Question bank — Geometric optics — rectilinear propagation, reflection, refraction

Light hamesha straight line mein travel karti hai. ::: False — sirf homogeneous medium mein. Jahan speed smoothly vary karti hai (road ke upar garmi, atmosphere), rays curve karti hain, kyunki least-time path ab straight nahi rahi. Dekho Fermat's principle. Angle of incidence, angle of reflection ke barabar hota hai rough (matte) wall ke liye bhi. ::: True — har chhoti facet par — har point phir bhi apni local normal ke against ${\theta }_i={\theta }_r$ follow karta hai. Facets har taraf point karti hain, isliye reflections scatter ho jaati hain (diffuse reflection); law khud kabhi nahi toot-ta. Jab light denser medium mein enter karti hai toh uski frequency kam ho jaati hai. ::: False — frequency source se fix hoti hai aur unchanged rehti hai. Wavelength ${\lambda }_{med}={\lambda }_0/n$ tak shrink hoti hai (${\lambda }_0$ vacuum wavelength ke saath) aur speed $v=c/n$ tak drop hoti hai; frequency wahi rehti hai isliye colour wahi rehta hai. Zyada refractive index ka matlab hai light us medium mein faster move karti hai. ::: False — $n=c/v$, isliye bada $n$ matlab chhota $v$. High index = optically denser = slower light. Total internal reflection tab ho sakta hai jab light air se glass mein jaaye. ::: False — yeh sirf denser se rarer mein jaate waqt hota hai, yaani jab starting index $n_1$, destination index $n_2$ se zyada ho. Air→glass mein $n_1<n_2$ hai: yeh normal ki taraf bend karta hai aur hamesha refract hota hai, isliye us direction mein koi critical angle nahi hai. Dekho Total internal reflection. Refraction ray ko bend karta hai, lekin reflection aur refraction alag physical principles se aate hain. ::: False — dono usi principle se nikalte hain, Fermat's least time. Reflection constant-speed special case hai; refraction changing-speed case hai. Exactly critical angle par light already totally internally reflect ho jaati hai. ::: False — critical angle par refracted ray surface ke saath graze karti hai (${\theta }_2=90°$). Total internal reflection uske baad shuru hota hai, jahan $\sin {\theta }_2$ 1 se zyada ho jaata. Agar tum ek light ray ki direction reverse karo toh woh exactly same path se waapas jaati hai. ::: True — reversibility. Snell's law $n_1\sin {\theta }_1=n_2\sin {\theta }_2$ dono sides mein symmetric hai, isliye source aur receiver swap karne par identical bent path milta hai. Pinhole camera mein bada hole sharp image deta hai. ::: False — bada hole ek candle point se kai straight rays ko screen ke alag-alag points par land karne deta hai, jisse blur hota hai. Rectilinear propagation se sharpness sirf tab milti hai jab hole chhota ho.

"Maine angle of incidence 60° mirror surface se measure kiya, isliye maine law mein 60° use kiya." ::: Error — sabhi optics angles normal se measure hote hain, surface se nahi. Sahi angle of incidence $90°-60°=30°$ hai. Pehle normal draw karo, hamesha. "Light glass mein slow hoti hai, isliye uski energy destroy ho jaati hai aur woh dim ho jaati hai." ::: Error — slowing speed aur wavelength badalta hai, energy conservation nahi. Dimming (agar ho) reflection/absorption losses se aati hai, speed change se nahi. "Snell's law hai $n_1\cos {\theta }_1=n_2\cos {\theta }_2$." ::: Error — yeh sine use karta hai, cosine nahi. Upar ke figure mein, least-time derivative horizontal offset $x/\sqrt{x^2+a^2}$ ($P$ par opposite over hypotenuse) ko $\sin {\theta }_1$ mein turn karta hai, cosine mein kabhi nahi. "Paani mein straw bent dikhta hai kyunki paani use magnify karta hai." ::: Error — yeh magnification nahi, refraction hai. Submerged part ki rays surface par bend karti hain, isliye woh ek shallower position se aati hui lagti hain; yeh break direction mein ek apparent shift hai. "Critical angle ke liye maine $\sin {\theta }_c=n_1/n_2$ use kiya jahan $n_1=1.5$, $n_2=1$." ::: Error — formula $\sin {\theta }_c=n_2/n_1$ hai (destination index over starting index, rarer over denser). Tumhara version $1.5>1$ deta hai, ek impossible sine — yeh clearly sign hai ki ratio ulta hai. "Pinhole mein image upright hoti hai kyunki light straight travel karti hai." ::: Error — straight travel hi exactly uska kaaran hai ki woh inverted hoti hai: top ki rays single hole se cross karke screen ke bottom par jaati hain. Straightness inversion ka kaaran hai, woh ise rokti nahi. "Boundary par light sabse chhoti distance choose karti hai, isliye woh seedhi nikal jaati hai." ::: Error — least time, least distance nahi, jab speeds alag hoti hain. Slow medium mein kam distance spend karna ek straight line se behtar hota hai, isliye ray bend karti hai.

Light denser medium mein enter karte waqt normal ki taraf kyun bend karti hai? ::: Wavefront ka woh side jo slow medium mein pehle enter karta hai peeche reh jaata hai, isliye front boundary ke normal ki taraf pivot karta hai — jaise ek marching row ek taraf se mud mein ghuste hue swing karti hai. Slower medium ⇒ chhota angle. Dekho Wavefronts and Huygens' principle. Least-time principle equal angles ke saath reflection kyun deta hai (math dikhao)? ::: Ek constant speed matlab least time = least path length $L(x)=\sqrt{x^2+a^2}+\sqrt{(d-x{)}^2+b^2}$. $dL/dx=0$ set karne par milta hai $\frac{x}{\sqrt{x^2+a^2}}=\frac{d-x}{\sqrt{(d-x{)}^2+b^2}}$; figure se left side $\sin {\theta }_i$ hai aur right $\sin {\theta }_r$, isliye $\sin {\theta }_i=\sin {\theta }_r$, hence ${\theta }_i={\theta }_r$. White light prism mein colours mein split kyun hoti hai lekin generally refraction mein colour-shift nahi hoti? ::: Colour frequency se tied hai, jo kabhi nahi badlti. Splitting isliye hoti hai kyunki $n$ frequency par thoda depend karta hai (dispersion), isliye har colour alag angle se bend karta hai. Dekho Dispersion. Optical fibre light ko bina leakage ke bends ke around kyun guide kar sakta hai? ::: Har baar jab light critical angle se upar wall se milti hai toh woh totally internally reflect hoti hai — koi refracted ray escape nahi hoti — isliye woh trapped rehti hai. Dekho Optical fibres. Hum full waves ki jagah rays se kyun kaam chalate hain? ::: Jab objects wavelength se bahut bade hote hain, diffraction negligible hoti hai aur energy straight arrows ke along flow karti hai. Rays waves ka simple, accurate limit hain large scale par. $n$ hamesha kam se kam 1 kyun hota hai? ::: Kyunki $n=c/v$ aur koi bhi signal medium mein $c$ se tez nahi jaata, isliye $v\le c$ aur ratio $\ge 1$ hota hai.

Ek ray ka kya hoga jo exactly normal ke saath surface hit kare (0° incidence)? ::: Woh bina kisi bend ke seedha nikal jaata hai: Snell's law ke dono sides par $\sin 0°=0$ hai, isliye ${\theta }_2=0°$ bhi. Speed phir bhi change hoti hai, lekin direction nahi. Kya hoga jab ${\theta }_1\to 90°$ (grazing incidence) denser medium ($n_2>n_1$) mein jaate waqt? ::: Refracted angle us sabse badi value ki taraf approach karta hai jahan tak woh ja sakta hai — $\sin {\theta }_2\to n_1/n_2<1$ — isliye grazing light bhi finite angle par enter karti hai. Yeh us light cone ko define karta hai jo ek machhli upar dekhte waqt see karti hai. Kya hoga agar dono media ka refractive index barabar ho ($n_1=n_2$)? ::: Bilkul koi bending nahi: Snell's law ${\theta }_1={\theta }_2$ deta hai. Optically boundary invisible hai — isi tarah index-matching liquids objects ko hide karte hain. Kya hoga agar light denser se rarer ($n_1>n_2$) mein critical angle se kam par jaaye? ::: Woh normally refract hoti hai, normal se door bend karti hai (${\theta }_2>{\theta }_1$), aur sirf partially reflect hoti hai. Total internal reflection ke liye angle ${\theta }_c$ se zyada hona chahiye. Ek ray kya karta hai jab medium ka index continuously change ho (gradient), sudden step mein nahi? ::: Woh smoothly curve karta hai, har point par higher-index (slower) region ki taraf bend karta hai. Yahi mirage hai: road ke paas garam low-index air rays ko upar ki taraf bend karti hai. Kya reflection light ki wavelength ya frequency badalta hai? ::: Dono nahi — bounce karne se pehle aur baad medium same hota hai, isliye $v$, $\lambda$ aur $f$ sab unchanged rehte hain. Sirf direction flip hoti hai.