Why a Wave Theory of Light
Two competing models of light dominated early optics. In 1637, Descartes gave the corpuscular model and derived Snell's law from it; the model was later developed by Isaac Newton in his book OPTICKS, and because of that book's popularity the corpuscular picture is often attributed to Newton. The corpuscular model predicted that when a ray bends towards the normal on refraction, the speed of light is greater in the second (denser) medium.
In 1678 the Dutch physicist Christiaan Huygens put forward the wave theory of light. The wave model explained reflection and refraction equally well, but it predicted the opposite of the corpuscular model: when the wave bends towards the normal, the speed of light is less in the second medium. Foucault's 1850 experiment showed the speed of light in water is less than in air, confirming the wave prediction. Thomas Young's 1801 interference experiment had already established firmly that light is a wave phenomenon.
| Aspect | Corpuscular model | Wave model (Huygens) |
|---|---|---|
| Proposed by | Descartes (1637), developed by Newton | Christiaan Huygens (1678) |
| Speed in denser medium | Greater than in rarer medium | Less than in rarer medium |
| Experimental verdict | Contradicted by experiment | Confirmed (Foucault, 1850) |
| Explains interference / diffraction | No | Yes |
What Is a Wavefront
The central object in Huygens' principle is the wavefront. NCERT introduces it with a familiar image: when a small stone is dropped on a calm pool of water, waves spread out from the point of impact and every point on the surface starts oscillating. A photograph taken at any instant shows circular rings on which the disturbance is maximum. All points on such a ring are at the same distance from the source, so they oscillate in phase.
A wavefront is therefore defined as the locus of points that oscillate in phase — equivalently, a surface of constant phase. The speed with which the wavefront moves outwards from the source is the speed of the wave, and the energy of the wave travels in a direction perpendicular to the wavefront. This perpendicularity is the seed of the ray concept that appears later.
A point source S emits a spherical wavefront. At large distance, a small patch of the sphere flattens to a plane wavefront. Rays (arrows) are everywhere perpendicular to the wavefront.
Types of Wavefront
The shape of a wavefront is fixed by the geometry of the source and the medium. NCERT and NIOS together identify three standard shapes that appear repeatedly in NEET questions.
| Wavefront | Source / situation | Geometry |
|---|---|---|
| Spherical | Point source emitting uniformly in all directions in an isotropic medium | Concentric spheres centred on the source |
| Cylindrical | Line source (a slit or a linear filament) | Coaxial cylinders around the line |
| Plane | Source at a very large distance; a small portion of a spherical or cylindrical wavefront | Parallel flat surfaces; parallel rays |
A diverging point source therefore gives a spherical wave; far from the source, a small portion of that sphere can be approximated as a plane wave. This is exactly why light from a distant star reaches the Earth as a plane wavefront, and why a point source placed at the focus of a convex lens emits light that leaves the lens as a plane wavefront.
Statement of Huygens' Principle
Huygens' principle is essentially a geometrical construction: given the shape of a wavefront at any time, it allows us to determine the shape of the wavefront at a later time. The principle has two parts, stated below in the NIOS form.
1. Each point on a wavefront becomes a source of a secondary disturbance which spreads out in the medium as a secondary wavelet, with the speed of the wave.
2. The position of the wavefront at any later instant is obtained by drawing the forward common tangent — the envelope — to all these secondary wavelets at that instant.
In an isotropic medium the energy carried by the waves is transmitted equally in all directions, so the secondary wavelets are themselves spheres. A crucial rider that NIOS states explicitly: the wavefront does not travel in the backward direction.
Constructing the New Wavefront
To apply the principle, consider a wavefront $F_1F_2$ at time $t = 0$. Each point on it acts as a secondary source. After a time $\tau$, every secondary wavelet has expanded into a sphere of radius
$$ r = v\,\tau $$
where $v$ is the speed of the wave in the medium. Drawing the common forward tangent to all these spheres gives the new wavefront $G_1G_2$. For a diverging spherical wavefront, $G_1G_2$ is again spherical and concentric with the original centre $O$; for a plane wavefront, the new wavefront is again a plane, advanced by $v\tau$.
Points a, b, c, d on the plane wavefront $F_1F_2$ each emit a secondary wavelet of radius $v\tau$. The forward common tangent $G_1G_2$ is the new plane wavefront. Rays are normal to both.
Once you can construct the new wavefront, the laws of reflection and refraction fall out by simple geometry. See Refraction and Reflection using Huygens' Principle.
The Backwave Problem
The construction has one well-known shortcoming. When tangents are drawn to the secondary wavelets, one obtains not only the forward wavefront $G_1G_2$ but also a backward wavefront $D_1D_2$. Physically, no such backwave is observed. Huygens accounted for this with an adhoc assumption: the amplitude of the secondary wavelets is maximum in the forward direction and zero in the backward direction. NCERT is candid that this assumption is not satisfactory, and that the genuine absence of the backwave is justified only by more rigorous wave theory.
Secondary wavelets travel forward, not backward
A common error is to treat Huygens' construction symmetrically and accept a backwave, or to forget that the wavefront advances only in the forward direction. The construction does generate a geometric backward tangent $D_1D_2$, but it does not represent a real wave.
Rule: Only the forward envelope of the secondary wavelets is the new wavefront. The backwave $D_1D_2$ does not exist.
A wavefront is perpendicular to the rays
Energy propagates perpendicular to the wavefront, so a ray is always normal to the wavefront. Marking the ray along (parallel to) the wavefront, or assuming the wavefront tilts at some other angle to the ray, is a frequent slip in wavefront-shape questions.
Rule: Ray ⊥ wavefront, always. The relative orientation between a wavefront and the direction of propagation is $90^\circ$.
Wavefront and Ray
The line drawn perpendicular to the wavefront, in the direction of energy flow, is the ray. In Huygens' construction the lines joining corresponding points of the old and new wavefronts are normal to both wavefronts and represent rays. Geometrical optics is the limiting field in which the finiteness of the wavelength is neglected; there a ray is defined as the path of energy propagation in the limit of wavelength tending to zero.
For a spherical wavefront the rays diverge radially from the source; for a plane wavefront the rays are mutually parallel. This single relationship — ray normal to wavefront — is what lets the wave picture reproduce all the ray-optics results from the previous chapter, including the action of prisms, lenses and mirrors as delays imposed on parts of an advancing wavefront.
State the shape of the wavefront in each case: (a) light diverging from a point source; (b) light emerging from a convex lens when a point source is at its focus; (c) the portion of the wavefront from a distant star intercepted by the Earth.
(a) Spherical (diverging) wavefront, centred on the point source. (b) A point source at the focus produces a parallel beam after the lens, so the emergent wavefront is plane. (c) The star emits spherical wavefronts, but at the Earth's enormous distance the intercepted patch is effectively a plane wavefront.
Huygens' principle in one screen
- A wavefront is a surface of constant phase — the locus of points oscillating in phase. Energy travels perpendicular to it.
- Shapes: spherical (point source), cylindrical (line source), plane (far source, or small patch of a sphere).
- Part 1: every point on a wavefront is a source of a secondary disturbance, sending out secondary wavelets at speed $v$.
- Part 2: the new wavefront is the forward common tangent (envelope) of the wavelets, of radius $v\tau$.
- The backwave $D_1D_2$ does not exist; only the forward envelope is physical.
- A ray is the line normal to the wavefront in the direction of energy propagation.