Calculate linear magnification (mirrors)
Scenario
Zoom in feature se aap photo ko `2x` ya `3x` bada kar dete ho.
Physics mein ek mirror kisi object ko kitna bada ya chota karta hai, usko numbers mein kaise napte hain?
Mental model
Magnification (`m`) bata-ta hai ki image, object se kitne guna badi (ya choti) hai.
Agar `m = 2` hai, toh image object se double height ki hai. Agar `m = 0.5` hai, toh image aadhi height ki reh gayi. Iska sign (`+/-`) yeh bata-ta hai ki image seedhi (erect) hai ya ulti (inverted).
Explanation
Magnification (`m`) simply height of image (`h'`) aur height of object (`h`) ka ratio hota hai. Formula mein ise likhte hain: `m = h' / h`.
Ek doosra tareeqa bhi hai magnification nikalne ka, jo image distance (`v`) aur object distance (`u`) se juda hota hai. Mirrors ke liye yeh relation hai: `m = -v / u`. Aap in dono ko jod kar ek super-formula bana sakte ho: `m = h'/h = -v/u`. Numerical solve karte time hum aksar issi ka cross-multiplication karke unknown values nikalte hain.
Magnification ka sign (`+` ya `-`) bohot saari kahani bolta hai. Agar `m` negative (`-`) hai, iska matlab image real and inverted hai (kyunki ulte image ki height negative hoti hai). Agar `m` positive (`+`) hai, toh image virtual and erect hogi.
Value ka number (magnitude) size batata hai. Agar `|m| > 1` (jaise `+3` ya `-2`), image magnified (badi) hai. Agar `|m| < 1` (jaise `+0.5` ya `-0.2`), image diminished (choti) hai. Agar `m = 1` ya `-1`, toh size equal hai.
Worked example
Problem: A concave mirror produces a magnification of `-3`. What does this mean about the image?
- Negative sign ko analyze karein.
- Magnitude (number) ko samjhein.
Answer: The image is real, inverted, and `3` times larger than the object.
Problem: Find the magnification of a mirror if an object placed at `u = -10 cm` forms an image at `v = +5 cm`.
- Distances wala magnification formula use karein.
- Given values ko substitute karein.
- Fraction ko simplify karein.
Answer: `m = +0.5` (Virtual, erect, and diminished)
Key points
- Height Formula: `m = h' / h` (where `h'` is image height, `h` is object height).
- Distance Formula: `m = -v / u` (for mirrors).
- Sign Meaning: `m` is negative for real, inverted images. `m` is positive for virtual, erect images.
Common mistakes
- Missing the minus sign in the formula: Formula `m = -v/u` hai. Students kabhi kabhi minus lagana bhool jate hain aur sirf `v/u` use kar lete hain. `-v/u` mirrors ke liye hai, `+v/u` lenses ke liye.
Recall questions
- What is the formula for magnification of a mirror in terms of object and image distance?
- If magnification m is positive, is the image real or virtual?
- What is the formula for magnification of a mirror in terms of v and u?
Questions & answers
A spherical mirror produces a magnification of -1 on a screen placed at a distance of 50 cm from the mirror. Write the type of mirror.
Concave mirror
Approach: m = -1 means it's a real, inverted image of the same size. Only a concave mirror can form a real image.
A mirror has m = +1.5. Is it a concave or convex mirror?
Concave, because it forms a magnified virtual image.
Approach: Convex mirrors always form diminished images (m < 1), so it must be concave.
Continue learning
Previous: Apply mirror sign convention
Previous: Cross-multiplication in proportions