A full lesson: a cartoon movie to start, then the particle-versus-wave fight, wavefronts and rays, why far-away sources give plane waves, Huygens principle built step by step, why light casts sharp shadows, NEET shortcuts, problems to solve yourself, and 12 MCQs.
A pebble makes circular ripples. Every point on a ripple acts as a new tiny source (Huygens), and far from the source the circles look straight: a plane wavefront, like light from the sun.
Fill a steel thali or a bucket with water and let it become completely still. Touch the centre once with a fingertip. A ring of ripples runs out to the rim, and every part of the ring arrives at the same moment. Now float a small piece of paper and tap again: the paper only bobs up and down, it does not ride outwards. What travels is a disturbance carrying energy, not the water.
Light is also a wave, but its ripples are only about half a micrometre apart and travel at 3 × 10⁸ m/s, so we never see them directly. This lesson gives you the language of waves (wavefront, ray, phase) and Huygens' clever trick for predicting where any wave will be next. Every later topic of this chapter, from reflection and refraction to interference and diffraction, is built on it.
"The ripple ring is the whole chapter in one picture. All points on one ring move in step. Hold on to that picture: it is exactly what we call a wavefront."
"If I tap the water twice as often, do the ripples move faster, or do they just come closer together?"
They come closer together. The speed v is set by the water, not by your finger. With v = fλ fixed, doubling the frequency halves the wavelength. Light behaves the same way: in a given medium, its speed is fixed by the medium.
Two models both explained how light reflects and bends. They disagreed on one measurable thing: is light faster or slower in glass and water than in air? Switch the model and slide the refractive index.
Only the speed along the surface is unchanged, so bending towards the normal needs a bigger speed. For n = 1.5, light would go at 4.5 × 10⁸ m/s in glass.
The wavefront slows down in glass: v = c/n = 2 × 10⁸ m/s for n = 1.5. This is what Foucault measured (in water).
Newton's authority, and the belief that waves need a material medium. Maxwell showed light is an electromagnetic wave: changing E and B fields create each other, so no medium is needed.
"Both models get the bending right. Science decided by measurement: light is slower in water. Write it in one line: towards the normal means slower, in the wave model."
A wavefront is the surface on which every point has the same phase. The speed at which it moves outwards is the wave speed. A ray is the direction of energy flow, always perpendicular to the wavefront. Pick a source, then drag the light meter (or use the slider) to see how bright the wave is at distance r.
| Source | Wavefront | Intensity I | Amplitude A |
|---|---|---|---|
| Point | Spherical (small bulb) | ∝ 1/r² | ∝ 1/r |
| Line | Cylindrical (tube light, slit) | ∝ 1/r | ∝ 1/√r |
| Distant | Plane (sunlight) | constant | constant |
"Intensity is power per area. A sphere's area grows as r², a cylinder's as r, a plane's not at all. And amplitude is always the square root: I ∝ A²."
"Two points lie on the same wavefront, 5 cm apart. What is the phase difference between them?"
Zero. That is the definition of a wavefront. Phase changes only along the ray: by 2π for every wavelength travelled, Δφ = (2π/λ)·Δx.
Look at a spherical wavefront through a window of width d = 1 m. Move the source away (slider or presets) and watch the bulge of the arc inside the window, the sagitta s, shrink. When s is far smaller than the wavelength, the wavefront is plane for all practical purposes.
The source is the centre, R is the radius, half the window d/2 is one side, and R − s is the other.
When the source is far, s is much smaller than R, so s² is negligible.
Double the distance, half the bulge. For the sun (R = 1.5 × 10¹¹ m) and d = 1 m: s ≈ 8 × 10⁻¹³ m, about a millionth of a wavelength. Perfectly plane.
"NCERT says it in one line: at a large distance, a small portion of a sphere can be taken as a plane. Now you know why, and you can even put a number on it."
Huygens principle is a geometrical construction: if you know a wavefront now, you can draw it at a later time t. Play the construction, or step through it. Change the medium and the number of secondary sources.
Each point acts as a source of secondary wavelets, all in phase (they lie on one wavefront).
Use the speed in the medium where the wavelet travels, not c.
Plane stays plane, sphere stays a (bigger) sphere, in a uniform medium.
"The backwave is the trap. Huygens removed it by assuming the wavelet amplitude is maximum forwards and zero backwards. NCERT calls this an ad hoc assumption, later justified by the rigorous wave theory."
"In Stage 5 the medium is uniform. What would happen to the new wavefront if the bottom half of the wavelets were in glass and the top half in air?"
The glass wavelets are smaller (c t/n), so the envelope tilts: the wavefront turns. That is refraction, derived from Huygens principle in Lesson 2.
A plane wave hits a wall with a gap. The picture below is computed live by adding up Huygens wavelets from every point of the gap. Compare a wide gap with a narrow one: the spreading depends only on the ratio of the gap width a to the wavelength λ.
A ray is the path of energy in the limit λ → 0. Light's λ (≈ 0.4–0.7 μm) is tiny next to mirrors, lenses and doors.
Light through a 1 m door: θ ≈ 5 × 10⁻⁷ rad. Sound (λ ≈ 1 m): it fills the next room. More in the diffraction lesson.
Changing electric and magnetic fields regenerate each other, so sunlight crosses 150 million km of empty space.
In an isotropic medium, always. Rays parallel ⇔ wavefront plane.
For intensity. Amplitude goes as the square root: 1/r, 1/√r, constant.
In glass (n = 1.5) for 2 ns: ρ = 2 × 10⁸ × 2 × 10⁻⁹ = 0.4 m.
Same wavefront: Δφ = 0. Wavefronts drawn one λ apart differ by 2π.
Parallel rays out means a plane wavefront out. Parallel rays into a convex lens converge: spherical wavefront shrinking to F.
"Towards the normal ⇒ faster" is Newton's (wrong) prediction; Foucault (1850) settled it.
"Most NEET questions on this lesson are one-liners: name the wavefront shape, give the angle between ray and wavefront, or pick the right fall-off. Learn the table in Stage 3 and you collect those marks in ten seconds."
Cover the solution, write the formula, and solve on paper. Open the hint only if you are stuck for more than a minute.
A small bulb radiates equally in all directions. Compare the intensity and the amplitude of its light at 2 m and at 6 m.
Point source: I ∝ 1/r² and A ∝ 1/r.
A long tube light gives intensity I₀ and amplitude A₀ at 1 m. Find both at 4 m.
Line source: I ∝ 1/r and A ∝ 1/√r.
A plane wavefront enters glass of refractive index 1.5. Using Huygens construction, how far ahead is the new wavefront after 2 ns? How far would it be in air?
Wavelet radius = v t with v = c/n.
Light from a bulb 5 m away passes through a window 1 m wide. Find the sagitta of the wavefront across the window. Repeat for sunlight (R = 1.5 × 10¹¹ m) and compare with λ = 550 nm.
s ≈ d²/(8R).
Light of wavelength 600 nm travels in air. Find the phase difference between two points 1.5 μm apart along the ray. What is it for two points on the same wavefront?
Δφ = (2π/λ) Δx.
Take c = 3 × 10⁸ m/s. Write the formula first, then click.
Score: 0 / 12
| If the question says… | Write this first | The trap |
|---|---|---|
| "wavefront" defined, "locus of points" | surface of constant phase | Calling the ray (energy path) the wavefront |
| "angle between ray and wavefront" | 90° | Answering 0° because "the ray moves with the wavefront" |
| "point source", "line source", "distant star" | spherical / cylindrical / plane | Calling sunlight spherical because the sun is a sphere |
| "intensity at distance r" from a source | I ∝ 1/r², 1/r or const by shape | Using 1/r² for a tube light or a slit |
| "amplitude at distance r" | A ∝ √I | Giving the intensity ratio for an amplitude question |
| "secondary wavelets after time t" | radius = v t = c t / n | Using c in a medium |
| "corpuscular theory predicts" | v_denser > v_rarer | Mixing it up with the wave model (v_denser < v_rarer) |
| "point source at focus of convex lens" | emerging wavefront is plane | Answering spherical because the source is a point |
Lesson 2 uses Huygens construction to prove the laws of reflection and Snell's law (and n = c/v). Interference, Young's double slit and diffraction all add up wavelets exactly like the gap picture in Stage 6.
Values used: c = 3 × 10⁸ m/s, visible λ ≈ 400–700 nm (550 nm for calculations), n(water) = 4/3, n(glass) = 1.5, Earth–Sun distance 1.5 × 10¹¹ m.
Follow the four steps: understand it, remember it, try it, then prove it with past papers.