Geometric optics — rectilinear propagation, reflection, refraction

2.5.1 · Physics › Optics

1. Rectilinear propagation

WHY seedha jaata hai? Ek uniform medium mein light ki speed har jagah same hoti hai, isliye do points ke beech least-time path seedhi line hoti hai (sabse chhota path). Koi bhi mod extra distance = extra time le lega.

WHAT evidence hai? Sharp shadows, pinhole cameras, eclipses.

2. Reflection

$θ_{i} = θ_{r}$ ko Fermat's least-time principle se derive karna

Figure — Geometric optics — rectilinear propagation, reflection, refraction

3. Refraction

Common mistakes (Steel-man + fix)

Active recall

Recall Test yourself (answers cover karo)

Rays govern karne wale teen laws batao. → straight-line propagation; $θ_{i} = θ_{r}$ ; $n_{1} sin θ_{1} = n_{2} sin θ_{2}$ .
Teeno kis single principle se follow hote hain? → Fermat's principle of least time.
Denser medium mein enter karte waqt ray kis taraf bend hoti hai? → normal ki taraf.
Refraction mein kya constant rehta hai: $f$ , $λ$ , ya $v$ ? → sirf frequency $f$ .

What does rectilinear propagation state?

Ek uniform medium mein light seedhi lines mein travel karti hai.

From which point are all optics angles measured?

Normal se (surface par perpendicular).

State the law of reflection.

θ_{i} = θ_{r}

, incident, reflected aur normal coplanar.

Define refractive index.

n = c / v

; vacuum mein light ki speed ka ratio medium mein uski speed se (

n \geq 1

State Snell's law.

n_{1} sin θ_{1} = n_{2} sin θ_{2}

What single principle yields reflection and refraction laws?

Fermat's principle of least time.

Which way does a ray bend going into a denser (higher-n) medium?

Normal ki taraf (

θ

decrease hota hai).

Formula for the critical angle (denser n1 → rarer n2)?

sin θ_{c} = n_{2} / n_{1}

In refraction, which of f, λ, v stay constant?

Frequency f constant rehti hai; λ aur v change hote hain.

Wavelength inside a medium of index n?

λ_{m e d} = λ_{0} / n

Pinhole magnification formula?

m = h / H = v / u

(similar triangles se, inverted image).

Recall Feynman: ek 12-saal ke bachche ko samjhao

Light ek super-fast runner ki tarah hai jo hamesha woh route chunti hai jisme kam se kam time lage. Flat ground par (speed har jagah same) sabse fast route seedhi line hai — isliye light seedhi jaati hai. Agar raaste mein mirror aa jaaye, to runner use touch karta hai aur utni hi dhalan se wapas aata hai jis par usne use mara tha. Agar use racetrack se deep sand mein cross karna ho (jahan woh slower run karta hai), to woh seedha nahi jaata — woh apna path angle karta hai taaki sand mein kam se kam time bitaaye. Wahi clever angling exactly wahi reason hai kyun ek straw paani ke glass mein bent dikhti hai!

Connections

Fermat's principle — teeno laws ke peeche master principle.
Total internal reflection aur Optical fibres — Snell's law ka direct consequence.
Wavefronts and Huygens' principle — wave-level reason kyun refraction light ko bend karta hai.
Mirrors and Lenses — reflection/refraction ko curved surfaces par apply karna.
Dispersion — $n$ wavelength par depend karta hai, white light ko colours mein split karta hai.