnified image behind the mirror.
Approach: `u = -10`, `f = -15` → `v = (u f) / (u - f) = 150 / 5 = +30 cm`.
Why do we prefer a convex mirror as a rear-view mirror over a concave one?
A convex mirror always gives a virtual, erect, diminished image with a wider field of view; a concave mirror can give large inverted real images, unsafe for driving.
Approach: Compare image nature from the formula sign of `v` for each.
Continue learning
Previous: Apply mirror sign convention