Calculate power of a lens
Scenario
Aap eye doctor ke paas gaye aur usne prescription par likha: `+2.0 D`.
Chashme ka yeh `+2.0` number kya darshata (indicate) hai?
Mental model
Lens ki taqat (Power) uski focal length ki ulti (reciprocal) hoti hai.
Jo lens light ko jitna jaldi (paas mein) bend karega, uski focal length utni choti hogi aur uski Power utni hi zyada hogi. Formula hai: `P = 1/f` (`f` hamesha meters mein hona chahiye).
Explanation
Kissi bhi lens ki asli kshamta (ability) yeh hai ki wo light ko kitna jyada bend, yaani converge ya diverge kar sakta hai. Is degree of convergence/divergence ko hum 'Power of a Lens' (`P`) kehte hain.
Jitni kam focal length (`f`) hogi, light utni hi jaldi bend hogi, aur isliye Power zyada hogi. Mathematically, Power is defined as the reciprocal of focal length. Iska formula hai: `P = 1 / f`. Yahan par ek strict rule hai: focal length (`f`) humesha meters (`m`) mein honi chahiye. Agar `f` centimeters mein di hai, toh usko pehle `100` se divide karke meter mein convert karna padega, ya phir directly formula `P = 100 / f` (in cm) use kar sakte hain.
Power ki SI unit `Dioptre` hoti hai, jise `D` se darshaya jata hai. `1 Dioptre` us lens ki power hai jiski focal length exactly `1 meter` hai.
Signs yahan bhi apply hote hain. Convex lens ki focal length positive hoti hai, toh uski power bhi positive (`+D`) hoti hai. Concave lens ki focal length negative hoti hai, isliye uski power negative (`-D`) hoti hai. Jab doctor `+2.0 D` likhta hai, uska seedha matlab hai Convex lens.
Worked example
Problem: Find the power of a concave lens of focal length `2 m`.
- Focal length pehle se meters mein hai. Concave ka matlab negative `f` hai.
- Power ka formula lagayein.
- Value daal kar answer nikaalein.
Answer: P = -0.5 D
Problem: A doctor prescribes a corrective lens of power `+1.5 D`. Find the focal length of the lens and identify its type.
- Formula `P = 1/f` ka istemal karein.
- Equation ko rearrange karke `f` nikaalein.
- Value ko meters mein calculate karein.
- Positive power ka matlab hai ki yeh convex lens hai.
Answer: f = +0.667 m, Convex lens
Key points
- Power Formula: `P = 1 / f` (where `f` is in meters). If `f` is in cm, use `P = 100 / f`.
- SI Unit: `Dioptre` (`D`).
- Sign Relation: Power of a convex lens is positive (`+`). Power of a concave lens is negative (`-`).
Common mistakes
- Forgetting to convert cm to meters: Sabse badi mistake! Agar question mein `f = 20 cm` diya hai, aur bachha `P = 1/20 = 0.05 D` likh de, toh galat hai. `P = 100/20 = +5 D` sahi answer hai.
Recall questions
- What is the SI unit of power of a lens?
- Does a concave lens have positive or negative power?
- What is the SI unit of power of a lens?
Questions & answers
A lens has a power of -2.5 D. What is the focal length and nature of the lens?
Focal length = -40 cm, Nature = Concave lens.
Approach: P = -2.5. f = 1/P = 1/-2.5 = -0.4 m = -40 cm. Minus sign means concave.
Find the power of a concave lens of focal length 2 m.
P = -0.5 D
Approach: Concave lens has negative f, so f = -2 m. P = 1 / -2 = -0.5 D.
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