Sign convention for coordinates
Scenario
Aap ek map par apne ghar se 5km chalte ho. Par kis direction mein? Right (East) ya Left (West)?
Physics mein direction ko math ke numbers mein kaise badalte hain?
Mental model
Graph paper ka + aur - wala khel.
Origin (0,0) ke right mein sab positive, left mein negative. Upar positive, neeche negative. Yeh same graph paper logic physics mein distances ko measure karne mein use hota hai.
Explanation
Light chapter mein mirrors aur lenses ke formulas use karne ke liye, humein har distance ko ek proper sign (+ ya -) dena padta hai. Iske liye Cartesian Coordinate System ka use kiya jata hai. Is system mein ek origin (pole ya optical centre) hota hai, jahan se saare measurements liye jate hain.
X-axis (horizontal line) par, origin ke right side wale distances ko positive (+ve) maana jata hai. Origin ke left side wale distances negative (-ve) hote hain. Light hamesha left se aati hui maani jati hai, isliye object usually left mein hota hai aur uski distance negative hoti hai.
Y-axis (vertical line) par, origin se upar ki taraf (principal axis ke upar) ki height ko positive (+ve) liya jata hai. Jo image inverted (ulti) banti hai, woh axis ke neeche hoti hai, isliye uski height negative (-ve) mani jati hai.
Yeh signs itne zaroori hain ki agar aap formula mein ek negative sign miss kar doge, toh pura answer galat aayega, chahe aapka math kitna bhi strong ho. Signs sirf direction ya orientation batate hain.
Worked example
Problem: An object is placed 15 cm to the left of the origin. Its image forms 10 cm to the right of the origin. Find their coordinate positions.
- Object is on the left, so its coordinate is negative.
- Image is on the right, so its coordinate is positive.
Answer: Object at x = -15 cm, Image at x = +10 cm
Problem: A tree of height 5 m stands above the ground, and its reflection forms 5 m below the ground level. Write their vertical coordinates.
- Tree is standing upright (above axis), so height is positive.
- Reflection is pointing downwards (below axis), so height is negative.
Answer: y_tree = +5 m, y_reflection = -5 m
Key points
- Origin: All distances are measured from the Origin (0,0).
- X-axis Convention: Right is positive (+). Left is negative (-).
- Y-axis Convention: Upward is positive (+). Downward is negative (-).
Common mistakes
- Measuring without considering origin: Students direct value put kar dete hain bina left-right soche. Always check if the point is on the left (-) or right (+) of the origin.
Recall questions
- Distances measured below the origin on the Y-axis are considered positive or negative?
- Distances on the left of the origin are assigned which sign?
- What is the sign of distance measured to the right of the origin?
Questions & answers
If an ant is 4 units left of the y-axis and 3 units below the x-axis, what are its coordinates?
(-4, -3)
Approach: Left means negative x, below means negative y.
If an object is placed 20 cm in front of a mirror, what is its object distance according to sign convention?
-20 cm
Approach: The object is always placed to the left of the mirror, so it is negative.
Continue learning
Next: Apply mirror sign convention