Huygens' principle — wavefront propagation: Question bank

2.5.10 · D5 · Physics › Optics › Huygens' principle — wavefront propagation

True or false — justify

The ray and the wavefront point in the same direction.

False. Ray woh line hai jiske along energy travel karti hai, aur yeh wavefront ke perpendicular hoti hai — kabhi parallel nahi. Inhe confuse karna Huygens ki sabse common galti hai.

Every point on a wavefront emits wavelets, so a plane wave must smear out into a blur as it advances.

False. Har point ek poori sphere of wavelets emit karta hai, lekin sirf forward common tangent hi survive karta hai; sideways aur backward contributions envelope ke along out of phase hote hain aur cancel ho jaate hain, isliye plane ek sharp plane hi rehti hai.

The backward wavelet is ignored because Huygens simply forgot about it.

False. Ise ek physical reason ki wajah se ignore kiya jaata hai: obliquity factor

\frac{1}{2} (1 + cos θ)

θ = 18 0^{\circ}

(backward) pe

0

ho jaata hai, wahan amplitude ko khatam kar deta hai. Huygens ne ise haath se drop kiya tha, lekin Fresnel–Kirchhoff Diffraction ne baad mein is drop ko justify kiya.

When light enters glass and slows down, its frequency drops.

False. Wavefronts boundary ke across continuously join hote hain, isliye per second aane wale crests ki count change nahi ho sakti — frequency conserved rehti hai. Sirf speed aur wavelength change hoti hai:

λ_{2} / λ_{1} = v_{2} / v_{1}

A slower wave in glass carries less energy than in air.

False. Yahan speed phase propagation ki speed hai; intensity amplitude pe depend karti hai, speed pe nahi. Slow hona aur energy khona ek hi cheez nahi hai.

Huygens' construction can predict the intensity of the diffraction pattern, not just its shape.

False (naive version ke liye). Bare Huygens sirf nayi wavefronts ki geometry deta hai, lekin intensities ke liye aapko Fresnel ke added ingredients chahiye — obliquity factor aur correct phase summation. Dekho Fresnel–Kirchhoff Diffraction.

The secondary wavelets from all points of a plane wavefront have the same radius after time

t

True. Yeh sab ek hi medium speed

v

share karte hain aur sab ek hi waqt par in-phase start hue the, isliye har radius

r = v t

hai. Collinear centres pe equal radii hi tangent ko flat rakhti hai.

For a plane wave hitting a flat mirror, the angle of incidence equals the angle of reflection because "that's just a law."

Misleading. Yeh ek derived result hai:

B C = A E = v t

△ A B C ≅ △ A E C

banta hai, jo

∠ i = ∠ r

force karta hai. Huygens explain karta hai kyun yeh law hold karta hai. Dekho Laws of Reflection.

Spot the error

"Wavefronts near a point source are plane, and far away they become spherical."

Ulta hai. Point source ke paas wavefronts spherical hote hain; door curvature negligible ho jaata hai aur woh plane lagte hain. Ek line source cylindrical fronts deta hai.

"In Snell's law from Huygens,

\frac{sin i}{sin r} = \frac{v _{2}}{v _{1}}

Ratio ulta hai.

B C = v_{1} t

(incident side) aur

A D = v_{2} t

(refracted side) common hypotenuse

A C

par hain, isliye

\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = \frac{n _{2}}{n _{1}}

milta hai. Incident speed upar hoti hai.

"Because

n = c / v

, a larger refractive index means a faster wave in that medium."

Relationship ulti hai.

n = c / v

ka matlab hai bada

n

⇒ chota

v

. Denser (high-

n

) media light ko slow karta hai aur use normal ki taraf mod deta hai. Dekho Snell's Law and Refractive Index.

"The new wavefront is the tangent to the wavelets and the backward tangent, taken together."

Backward tangent discard karni hogi. Sirf forward envelope hi ek real wavefront hai; backward wale ki amplitude obliquity factor ki wajah se zero hoti hai.

"Since

λ = v / f

and

f

is fixed, wavelength stays the same going into glass."

Conclusion premise ko contradict karta hai.

f

fixed hai lekin

v

chota hai, matlab

λ = v / f

glass mein chota hoga. Denser medium mein wavelength shrink hoti hai.

"A ray is what actually bends; the wavefront just tags along."

Wavefront ka tilt hi cause hai. Kyunki surface ke sabse paas wala wavefront ka end pehle pohonchta hai, poora front tilt karta hai, aur ray (us ke perpendicular) result ke roop mein murt jaati hai. Dekho Phase and Path Difference.

Why questions

Why do we track surfaces of equal phase rather than surfaces of equal amplitude?

Kyunki phase hi interference ko govern karta hai — jahan wavelets add ya cancel hoti hain. Equal-phase surfaces track karne se hum wave equation ko har jagah solve kiye bina bright/dark aur bending predict kar sakte hain. Dekho Wave Optics — Interference.

Why does a plane wave stay a plane wave in a uniform medium?

Sab secondary wavelets ka radius

v t

equal hota hai aur unke centres ek straight line par hote hain, isliye unka common tangent ek aur straight line hoti hai jo original ke parallel hoti hai — aur

v t

distance aage badhti hai.

Why does Huygens' principle naturally explain diffraction around an edge?

Edge par wavefront ke points abhi bhi spherical wavelets emit karte hain, aur edge ke baad koi neighbours nahi hote jo unhe sideways cancel kar sakein, isliye wave geometric shadow mein curl kar jaati hai. Yahi wajah hai ki Diffraction hoti hai.

Why must the two slits in Young's experiment be treated as sources in phase?

Ek hi wavefront dono slits pe simultaneously pohonchti hai, isliye har slit ek secondary source ban jaata hai jo in step emit karta hai. Equal-phase sources hi Young's Double Slit Experiment mein stable interference pattern produce karte hain.

Why is frequency, not wavelength, the quantity conserved across a boundary?

Wavefronts interface par break ya pile up nahi ho sakti — crests continuously pass karte rehte hain — isliye crests per second ki count (frequency) dono sides par match karne ke liye forced hai.

Why does the obliquity factor take the specific value

\frac{1}{2} (1 + cos θ)

Yeh straight forward (

θ = 0

) pe maximum (

= 1

) hona chahiye aur straight backward (

θ = 18 0^{\circ}

) pe vanish (

= 0

) hona chahiye;

\frac{1}{2} (1 + cos θ)

dono endpoints ko satisfy karne wala simplest smooth function hai, jo unphysical backward wave ko khatam karta hai.

Edge cases

At exactly normal incidence (

i = 0

), does Huygens' reflection/refraction still work?

Haan, degenerately.

i = 0

ke saath poora wavefront ek saath surface se milta hai, isliye

∠ r = 0

bhi hota hai aur

sin i / sin r

0/0

ban jaata hai — lekin speeds ka ratio phir bhi limit ke roop mein recover hota hai; wave seedha reflect/refract karta hai.

What happens to the refracted wavefront when light goes from a slower to a faster medium at a steep enough angle?

Critical angle se aage Huygens construction require karta hai ki

sin r > 1

, jo impossible hai — medium 2 mein koi forward tangent nahi banta, isliye wave totally internally reflect ho jaati hai. Dekho Snell's Law and Refractive Index.

What does a wavefront look like in the limit of infinite distance from a point source?

Spherical curvature

\to 0

ho jaati hai, isliye front ek ideal plane wave ban jaati hai. Yeh limiting case hai jo starlight ya distant laser ko plane waves treat karne ko justify karta hai.

Δ t \to 0

in the construction, what happens?

Har wavelet radius

r = v Δ t \to 0

ho jaata hai, isliye nayi wavefront purani par collapse ho jaati hai — yeh construction limit mein wavefront ki instantaneous advance ko describe karta hai, yaani uska velocity field.

What if two points on the wavefront are not in the same phase (a wave passing through a distorted medium)?

Unke wavelets alag times par start hote hain, radii differ karte hain, aur common tangent tilt ya curve ho jaata hai — exactly aise hi ek lens ya graded medium wavefront ko reshape karta hai aur beam ko mod deta hai.

Recall One-line takeaways

Ray ⟂ wavefront, never parallel. ::: Perpendicularity woh geometry hai jo tilting ko bending explain karne ke liye use karti hai. Only the forward envelope is real. ::: Obliquity factor $\frac{1}{2} (1 + cos θ)$ backward wave ko zero kar deta hai. Frequency is conserved, wavelength and speed change. ::: Continuous wavefronts crests ko pile up ya vanish nahi hone dete.

Connections

Huygens' Principle — Wavefront Propagation (parent)
Wave Optics — Interference
Young's Double Slit Experiment
Diffraction
Snell's Law and Refractive Index
Laws of Reflection
Fresnel–Kirchhoff Diffraction
Phase and Path Difference