In geometric optics, light is often represented with simple shapes that make direction and position easier to analyze. This approach connects the geometry of traveling light to the underlying wave picture.

Wavefronts and rays

A wavefront is a useful way to describe the shape of a light wave at one instant.

A wavefront is not a path that light follows. Instead, it shows where the wave has the same stage of oscillation at many different locations. In two-dimensional sketches, wavefronts are usually drawn as lines, but in three dimensions they are surfaces.

A light ray is the geometric partner of the wavefront idea.

A ray does not represent a physical object inside the light. It is a model that shows direction. In geometric optics, this model is especially useful because direction can often be tracked with straight lines.

Why the ray is perpendicular to the wavefront

The key relationship in this topic is that a light ray is drawn at a right angle to a wavefront. If a wavefront marks all points reached by the wave at the same moment, the next wavefront forms a short distance ahead in the direction the wave advances.

This diagram applies Huygens’ construction: each point on an old wavefront emits a secondary wavelet, and the new wavefront is the envelope tangent to those wavelets. The propagation direction (ray) is perpendicular to the wavefront, connecting the geometric “ray” picture to the underlying wave model. Source

That advance happens normal to the wavefront, so the ray points straight outward from it.

This is why the ray and wavefront should never be drawn along the same line. The wavefront shows the shape of the wave; the ray shows the travel direction. They describe the same light in two different ways.

When the medium is uniform and the light travels steadily, the ray is straight. The straight-line model is central to geometric optics because it makes light paths easy to represent and interpret.

Direction of travel

The arrow on a ray matters. It tells you which way the light wave is moving. Without the arrow, a line could represent two possible directions. With the arrow, the diagram shows the actual propagation of the light.

For example:

• if the wave moves to the right, the rays point to the right

• if the wave spreads outward from a source, the rays point away from the source

• if the wave travels downward, the rays point downward

In each case, the wavefront stays perpendicular to the ray. The geometry changes with the shape of the wavefront, but the perpendicular relationship does not.

Successive wavefronts

Wavefront diagrams usually show several wavefronts at once. Each one represents the same wave at a later instant. A single ray should cross successive wavefronts one after another, not jump randomly between them. This helps show that the light is moving continuously through space.

If the wavefronts are evenly spaced in a diagram, the light is being represented as advancing uniformly in that region. The exact spacing can also relate to wavelength, but for this topic the main point is simpler: the sequence of wavefronts and the direction of the rays must agree.

Common wavefront shapes

Plane wavefronts

A plane wavefront is drawn as a set of parallel straight lines. This represents light whose wave shape is essentially flat over the region being studied. Because each wavefront line is parallel to the others, the rays are also parallel to one another.

Plane wavefronts are shown as a set of equally spaced parallel lines, while rays are drawn as straight arrows normal to those lines. The figure reinforces that in a uniform region the ray direction is constant, so all rays remain parallel as the wave advances. Source

Each ray crosses the wavefronts at right angles and points in the common direction of travel.

Plane wavefronts are often used when the light source is very far away or when only a small part of a larger wave is being considered.

Circular or spherical wavefronts

Light from a small source is often represented by curved wavefronts. In two-dimensional diagrams, these are usually circular arcs. In three dimensions, they are spherical surfaces. The rays are drawn radially outward, perpendicular to the curved wavefront at every point.

The figure contrasts plane wavefronts with spherical wavefronts and shows that the direction of travel is the local normal to the wavefront. For spherical wavefronts, that normal points radially outward, so rays spread away from the source while remaining perpendicular to the curved fronts. Source

This means different points on the same wavefront generally have different ray directions. The light still follows the same rule everywhere: each ray is perpendicular to the local wavefront.

Reading and drawing diagrams

To interpret a diagram of wavefronts and rays, focus on geometry rather than artistic detail.

• Identify the shape of the wavefronts first.

• At any chosen point on a wavefront, draw a line at $90^\circ$ to the wavefront.

• Add an arrow to show the direction the wave moves.

• If several rays are shown for the same wave, make sure they are consistent with the same wavefront shape.

• Use only enough rays to show the pattern clearly; a few representative rays are usually sufficient.

A curved wavefront requires different perpendicular directions at different points. A straight wavefront gives the same perpendicular direction everywhere. This is a fast way to check whether a diagram is physically sensible.

What the model helps you see

Using both wavefronts and rays connects the wave picture of light with the geometric picture used throughout optics. Wavefronts tell you about the shape of the advancing wave. Rays tell you the direction of that advance. Together, they let you translate between “where the wave is” and “which way the light is going.”

This combination is powerful because it removes unnecessary complexity from many optical situations. Instead of tracking every oscillation of the electromagnetic wave, you use wavefronts to represent equal phase and rays to represent motion. That is the central idea of this subsubtopic.

Common mistakes to avoid

• drawing rays tangent to a wavefront instead of perpendicular to it

• forgetting the arrow that shows the direction of travel

• treating a wavefront as the path taken by a single part of the light

• assuming one ray is the entire beam rather than a representative direction

• drawing curved rays in a uniform region when the model calls for straight lines