Everyday Light Phenomena: Rainbows, Halos, Mirages, and Color Effects

From “rules” to sights: which core idea is at work?

Many outdoor light effects can be explained by combining a few recurring mechanisms: refraction (bending as light travels through a medium), dispersion (different wavelengths bend by different amounts), reflection (including reflections inside droplets or crystals), and total internal reflection (TIR) (light trapped and reflected when trying to exit at too steep an angle). This chapter focuses on recognizing which mechanism dominates in a given scene and building a mental “ray story” that matches what you observe.

Dispersion: why colors separate

Dispersion means the refractive index depends on wavelength: in many transparent materials (including water), shorter wavelengths (blue/violet) bend more than longer wavelengths (red). You can treat this as “Snell’s law with a slightly different index for each color,” so each color follows a slightly different path.

Observation-first model

• If a beam enters a medium and exits after one or more bends, the exit angle depends on color.
• If many rays exit at slightly different angles, you see a spread of colors.
• If geometry causes many rays of a given color to cluster near one direction, that direction looks bright in that color (a “caustic”/concentration effect).

This “clustering” idea is crucial for rainbows: the rainbow is not just “colors separated,” but “colors separated and concentrated near particular angles.”

Primary rainbow: step-by-step ray story

A primary rainbow forms when sunlight interacts with countless spherical water droplets (rain, spray, mist) with the Sun behind the observer. Each droplet sends some light back toward you after a specific sequence: refraction in → one internal reflection → refraction out, with dispersion at each refraction.

Step-by-step conceptual model (one droplet)

1. Enter the droplet (refraction + dispersion): A ray of sunlight bends toward the droplet’s normal. Blue/violet bend a bit more than red.
2. Reflect once inside: The ray hits the back interior surface and reflects. (This is internal reflection; it may be partial or total depending on angle, but the key is that the ray turns around inside the droplet.)
3. Exit the droplet (refraction + dispersion again): The ray bends away from the normal as it leaves. Colors separate further.
4. Angle concentration: For each color, there is a favored exit direction where many nearby incoming rays leave at nearly the same angle. That produces a bright arc at a characteristic angle from the antisolar point (the point opposite the Sun).

Color order and geometry you can check outdoors

• The primary rainbow has red on the outside and violet on the inside.
• It forms a circle centered on the antisolar point. If you can see your shadow, the rainbow is centered on the shadow’s head.
• Typical angular radius is about 42° for red and 40° for violet (values vary slightly with wavelength and droplet conditions).

Practical “build it” exercise

• Stand with the Sun behind you and look toward rain or mist.
• Locate the darkest region just inside the primary bow (often visible as a contrast band). This helps you see the arc.
• Note the color order: red outer edge, violet inner edge.

Secondary rainbow: why it’s dimmer and reversed

The secondary rainbow comes from a similar droplet interaction but with two internal reflections: refraction in → reflection → reflection → refraction out. Each extra reflection reduces intensity (more loss), so the secondary bow is usually fainter and broader.

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Step-by-step conceptual model (compare to primary)

1. Enter (refraction + dispersion): Same as primary.
2. Two internal reflections: The ray bounces twice inside the droplet, changing its exit direction more dramatically.
3. Exit (refraction + dispersion): Colors separate, but the geometry now sends the concentrated rays to a larger angular radius.

Key observable signatures

• The secondary rainbow appears outside the primary (larger radius, often around 50–53°).
• Color order is reversed compared with the primary: red on the inside, violet on the outside.
• Between the primary and secondary bows there is often a darker band called Alexander’s band, caused by fewer rays emerging at those angles.

Mirages: refraction in a gradient, not at a sharp boundary

Mirages are caused by continuous refraction through air whose refractive index changes with height. Since refractive index depends on air density, and density depends on temperature, temperature gradients bend rays. Instead of a single “bend at a surface,” rays curve gradually.

Inferior mirage (hot ground): “wet road” illusion

On a hot day, air near the ground is much warmer (less dense, lower refractive index) than air above. Rays traveling downward into lower-index air bend away from the normal progressively, which can curve them upward before they hit the ground. Your eye interprets the ray as coming from below, creating an apparent reflection-like image.

Step-by-step observation model

1. Set the gradient: Hot surface heats the lowest air layer; index decreases toward the ground.
2. Ray bending: Light from the sky or distant bright objects enters the gradient and curves upward.
3. Apparent source: Your brain traces the ray back in a straight line, placing the source below the horizon line—like a puddle reflection.
4. Shimmering: Turbulence makes the gradient fluctuate, so the apparent image ripples and dances.

Practical check: The “water” patch often disappears when you get close because the viewing geometry changes and the ray paths no longer reach your eyes the same way.

Superior mirage (temperature inversion): floating and stacked images

A temperature inversion occurs when colder, denser air lies below warmer air (often over cold water, ice, or at night). Now refractive index can be higher near the surface and lower above, bending rays in the opposite sense compared with a hot road.

What it can produce

• Raised (superior) images: Distant objects appear higher than they are—ships can look like they float.
• Distortion and stretching: Objects may look vertically smeared.
• Multiple images (stacking): Strong gradients can create layered, inverted/upright segments (complex “ducting” situations).

Field cues

• Often seen over cold oceans/lakes or snowfields.
• Most noticeable when looking near the horizon at distant objects.

Halos and sundogs: refraction through ice crystals

Halos and sundogs (parhelia) are produced by sunlight interacting with ice crystals in high, thin clouds (cirrostratus) or very cold air. Unlike spherical droplets, ice crystals are often hexagonal prisms or plates, so they act like tiny refracting prisms with preferred angles.

22° halo (common)

• Appears as a ring around the Sun or Moon with a radius of about 22°.
• Caused primarily by refraction through randomly oriented hexagonal crystals.
• Often looks whitish with a faint reddish inner edge because dispersion exists but is not as dramatic as in rainbows (and the ring is broadened by crystal orientations).

Sundogs (bright side spots)

• Appear as two bright patches to the left and right of the Sun, typically at the same elevation.
• Often produced when plate-like crystals are partially aligned as they fall, enhancing certain ray paths.
• May show some color, usually red nearest the Sun.

Practical angle trick: Your clenched fist at arm’s length spans roughly 10°. Two fists from the Sun gets you near 20°, close to the 22° halo radius.

Why the sky is bright and colored: scattering as “directional redistribution”

Air molecules and small particles scatter sunlight, redirecting some of it into your line of sight from many directions. Conceptually: scattering takes light that was traveling straight from the Sun and spreads it across the sky dome.

Key observations tied to simple ideas

• Blue daytime sky: Shorter wavelengths are scattered more efficiently by small-scale scatterers, so the sky away from the Sun is enriched in blue light.
• White glare/haze: Larger particles (dust, water droplets) scatter more evenly across wavelengths, washing out color and increasing brightness near the Sun.
• Red/orange sunsets: When the Sun is low, sunlight travels a longer path through the atmosphere; more blue light is scattered out of the direct beam, leaving the transmitted sunlight redder.

Simple experiment: Compare the color of the sky 90° away from the Sun versus near the Sun. The near-Sun region is often brighter and whiter due to forward scattering and glare, while the side sky can look deeper blue on clear days.

Phenomenon mapping exercises (identify the optical effects)

For each scenario, list the dominant mechanisms (choose from: refraction gradient, dispersion, internal reflection, TIR, scattering, crystal refraction) and justify with one visual clue.

Exercise set A: quick identification

• A1: You see a bright colored arc after a rain shower; red is on the outer edge; the arc is opposite the Sun. What effects?
• A2: A faint second arc appears outside the first; its colors are reversed; the region between arcs looks darker. What effects?
• A3: A “puddle” reflection of the sky appears on a hot highway, shimmering and moving as cars pass. What effects?
• A4: A ring around the Moon on a cold night; mostly white with a slight reddish inner edge. What effects?
• A5: Two bright spots appear left and right of the Sun in thin high clouds; slight rainbow tint. What effects?
• A6: The Sun looks orange-red near the horizon; the sky above it is pale and hazy. What effects?

Exercise set B: explain the ray story in 2–3 steps

• B1: “Floating ship” near the horizon over cold water in the morning. Describe the temperature structure and how rays curve.
• B2: Primary rainbow color order. Explain why red ends up outside and violet inside using dispersion and exit angles.
• B3: Why is the secondary rainbow dimmer? Mention what changes in the droplet path.

Answer key (compact)

• A1: Refraction + dispersion + one internal reflection (primary rainbow); clue: red outside, opposite Sun.
• A2: Same plus two internal reflections (secondary rainbow) + angular gap (Alexander’s band); clue: reversed colors, outside primary.
• A3: Refraction in a vertical temperature gradient (inferior mirage) + turbulence; clue: shimmering, “wet” look on hot surface.
• A4: Refraction through ice crystals (22° halo) + weak dispersion; clue: ring centered on Moon/Sun.
• A5: Refraction through partially aligned plate crystals (sundogs); clue: bright side spots at Sun’s height.
• A6: Scattering + long atmospheric path length; clue: reddened Sun, washed-out/bright haze.