Foundations — Optical instruments — human eye, simple microscope, compound microscope, telescope

2.5.8 · D1 · Physics › Optics › Optical instruments — human eye, simple microscope, compound

Yeh page kuch bhi assume nahi karta. Jab tak tum parent note ke magnifying-power formulas haath mein lo, tumhe har symbol dekh ke seedha padhna aana chahiye. Hum unhe ek-ek karke banate hain, har ek agle ke kaandhon par khada hokar.

1. Height $h$ — kisi cheez ki asli size

Picture: $h$ lambai ka ek seedha khada arrow. Arrow object ke neeche se upar tak jaata hai; uski lambai hi $h$ hai.

Topic ko yeh kyun chahiye: hum discover karenge ki yeh asli size woh nahi jo decide karti hai ki cheez kitni badi dikhti hai. Ise $h$ naam dene se hum us hairaan karne wale fact ko prove kar sakte hain, bas assert nahi karte.

2. Distance $u$ (aur $v$, $D$) — woh kitni door hai

Picture: line of sight ke saath ek horizontal ruler rakha hai. Object ek tick par baitha hai, aankh/lens doosre par; unke beech ka gap $u$ hai. Formulas in gaps ki parwah karte hain, na ki is baat ki ki tumne ruler ki "zero" kahaan likhi.

$u$ aur $v$ ke sign conventions (kyun kuch negative hote hain) Lens equation and sign conventions mein banaye gaye hain — abhi ke liye inhe bas distances ki tarah padho.

3. Angle $\theta$ — woh kitna dikhta hai

Yahi woh symbol hai jis par poora subject khada hai.

Picture: $h$ height ka object arrow $u$ door baitha hai. Do rays tumhari aankh se uski tip aur base tak jaati hain, ek wedge banati hain. Us wedge ka opening $\theta$ hai.

4. Tool $\tan$ kyun hai, aur hum ise drop kyun kar sakte hain

Wedge ki picture ko ek number mein badalne ke liye humein ek aisa rule chahiye jo angle $\theta$ ko sides $h$ aur $u$ se jode. Woh rule tangent hai.

Yeh tool kyun, koi aur kyun nahi? Humein object ke base par ek right angle mila hai, humare angle ke opposite $h$ height hai, aur uske saath $u$ distance hai. Teen trig ratios mein se sirf $\tan$ hi exactly opposite over adjacent use karta hai — woh do quantities jo hamare paas actually hain. Sine ko slant hypotenuse chahiye hoga (hum use kabhi measure nahi karte); cosine height ko ignore kar deta. Isliye $\tan$ woh ek ratio hai jo $h$ aur $u$ mein baat karta hai.

Picture / yeh kyun legal hai: ek patli wedge ke liye seedha object-arrow aur woh curved arc jo woh sweep karta us mein almost koi farq nahi. Isliye angle (arc-based) aur uska tangent (straight-side-based) agree karte hain. Isliye parent bina kisi apology ke ${\theta }_0\approx \tan {\theta }_0=h/D$ likhta hai.

5. Magnifying power $M$ — woh score jo hum rakhte hain

Ab hum state kar sakte hain ki har instrument ko kis par grade kiya jaata hai.

Angles ka ratio kyun, heights ka kyun nahi? Kyunki retina sirf wedge padhta hai. Do objects jinka $\theta$ equal hai woh equal-sized images banate hain chahe unki asli heights $h$ wildly alag ho. Isliye "bigger" ka honest measure angle ratio hai. Isliye parent har jagah angular magnification par insist karta hai — Linear vs angular magnification mein deeper explanation hai.

6. Focal length $f$ aur power $P$ — lens ki strength

Picture: flat parallel rays lens mein enter karti hain aur ek single dot mein squeeze hoti hain; lens-to-dot ka gap $f$ hai.

Topic ko $f$ kyun chahiye: har instrument formula ($D/f$, $f_o/f_e$, $L/f_o$) actually ek statement hai ki har lens kitni strongly light bend karta hai. $f$ naam dene se hum lenses ko ek number se compare kar sakte hain.

7. Subscripts — objective vs eyepiece

Do lenses wale instruments mein yeh batana padta hai ki kaun sa lens.

Picture: ek tube. Object baayein, objective lens, ek gap $L$, eyepiece lens, tumhari aankh daayein. Light object → objective → eyepiece → eye flow karti hai, isliye subscripts bas left to right padhte hain.

Topic ko inki kyun zaroorat hai: microscope aur telescope dono do lenses chain karte hain. Labels ke bina hum yeh nahi likh sakte ki "objective ek picture banata hai, eyepiece us picture ko magnify karta hai" — poori two-stage story in subscripts mein rehti hai.

8. Lens equation — woh machine jo images place karti hai

Yeh kyun aata hai: instrument ke saath visual angle jaanne ke liye, humein pata hona chahiye ki lens image kahaan pheinkta hai (uska $v$) aur kitna bada (uska magnification). Lens equation woh akela tool hai jo jawaab deta hai "object aur lens diye, image kahaan hai?"

Prerequisite map

Ise is tarah padho: heights, distances aur $\tan$ angle banate hain; angle magnification banata hai; power focal length set karta hai jo lens equation aur image position drive karta hai; subscripts do lenses chain karne dete hain. Saari streams topic mein gir jaati hain.

Equipment checklist

Khud test karo — daayiin side cover karo.

Connections

• Parent topic
• Lens equation and sign conventions
• Linear vs angular magnification
• Power of a lens and dioptres
• Resolving power and diffraction limit
• Defects of vision — myopia, hypermetropia
• Reflecting telescope (Cassegrain) vs refracting