Foundations — Newton's rings — derivation

2.5.13 · D1 · Physics › Optics › Newton's rings — derivation

Yeh page kuch bhi assume nahi karta. Derivation padhne se pehle tumhe symbols aur pictures ki ek choti si dictionary mein fluent hona hoga. Hum unhe ek-ek karke banate hain, har ek pichle pe tikaa hua.

0. Light ray asal mein kya hoti hai (hamaari starting picture)

Figure dekho: kala incoming ray surface pe ek reflected arrow aur ek transmitted arrow mein split ho jaata hai. Yeh kyun important hai? Kyunki Newton's rings do rays se banti hain jo alag ho jaati hain, thodi alag distances travel karti hain, phir dobara mil jaati hain. Unhe track karne ke liye humein "har ek ne kitni door travel kiya" ke liye ek bhasha chahiye.

1. Wavelength $\lambda$ — light ka ruler

Laal curve ek wave hai; laal bracket ek $\lambda$ mark karta hai. Visible light ke liye $\lambda$ bahut chhota hota hai — lagbhag $\lambda =589\text{nm}=589\times 10^{-9}\text{m}$, yaani insaan ke baal ki chaurai ka lagbhag paanch-sauwan hissa.

2. Path difference $\Delta$ aur interference

Figure mein, waves ki upar wali jodi exactly ek poore $\lambda$ se shift hai — crest pe crest, woh reinforce karti hain (laal = bright result). Neeche wali jodi aadhe $\lambda$ se shift hai — crest trough se milti hai, woh kuch nahi mein flat ho jaati hain (dark). Yeh akela picture poore topic ka engine hai. Kyun recombine hoti waves is tarah add hoti hain iski deeper story ke liye Interference — path difference & coherence dekho.

3. Refractive index $\mu$ — kyun kisi material ke andar ki doori extra count hoti hai

4. Reflection pe $\lambda /2$ phase flip (Stokes)

5. Thickness $t$, radius $r$, lens radius $R$ — geometry ke symbols

Figure plano-convex lens (upar se curved, neeche se flat) ko flat plate pe tikaa hua dikhata hai. Teen alag lengths kyun? Kyunki payoff formula ek aisi cheez ko jo tum measure kar sakte ho ($r$, sideways microscope se) ek aisi cheez se jod deta hai jo tum directly dekh nahi sakte ($t$, microscopic gap) lens ki fixed shape ($R$) use karke. Unka relation near-parabola $t\approx r^2/2R$ hai, yehi wajah hai ki rings baahir ki taraf crowd karti hain. Wedge fringes / air wedge se compare karo, jahan gap linearly badhti hai.

Prerequisite map

Isse upar se neeche padho: ruler aur difference optical path ko feed karte hain; flip use correct karta hai; geometry $t$ supply karti hai; saath milke woh ring conditions produce karte hain jo parent derivation radius formulas mein convert karta hai. Yehi machinery Michelson interferometer ko bhi power karti hai.

Equipment checklist

Daayaan side cover karo aur khud ko test karo — tum tab hi ready ho jab har jawaab instant ho.