Calculate linear magnification (lenses)
Scenario
Microscope mein lens lagakar dekhte hain toh bacteria `100` guna bada dikhta hai.
Yeh `100x` zoom ka number exactly kaise calculate hota hai?
Mental model
Mirror magnification jaisa hi hai, bas `v/u` formula ka minus sign gayab ho gaya.
Lens mein bhi `m = h'/h` hota hai. Lekin distance wale formula mein `m = +v/u` hota hai (mirror mein `-v/u` tha). Agar `m` positive hai toh virtual/erect, aur negative hai toh real/inverted.
Explanation
Magnification (`m`) humein bataata hai ki image, object ke mukable kitni badi ya choti bani hai. Ratio form mein, iska formula hamesha `m = h' / h` hota hai (height of image divided by height of object).
Lenses ke case mein, magnification ko object distance (`u`) aur image distance (`v`) se link karne wala formula thoda sa badal jata hai. Mirrors mein hum `m = -v/u` use karte the. Lenses mein light us-paar nikal jati hai, aur formula ban jata hai `m = v/u` (without any negative sign in front).
Aap in dono ko mila kar ek useful equation bana sakte ho: `m = h'/h = v/u`. Numericals solve karte time yeh bahut kaam aata hai.
Sign of `m` ka meaning bilkul mirror jaisa hi rehta hai. Agar `m` negative (`-`) hai, toh samajh lijiye height of image minus mein hai, yani image Inverted aur Real hai. Agar `m` positive (`+`) hai, toh image Erect aur Virtual hai.
Values ko dekhein toh: Agar `m` ki value (minus/plus ignore karke) `1` se zyada hai, toh image badi hai (Magnified). Agar `1` se choti hai (jaise `0.5`), toh image choti (Diminished) bani hai.
Worked example
Problem: An object `5 cm` high is held `25 cm` away from a converging lens. If the image is formed `50 cm` on the other side of the lens, find the magnification.
- `u` aur `v` ke signs pehchanein.
- Lenses ka magnification formula apply karein.
- Values ko formula mein daalein.
Answer: `m = -2`
Problem: A concave lens has magnification of `+0.5`. If the object height is `4 cm`, what is the image height?
- Magnification ka height wala formula use karein.
- Known values ko substitute karein.
- Cross-multiply karke `h'` ki value nikaalein.
Answer: `h' = 2 cm`
Key points
- Height Ratio: `m = h' / h`
- Distance Ratio for Lenses: `m = v / u` (Notice there is NO minus sign here, unlike mirrors).
- Interpreting 'm': Negative `m` = Real & Inverted. Positive `m` = Virtual & Erect.
Common mistakes
- Using -v/u for lenses: Formula confusion is extremely common. Remember: Lens Formula has a minus (`1/v - 1/u`), so its Magnification has a plus (`v/u`). Mirror Formula has a plus (`1/v + 1/u`), so its Magnification has a minus (`-v/u`).
Recall questions
- What is the formula for magnification of a lens in terms of v and u?
- If a lens produces magnification of -3, is the image real or virtual?
- What is the formula for magnification of a lens in terms of v and u?
Questions & answers
Find the magnification of an image formed by a lens if object distance is -20 cm and image distance is -10 cm.
0.5
Approach: m = v/u = -10 / -20 = +0.5.
If a lens produces a magnification of -2, what is the nature of the image?
Real and inverted.
Approach: Negative sign in magnification indicates a real and inverted image.
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