A rainbow forms when sunlight enters airborne water droplets, refracts and disperses, reflects from the inside of each droplet, and refracts again as it leaves. The colors reach an observer most strongly at particular angles, producing the familiar circular arc with red on the outside and violet on the inside.
Rain is therefore not enough by itself. You need sunlight behind the observer and water droplets in front, which is why rainbows are commonly seen when a shower is ending and sunlight breaks through from the opposite side of the sky.
For IB students, a rainbow is a useful application of refraction, Snell's law, dispersion, reflection, refractive index, and ray geometry. It is not a separate major syllabus topic, but it brings together ideas within C.3 Wave phenomena in the current IB Physics course.
Why do rainbows form?
A primary rainbow is produced by three main stages inside many approximately spherical raindrops:
- Refraction and dispersion on entry: Sunlight passes from air into water, slows down and bends toward the normal. Different wavelengths bend by slightly different amounts.
- Internal reflection: Part of the light reflects from the back internal surface of the droplet.
- Refraction on exit: The reflected light passes from water back into air, bends away from the normal, and becomes more widely separated by color.
A single droplet sends different colors in different directions. The rainbow that you see is the combined light from a vast number of droplets positioned at the correct angles relative to your eyes and the Sun.
This distinction matters: a droplet does not normally send the entire visible spectrum to one observer. A droplet near the top of the primary bow may send red light to your eyes, while a slightly lower droplet sends violet light. Together, the illuminated droplets create the appearance of continuous colored bands.
Refraction: why light bends at a raindrop
Refraction is the change in direction of a wave caused by a change in wave speed as it crosses a boundary. Light travels more slowly in water than in air, so a ray entering water obliquely bends toward the normal.
The refractive index of a material is defined by:
n = c / v
Here, c is the speed of light in a vacuum and v is its speed in the material. Water has a higher refractive index than air, so light has a lower speed in water.
The angles are related by Snell's law:
n₁ sin θ₁ = n₂ sin θ₂
The angles θ₁ and θ₂ must be measured from the normal, not from the surface. This is a frequent source of lost marks in IB Physics calculations.
When light crosses from air into water:
- its speed decreases;
- its wavelength decreases;
- its frequency remains constant;
- its direction changes unless it arrives along the normal.
Frequency remains constant because the oscillations must remain continuous across the boundary. Since v = fλ, a reduction in speed with unchanged frequency produces a shorter wavelength in water.
For a broader review of this material, use RevisionDojo's IB Physics C.3 Wave Phenomena Notes and the focused notes on reflection, refraction, and diffraction.
Dispersion: where the rainbow's colors come from
Sunlight appears white, but it contains a continuous range of visible wavelengths. Dispersion occurs because the refractive index of water depends slightly on wavelength.
Violet light has a shorter wavelength and experiences a slightly greater refractive index in water than red light. It is therefore refracted more strongly. Red light, with its longer wavelength, is refracted less.
| Color region | Approximate relative wavelength | Refractive index in water | Refraction |
|---|---|---|---|
| Red | Longer | Slightly lower | Bends less |
| Green | Intermediate | Intermediate | Intermediate bending |
| Violet | Shorter | Slightly higher | Bends more |
The separation begins when sunlight enters the droplet and is increased when the light leaves. Reflection changes the ray's direction but is not itself the main cause of color separation.
A rainbow is also a continuous spectrum, not seven physically separate stripes. The familiar list of red, orange, yellow, green, blue, indigo, and violet is a convenient classification imposed on a smooth progression of wavelengths. Human color perception and atmospheric conditions affect how clearly the individual bands appear.
What happens inside one raindrop?
Imagine parallel sunlight striking different positions on a spherical droplet. Each ray meets a differently oriented normal because the surface is curved.
At the front surface, some light reflects away, while the rest enters and refracts. At the rear surface, part of the light leaves the droplet and part reflects internally. The internally reflected portion returns to the front of the droplet, where some of it refracts out toward the observer.
The primary rainbow therefore follows this sequence:
refraction → one internal reflection → refraction
The reflection involved should not automatically be called total internal reflection. For the rays responsible for the primary rainbow, the rear surface generally produces partial internal reflection: some energy is reflected, while some is transmitted out of the droplet. Total internal reflection requires incidence from a higher-index medium at an angle greater than the critical angle, which is not the condition for every rainbow-forming ray.
This loss of light at each boundary helps explain why a rainbow is much dimmer than direct sunlight.
Why is the primary rainbow near 42 degrees?
Sunlight enters droplets across a range of positions, so the outgoing rays also cover a range of directions. However, many nearby incident rays emerge concentrated around a particular direction called the angle of minimum deviation or stationary-deviation direction.
For primary-rainbow rays, red light appears at an angular radius of about 42° from the antisolar point. Violet appears closer to 40° because it is refracted more strongly. The exact values vary slightly with wavelength and the refractive index of the water.
The antisolar point is the point directly opposite the Sun from the observer. If the Sun is behind you, it lies approximately in the direction of the shadow of your head. The primary bow is centered on this point, not on a cloud or a fixed location in the landscape.
The concentration of rays near these angles makes the bow bright enough to see. Rays emerging at substantially different angles spread their energy more widely and do not produce an equally sharp band.
An IB explanation should therefore go beyond saying that light is “split by raindrops.” A stronger response connects the observations to the physics:
- wavelength-dependent refractive index explains the colors;
- refraction and internal reflection redirect sunlight toward the observer;
- minimum-deviation geometry concentrates the emerging rays;
- a fixed viewing angle explains the circular shape.
Why is a rainbow curved?
Every droplet capable of sending red primary-rainbow light to your eye lies about 42° from the antisolar direction. The possible directions form the surface of a cone with your eye at its vertex.
The circular base of that viewing cone appears as a circle centered on the antisolar point. From the ground, the horizon usually blocks the lower part, so you normally see an arc rather than a complete circle. From an aircraft or a high viewpoint, a nearly complete circular rainbow may be visible if illuminated droplets exist below the observer.
The rainbow has no fixed physical position. If you move, the viewing cone moves with you, and different droplets send light into your eyes. Two observers therefore do not receive rainbow light from exactly the same collection of droplets.
The Sun's altitude also affects how much of the bow is visible. When the Sun is low, the antisolar point is relatively high and a large arc can appear above the horizon. When the Sun is more than about 42° above the horizon, the center is far enough below the horizon that an ordinary primary bow produced by distant rain is usually not visible from level ground.
Why does the color order run from red to violet?
In a primary rainbow, red has the larger angular radius, close to 42°, while violet has the smaller radius, close to 40°. Red therefore appears on the outer edge, and violet appears on the inner edge.
This can initially seem inconsistent with the statement that violet bends more. The key is to consider the ray's complete path, including both refractions and the internal reflection. Greater refraction produces the smaller final angular radius around the antisolar point.
| Feature | Primary rainbow | Secondary rainbow |
|---|---|---|
| Internal reflections | One | Two |
| Approximate angular radius | 40° to 42° | About 50° to 53° |
| Red position | Outer edge | Inner edge |
| Violet position | Inner edge | Outer edge |
| Relative brightness | Brighter | Fainter |
A ray diagram should show normals at every curved boundary. Drawing angles relative to a horizontal or vertical line rather than the local normal produces incorrect refraction directions.
How does a secondary rainbow form?
A secondary rainbow forms when light reflects twice inside a droplet before emerging. Its ray sequence is:
refraction → two internal reflections → refraction
The extra reflection changes the exit geometry, so the secondary bow appears outside the primary at an angular radius of roughly 50° to 53°. It also reverses the color order, placing violet on the outside and red on the inside.
Secondary rainbows are fainter because additional light is transmitted out of the droplet or otherwise lost at each encounter with the surface. The region between the primary and secondary bows can look unusually dark because relatively little rainbow light is directed there. This region is known as Alexander's dark band.
Why rainbows often appear after rain
Rainbows do not depend on rain having stopped. They can form during rain, in waterfall spray, sea spray, mist, or water from a garden hose. What matters is the simultaneous presence of direct sunlight and suspended water droplets in the correct relative directions.
The phrase “after rain” describes a common weather arrangement. A shower may move away from the observer while the sky clears behind them, allowing low sunlight to illuminate droplets in front. The brightest conditions often occur when:
- the Sun is unobstructed and behind the observer;
- rain or spray is present opposite the Sun;
- the Sun is fairly low in the sky;
- the background behind the bow is dark enough to provide contrast;
- the droplets are large enough to produce clearly separated colors.
Cloud cover between the Sun and the droplets prevents a bright bow because diffuse light arrives from many directions. Rainbow geometry depends on strongly directional sunlight.
IB Physics exam connections
The current IB Physics course, first assessed in 2025, places reflection and refraction within C.3 Wave phenomena. A rainbow may be used as an unfamiliar context for testing established wave principles, even though memorizing a detailed theory of rainbows is not presented as a separate syllabus requirement in the public subject brief.
You should be ready to:
- define refraction in terms of changing wave speed;
- apply
n = c/vand Snell's law; - state that frequency is unchanged at a boundary;
- explain dispersion using wavelength-dependent refractive index;
- distinguish reflection, refraction, dispersion, and diffraction;
- interpret a ray diagram using normals at curved surfaces;
- explain why a primary and secondary bow have different brightness and color order.
A concise exam-quality explanation might read:
Sunlight refracts and disperses as it enters a raindrop because the refractive index of water varies with wavelength. After partial internal reflection, the light refracts again as it leaves. Different wavelengths emerge most strongly at different angles, so many droplets around the antisolar direction produce a colored circular arc.
Do not write that water “creates” the colors or that every droplet acts only as a mirror. Also avoid confusing dispersion, which separates wavelengths through wavelength-dependent refraction, with diffraction, which is the spreading of waves around obstacles or through apertures.
RevisionDojo's topic-wide IB Physics Topic C: Wave Behaviour notes provide the wider exam-focused framework without turning this single application into a replacement for the full topic. You can then use the IB Physics waves exam guide and Physics Questionbank to practise applying the same principles in unfamiliar contexts.
Common mistakes to avoid
- Saying reflection alone makes the colors: The colors are separated primarily by dispersion during refraction.
- Calling every internal reflection total internal reflection: Rainbow-forming rays generally undergo partial internal reflection.
- Measuring angles from the surface: Snell's law angles are measured from the normal.
- Claiming frequency changes in water: Frequency stays constant; speed and wavelength change.
- Treating the rainbow as a physical object: Its apparent position depends on the observer.
- Describing seven discrete wavelengths: The visible spectrum is continuous.
- Forgetting the observer-Sun geometry: The Sun must be behind the observer, with droplets in front.
When revising, draw the primary ray path from memory and label both refractions, the internal reflection, and the normals. Jojo AI can help identify missing terminology, while RevisionDojo IB Physics resources provide notes, flashcards, and targeted practice for the wider waves unit.
Conclusion
Rainbows form because spherical water droplets redirect and disperse sunlight. Refraction separates the wavelengths, partial internal reflection turns some of the light back toward the observer, and the second refraction increases the separation of the colors.
The bow is curved because the strongest emerging rays reach the observer along a cone centered on the antisolar point. In the primary bow, red appears near the outer 42° edge and violet near the inner 40° edge; a second internal reflection produces a fainter secondary bow with reversed colors. To consolidate the underlying IB Physics optics, use RevisionDojo's Wave Behaviour notes, Questionbank, Flashcards, and Jojo AI for explanation practice.
Sources and referenced URLs
External sources
- NOAA: What Causes a Rainbow?
- US National Weather Service: How Do Rainbows Form?
- University of St Andrews: Rainbows and minimum-deviation geometry
- International Baccalaureate: DP Physics subject brief, first assessment 2025
- International Baccalaureate: Physics curriculum updates