Foundations — Thin film interference — reflected and transmitted

2.5.12 · D1 · Physics › Optics › Thin film interference — reflected and transmitted

Parent note Thin film interference — reflected and transmitted padhne se pehle, usme aane wala har symbol tumhara hona chahiye. Neeche, har symbol build kiya gaya hai plain words → ek picture → kyun topic ko iski zaroorat hai, ek aisi order mein jahan har cheez pichli par tikti hai.

1. Wave actually kya hoti hai: $\lambda$ (wavelength) aur "in step"

Ek rope imagine karo jo tum upar-neeche hilaate ho. Ek travelling wave crests (oonche points) aur troughs (neeche points) ka ek repeating pattern hota hai jo aage badhta hai.

Figure dekho: horizontal red arrow exactly ek $\lambda$ span karta hai. Green wave dekho: yeh ek identical wave hai jo sideways shift hui hai. Do waves:

• in step (in phase) hoti hain agar unke crests align karein — woh add hokar ek badi wave banaati hain (bright),
• out of step (out of phase) hoti hain agar ek ka crest doosre ke trough par baithe — woh cancel kar deti hain (dark).

Cover karo aur recall karo:

2. Interference aur coherence

Jab do waves overlap karti hain aur unki heights point-by-point add hoti hain, hum result ko interference kehte hain. Yeh Interference of light ka dhadakta dil hai aur tumhe yeh pehli baar Young's double slit mein milta hai.

Ek thin film mein do rays usi ek original wave se aayi hain (woh split hui thi), isliye woh automatically coherent hoti hain — yahi wajah hai ki films stable colours dikhati hain aur sirf grey mein flicker nahi karti.

3. Path difference $\Delta$

Ab key measurable quantity.

Figure mein lower wave ek detour leti hai aur extra length $\Delta$ travel karti hai. Woh rule jo $\Delta$ ko bright/dark se jodata hai wahi poora game hai:

Topic ko $m$ kyun chahiye? Kyunki kaafi saari thicknesses bright deti hain — har whole number wavelengths ke liye ek. $m$ count karta hai ki kaun si wali hai.

4. Refractive index $n$, aur kyun light glass ke andar "zyada mehngi padhti hai"

Ek medium ke andar light slow ho jaati hai, isliye uske crests zyada paas aa jaate hain — wavelength andar shrink ho jaati hai:

${\lambda }_{\text{film}}=\frac{\lambda }{n}$

Figure dekho: same wave, lekin teal medium mein ($n>1$) crests squeeze ho gaye hain — utni hi physical distance mein zyada crests fit ho rahe hain.

Recall:

5. Angles: ${\theta }_i$, ${\theta }_r$, aur Snell's law

Light seedhi nahi padti. Hume directions normal se maapni hoti hain — ek imaginary line jo surface ke perpendicular hoti hai.

Unhe link karne wala rule Snell's law hai:

$\sin {\theta }_i=n\sin {\theta }_r$

Topic ko $\cos {\theta }_r$ kyun chahiye: film thickness $t$ seedhe across (normal ke along) maapi jaati hai, lekin ray slanted travel karti hai. Slanted trip ka normal direction par projection hi count hota hai, aur projecting = $\cos {\theta }_r$ se multiply karna. Yahi exact wajah hai ki extra path $2t\cos {\theta }_r$ hai na ki $2t/\cos {\theta }_r$.

6. Thickness $t$

Ray neeche aur wapas upar jaati hai, isliye woh thickness do baar cross karti hai — yahi wajah hai ki $2nt\cos {\theta }_r$ mein factor 2 aata hai: 2 crossings × index $n$ × depth $t$ × projection $\cos {\theta }_r$.

7. Reflection par phase change: $\lambda /2$ ka "hiccup"

Yeh sabse tricky symbol hai, isliye ise dheere build karo. Dekho Phase change on reflection.

Figure mein top wave (rarer→denser) inverted wapas aati hai; bottom wali (denser→rarer) same taraf upar wapas aati hai.

Recall:

8. Reflected vs transmitted, aur energy conservation

Kuch light wapas bounce hoti hai (reflected), kuch pass through hoti hai (transmitted). Conservation of energy ke hisaab se, jo light reflect nahi hoti woh transmit honi chahiye — isliye dono patterns complementary hain (photographic negatives). Jahan reflection bright hai, transmission dark hai. Yeh fact taiyaar rakho; isliye parent do swapped formula boxes deta hai.

Sab kuch topic ko kaise feed karta hai

Equipment checklist

Har ek padho; tab tak click mat karo jab tak bina hesitation ke jawaab na de sako.