eduKate Learning Manual
Science | Light, Water & Atmosphere
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The Rainbow

Why a Rainbow Is Really a Circle

Big Question: How can millions of raindrops separate sunlight into colours and send those colours toward one observer in the geometry of a circle?

This Learning Manual begins at Primary Science level with light and water. It then opens into optics, geometry and atmospheric phenomena while keeping the simple model intact.

Quick Answer

Sunlight contains many wavelengths of visible light. When a ray enters a raindrop at an angle, it changes direction by refraction. Different wavelengths refract by slightly different amounts, producing dispersion. Some light reflects from the back of the droplet and then refracts again as it leaves.

For the primary rainbow, much of the light reaching an observer is concentrated near a direction about 42° from the point directly opposite the Sun. Because all directions at the same angular distance from that antisolar point form a circle, the rainbow is circular in geometry. The ground usually blocks the lower part, so we see an arc.

• Sun behind you.
• Water droplets in front of you.
• Refraction as light enters.
• Internal reflection inside the droplet.
• Refraction and dispersion as light leaves.
• Observer receives selected directions.
• Those directions form a circular cone around the antisolar line.

The arc is what the landscape lets you see of a circular optical geometry.

What You Will Learn

• Why sunlight can be separated into colours.
• What refraction means.
• What reflection inside a droplet does.
• Why different colours leave at slightly different angles.
• Why red appears outside violet in a primary rainbow.
• Why a rainbow is circular.
• Why the ground hides part of the circle.
• Why two observers do not receive exactly the same rainbow rays.
• Why secondary rainbows reverse the colour order.
• Why the sky between two rainbows can look darker.
• How water sprays can make small rainbows.
• Why models and geometry help Science explain what eyes see.

Part 1 — White Sunlight Is Not One Simple Colour

Sunlight looks white because many wavelengths of visible light enter the eye together. When those wavelengths are separated, we perceive a continuous spectrum of colours.

The familiar sequence red, orange, yellow, green, blue and violet is a convenient set of labels. The spectrum itself is continuous rather than divided by hard boundaries.

Isaac Newton famously used a prism to demonstrate that white light could be separated and recombined, but rainbow physics had already been studied experimentally in water-filled spheres centuries earlier by al-Fārisī and, independently in medieval Europe, Theodoric of Freiberg.

Part 2 — Refraction: Light Changes Direction at a Boundary

When light passes from one transparent medium into another, its speed changes. If it crosses the boundary at an angle, its direction generally changes too. This bending is called refraction.

In a rainbow, sunlight moves from air into water and later from water back into air. Each boundary can change the direction of the ray.

air → water: bend. water → air: bend again.

Part 3 — Dispersion: Colours Bend by Different Amounts

Water’s refractive index depends slightly on wavelength. That means red, green and violet light do not all follow exactly the same path through the droplet.

The small difference is enough, across huge numbers of droplets, to spread sunlight into visible colour bands.

At Primary level, the useful model is:

white sunlight enters → colours separate → different directions emerge.

Part 4 — One Reflection Inside the Drop Builds the Primary Rainbow

A primary-rainbow ray is refracted entering the droplet, reflected once from the inside back surface and refracted again on the way out.

Not every ray follows exactly the same route. But a concentration of outgoing rays occurs near particular angles, making the bow bright enough to see.

Sunlight →  \
             \  refraction
              ( water drop )
               \          /
                \ reflect/
                 \      /
                  \    /
                   \  / refraction out
                    \/
                 observer

Boundary: this is a path sketch, not a scale diagram.

Part 5 — Why About 42 Degrees?

For the primary rainbow, rays cluster near a minimum-deviation geometry. Red light is seen near an angular radius of roughly 42° from the antisolar direction, with violet somewhat inside it.

The exact angle depends slightly on wavelength and refractive conditions. “42°” is therefore a useful approximate anchor, not a magical universal number for every colour and every circumstance.

Part 6 — Find the Antisolar Point

Stand with the Sun behind you.

Imagine a straight line from the Sun through your head and continuing into the sky in front of you. The point opposite the Sun on that line is the antisolar point.

The primary rainbow is centred on that point.

Sun → observer → antisolar point.

Part 7 — Why a Circle?

Suppose red rainbow light reaches your eye from droplets located about 42° away from the antisolar direction.

There are many possible directions that are 42° away: above, below, left, right and every direction between. Together they form the surface of a cone with your eye at the tip.

Where that cone intersects the distant field of droplets, you see a circle.

same angle in every direction around a centre → circle.

Part 8 — Why Do We Usually See Only an Arc?

From the ground, the antisolar point is often at or below the horizon. The lower part of the rainbow circle would require suitable illuminated droplets below the horizon—and the Earth blocks that view.

From a high aircraft or mountain, droplets can exist below the observer’s horizontal line of sight. Then more of the circle becomes visible.

The missing part was not absent from the geometry. It was hidden by the observer’s position and the ground.

Part 9 — Why a Rainbow Moves When You Move

A rainbow is not painted onto a distant cloud. The rays reaching your eye satisfy a particular angle relative to your Sun–observer line.

If you move, the set of droplets that can send suitable rays to your eye changes. The apparent bow moves with you.

This is why you cannot walk to the “end.” The optical condition keeps relocating with the observer.

Part 10 — Why Two People See Different Rainbow Light

Two observers standing several metres apart can both say they see “the rainbow,” but the rays entering their eyes come from somewhat different droplets.

The overall pattern can look nearly identical because the rain field is large and the Sun is extremely distant. But the actual photon paths are observer-specific.

same phenomenon ≠ same individual rays.

Part 11 — Why Red Is on the Outside

In the primary rainbow, red light emerges at a slightly larger angular radius than violet light. That places red on the outer edge and violet toward the inner edge.

Do not teach the colour order as an arbitrary sequence. Attach it to the mechanism: wavelength affects refraction, and refraction affects exit direction.

Part 12 — Why a Secondary Rainbow Reverses the Colours

Some light reflects twice inside the droplet before emerging. This produces the fainter secondary rainbow outside the primary bow.

The extra internal reflection changes the geometry and reverses the order of colours: red is toward the inner side of the secondary bow and violet toward the outer side.

one internal reflection → primary bow. two internal reflections → secondary bow.

Part 13 — Why Is the Area Between Two Rainbows Darker?

When a bright primary and secondary rainbow appear together, the region between them can look noticeably darker. This is called Alexander’s band.

The ray geometry sends less scattered rainbow light toward the observer from the angular region between the bows. The contrast makes the band visible.

Part 14 — A Rainbow Does Not Contain Seven Sharp Stripes

The mnemonic ROYGBIV is useful, but the rainbow spectrum changes continuously with wavelength. Human colour categories divide that continuum for communication and memory.

Individual perception, brightness, droplet size and background can also change how many colour bands seem visible.

Part 15 — Why Some Rainbows Look White

Very small droplets, such as those in fog, can produce a fogbow. Diffraction becomes important and smears the colour separation, making the bow appear broad and pale or almost white.

This is a useful boundary: the simple geometric-ray model explains a great deal, but wave effects matter when particle sizes become small enough.

Part 16 — Can Moonlight Make a Rainbow?

Yes. A sufficiently bright Moon can illuminate droplets and produce a lunar rainbow, or moonbow. The light is usually too dim for human colour vision to respond strongly, so the bow may look pale even when a camera records colour.

The mechanism remains the same: source, droplets, refraction, reflection, observer.

Follow One Ray of Red Light

1. A photon begins in sunlight travelling toward rain in front of you.
2. It enters a spherical raindrop.
3. Its direction changes by refraction.
4. It travels through the water.
5. Part of its light reflects from the far internal surface.
6. It travels back toward the front of the drop.
7. It refracts again as it leaves water for air.
8. If the outgoing direction matches your eye’s position, you receive it.
9. Many droplets at similar angular positions send red light toward you.
10. Your visual system combines those rays into the red outer region of the bow.

Follow One Ray of Violet Light

The sequence is similar, but violet light experiences a slightly different refractive index and therefore follows a slightly different path. That small angular difference becomes a visible separation when repeated across countless droplets.

tiny wavelength-dependent bend → large visible colour pattern.

A Text Diagram You Can Draw Anywhere

                 droplets
          *   *   *   *   *
             \  rainbow rays
              \      42°
SUN  → → →   [ YOU ]---------------- antisolar point
 behind you       \ 
                   \  same angle around centre
                    \ forms circular cone

Ground blocks much of lower circle → visible arc

Boundary: the diagram compresses three-dimensional cone geometry onto a flat page.

Think Like a Scientist: Make a Small Rainbow

On a sunny day, a fine mist from a safe garden spray can create a miniature rainbow if the Sun is behind you and the mist is in front.

1. Stand with the Sun behind you.
2. Spray a fine mist away from people and electrical equipment.
3. Look into the illuminated droplets in front of you.
4. Move sideways and notice how the bow shifts.
5. Raise or lower the spray and observe how the visible section changes.
6. Record observations before explanations.

Never stare directly at the Sun. The Sun’s position can be inferred from shadows.

Observation vs Inference

• Observation: red appears outside violet.
• Observation: the bow shifts when the observer moves.
• Observation: the bow appears opposite the Sun.
• Inference: different wavelengths are leaving droplets at different angles.
• Model test: reproduce the effect using water droplets or a spherical water-filled vessel.

Common Misconceptions and How to Repair Them

Misconception	Why it sounds plausible	Better model
A rainbow is an object at a fixed place.	It looks attached to distant scenery.	Its observed position depends on Sun, droplets and observer geometry.
A rainbow has two physical ends.	Ground-level view shows an arc.	The bow is part of a circle; the ground hides the lower region.
Raindrops contain coloured paint-like bands.	Colours emerge from rain.	Sunlight is dispersed because wavelengths refract differently.
Light only reflects inside a raindrop.	Reflection is easy to imagine.	Refraction occurs entering and leaving, with internal reflection between.
Every observer sees exactly the same rays.	The rainbow looks shared.	Different observers receive rays from different droplets.
A rainbow has exactly seven colours.	ROYGBIV is taught in school.	The visible spectrum is continuous; named colour bands are categories.
A double rainbow is a copy of the first.	It resembles another arc.	The secondary bow uses two internal reflections and has reversed colour order.

Checkpoint Questions

1. What is refraction?
2. What is dispersion?
3. What happens to a primary-rainbow ray inside a droplet?
4. Why are colours separated?
5. What is the antisolar point?
6. Why is the rainbow centred opposite the Sun?
7. Why is the rainbow circular?
8. Why do we usually see only an arc?
9. Why does the rainbow seem to move with the observer?
10. Why do two observers receive different rainbow rays?
11. Why is red outside violet in a primary rainbow?
12. What causes a secondary rainbow?
13. Why are its colours reversed?
14. What is Alexander’s band?
15. Why can a fogbow appear almost white?

Apply It: Three Observers

Three people observe rain illuminated by the same low Sun.

• Observer A: standing on level ground.
• Observer B: on a tall aircraft with rain below.
• Observer C: standing 50 metres to the side of Observer A.

Predict who may see more of the circle, whether A and C receive light from exactly the same droplets, and where each bow is centred.

Answer Key

Open after attempting the questions

Observer B may see more of the circular rainbow because illuminated droplets can lie below the observer. A and C see similar geometry but receive rays from different sets of droplets because their positions differ. Each rainbow is centred on that observer’s own antisolar point.

Can You Explain WHY?

• Why can the same rain shower make a rainbow for one observer but not another?
• Why does moving sideways change the droplets contributing to your bow?
• Why is a rainbow circular rather than straight?
• Why does the ground hide part of the circle?
• Why does a second internal reflection reverse the colour order?
• Why is a water-filled sphere a useful model of a raindrop?

Singapore Field Connection

Singapore’s frequent convective showers can place bright sunlight and rain near one another—excellent rainbow conditions. Late-afternoon or early-morning showers are especially useful because a lower Sun places more of the primary bow above the horizon.

If the Sun is behind you and rain is ahead, use your shadow to estimate the antisolar direction. Do not look at the Sun directly.

Primary Science / PSLE Bridge

• light travels from a source to the eye;
• light can be reflected;
• light can change direction when it passes between materials;
• water can interact with light;
• white light contains a spectrum of wavelengths;
• observations depend on viewing position;
• models can represent mechanisms that are hard to observe directly.

Go Beyond Primary Science

Simple idea	Deeper layer
Light bends	Snell’s law and refractive index
Colours separate	Wavelength-dependent dispersion
Rainbow angle	Minimum deviation and ray caustics
Rainbow is circular	Three-dimensional cone geometry
Small droplets blur colours	Diffraction and wave optics
Extra faint bands	Interference and supernumerary bows

Deep Science Window — The Rainbow Is Made by Geometry and Probability

Sunlight enters droplets over many possible impact positions. Most rays leave in directions that do not create a bright feature for a particular observer. Near the rainbow angle, many nearby incoming paths produce outgoing rays concentrated into a narrow angular region.

This concentration makes a caustic: a bright optical structure created by ray geometry. Similar mathematics appears in the bright curved patterns at the bottom of a swimming pool.

Deep Science Window — A Rainbow Is Also a Wave Phenomenon

Geometrical optics explains the main bow extremely well, but light is also a wave. Interference and diffraction produce fine structures such as supernumerary bows, especially when droplets are small and similar in size.

This is an important Science lesson: a model can be correct within one scale and still require a deeper model when resolution increases.

Evidence Boundaries

• 42° is approximate. The angle differs slightly by wavelength and conditions.
• Seven colours ≠ seven physical stripes. The spectrum is continuous.
• Circle ≠ always visible circle. Observer height, droplet distribution and ground obstruction matter.
• Every rainbow ≠ identical. Droplet size and illumination alter appearance.
• Ray model ≠ entire optics. Wave effects produce additional details.
• Rainbow location ≠ fixed landscape location. It is observer-dependent geometry.
• Secondary bow ≠ reflected copy. It follows a distinct two-reflection path.

Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK

KNOW

Know light, wavelength, refraction, reflection, dispersion, raindrop, antisolar point, primary bow and secondary bow.

CONNECT

Connect sunlight to raindrops, refraction to colour separation, internal reflection to return paths and viewing angle to circular geometry.

EXPLAIN

Explain why the visible arc is part of a circle centred on the direction opposite the Sun from the observer.

APPLY

Use the model to predict rainbows from garden mist, aircraft views, double bows and different Sun heights.

CHECK

Ask whether the explanation includes source, droplet, light path, observer and geometry.

Where to Go Next

• Earth, Water, Atmosphere & the Celestial World
• Recognising How Light Travels
• Understanding Reflection in Everyday Contexts
• Understanding Rainfall and Water Collection

Research Sources and Further Reading

• US National Weather Service — How Do Rainbows Form?
• UK Met Office — Rainbows: Optical Wonders
• Encyclopaedia Iranica — Kamāl al-Dīn al-Fārisī
• OpenStax College Physics — Dispersion, the Rainbow and Prisms

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eduKate Learning Manuals are written so that a learner can begin simply, a parent can teach confidently, and both can keep going until the simple school model opens into real Science.