Apply mirror sign convention
Scenario
Agar aap mirror formula mein direct values daal do bina + aur - soche, toh answer 10 ki jagah -1.5 aa jayega.
Values ko formula mein daalne se pehle unka sign (+ ya -) kaise decide karein?
Mental model
Mirror ka pole (P) hi origin (0,0) hai.
Cartesian rules lagao: Mirror par P ko origin mano. Object left mein = u hamesha negative. Focus left mein (concave) = f negative. Focus right mein (convex) = f positive.
Explanation
Mirror problems ko solve karne ki first step hai question mein diye gaye distances ko signs (+ ya -) ke sath likhna. Isko hum 'New Cartesian Sign Convention' bolte hain.
Kuch golden rules hamesha fix rehte hain. Pehla rule: Object ko hamesha mirror ke left side rakha jata hai. Iska matlab object distance (u) **hamesha negative (-ve)** hogi, chahe koi bhi mirror ho.
Doosra rule focal length (f) ke baare mein hai. Concave mirror apni converging power se light ko aage (left) hi focus karta hai, isliye iska focus left mein hota hai, yani **f of concave is negative (-)**. Convex mirror ka focus mirror ke peeche (right) hota hai, isliye **f of convex is positive (+)**.
Image distance (v) depend karti hai ki image kahan ban rahi hai. Agar image real hai, toh wo front (left) mein banegi aur (v) negative hoga. Agar image virtual hai, toh wo behind the mirror (right) mein banegi, aur (v) positive hoga.
Upar aur neeche ki heights (h) bhi important hain. Object hamesha seedha (erect) khada hota hai, toh object height (h) is always positive. Agar image real/inverted (ulti) hai, toh uski height (h') negative hogi. Agar virtual/erect hai, toh height (h') positive hogi.
Worked example
Problem: An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Write the given values with proper signs.
- Object hamesha saamne (left side) rakha jaata hai.
- Yeh concave mirror hai, isliye focus left side par hota hai.
Answer: u = -20 cm, f = -15 cm
Problem: A convex mirror forms an image 5 cm behind the mirror for an object placed 10 cm in front of it. Write u and v with signs.
- Object hamesha mirror ke saamne hota hai.
- Image mirror ke peeche (right side) banti hai.
Answer: u = -10 cm, v = +5 cm
Key points
- Object Distance (u): Always negative (u = -).
- Focal Length (f): Concave = negative (-ve). Convex = positive (+ve).
- Image Distance (v): Real image = negative (left). Virtual image = positive (right).
Common mistakes
- Taking focal length of concave as positive: Remember, concave starts with 'C' like 'Cave', you go deep inside the negative axis. Concave 'f' is always negative.
Recall questions
- What is the sign of the object distance (u) for any spherical mirror?
- What is the sign of the focal length for a convex mirror?
- Where is the origin placed in the Cartesian sign convention for mirrors?
Questions & answers
State the sign convention for the height of a real and inverted image formed by a concave mirror.
Negative
Approach: Inverted images form below the principal axis (y-axis is negative).
For a convex mirror, is the focal length taken as positive or negative?
Positive, because the principal focus is behind the mirror.
Approach: Focus is on the right side of the pole, so it is positive.
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