12.3 Rainbows and halos

Rainbows and halos are captivating optical phenomena that occur when light interacts with water droplets and ice crystals in the atmosphere. These effects reveal fascinating insights into the behavior of light, atmospheric conditions, and the properties of airborne particles.

By studying rainbows and halos, we can uncover valuable information about atmospheric composition, particle size distributions, and upper-air conditions. These phenomena serve as natural tools for investigating atmospheric optics and provide a gateway to understanding complex light-matter interactions in Earth's atmosphere.

Formation of rainbows

• Rainbows form through complex interactions between sunlight and water droplets in the atmosphere
• Understanding rainbow formation provides insights into light behavior, atmospheric optics, and meteorological conditions
• Atmospheric Physics explores these phenomena to deepen our comprehension of Earth's atmosphere and its optical properties

Refraction and reflection

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• Light rays enter water droplets and undergo refraction bending toward the normal
• Internal reflection occurs at the back of the droplet redirecting light
• Rays exit the droplet refracting away from the normal
• Multiple refractions and reflections create the rainbow's circular shape

Dispersion of light

• White sunlight separates into its component colors due to wavelength-dependent refraction
• Shorter wavelengths (blue, violet) bend more than longer wavelengths (red, orange)
• Dispersion produces the characteristic rainbow spectrum (ROYGBIV)
• Angle of deviation varies for each color creating the spread of hues

Primary vs secondary rainbows

• Primary rainbow forms from one internal reflection within water droplets
• Secondary rainbow results from two internal reflections
• Color order reverses in secondary rainbows (violet on top, red on bottom)
• Alexander's dark band appears between primary and secondary rainbows due to ray geometry

Viewing angle requirements

• Rainbows always appear opposite the sun relative to the observer
• Primary rainbow forms at approximately 42° from the antisolar point
• Secondary rainbow appears at about 51° from the antisolar point
• Observer must be positioned with sun behind them to see a rainbow

Rainbow characteristics

• Rainbow features result from complex interactions between light, water droplets, and atmospheric conditions
• Studying these characteristics enhances our understanding of atmospheric optics and light behavior
• Atmospheric Physics utilizes rainbow properties to investigate atmospheric composition and dynamics

Color sequence

• Traditional rainbow displays colors in ROYGBIV order (red, orange, yellow, green, blue, indigo, violet)
• Color purity and distinctness vary based on droplet size and atmospheric conditions
• Supernumerary bows can appear below the primary bow adding extra color bands
• Color intensity changes with viewing angle and sun position

Angular size

• Primary rainbow spans approximately 42° from the antisolar point
• Secondary rainbow covers about 51° from the antisolar point
• Angular size remains constant regardless of observer distance from the rainbow
• Higher sun elevations produce smaller, lower arcs while lower sun positions create larger, higher arcs

Intensity variations

• Brightness varies across the rainbow due to different scattering angles
• Primary rainbow appears brighter than the secondary rainbow
• Intensity peaks near the red end of the spectrum
• Factors affecting intensity include droplet size, sun angle, and atmospheric conditions

Polarization effects

• Light in rainbows becomes partially polarized during refraction and reflection
• Polarization direction varies across the rainbow arc
• Strongest polarization occurs perpendicular to the rainbow arc
• Polarization effects can be observed using polarizing filters or specialized equipment

Types of rainbows

• Various rainbow types occur under different atmospheric and lighting conditions
• Studying these variations provides insights into atmospheric composition and optical phenomena
• Atmospheric Physics explores these rainbow types to better understand light-matter interactions in the atmosphere

Supernumerary bows

• Appear as faint, pastel-colored bands below the primary rainbow
• Result from interference between light waves within water droplets
• More prominent with smaller, uniformly-sized water droplets
• Spacing between supernumerary bows depends on droplet size

Fogbows

• Form in fog or mist with very small water droplets
• Appear as a white or faintly colored bow due to diffraction effects
• Often seen in mountainous or coastal areas with frequent fog
• Smaller angular size compared to typical rainbows

Moonbows

• Produced by moonlight rather than sunlight
• Appear fainter and less colorful than solar rainbows due to lower light intensity
• Best observed during full moon periods with clear, dark skies
• Human eyes may perceive moonbows as white or gray due to low light conditions

Double rainbows

• Consist of a primary and secondary rainbow appearing simultaneously
• Secondary bow forms above the primary with reversed color order
• Alexander's dark band separates the two bows
• Brightness ratio between primary and secondary bows approximately 1:1/40

Halo phenomena

• Halos form through interactions between light and ice crystals in the atmosphere
• These optical effects provide valuable information about upper atmospheric conditions
• Atmospheric Physics studies halo phenomena to investigate cirrus cloud properties and ice crystal formation

Ice crystal optics

• Hexagonal ice crystals act as prisms refracting and reflecting light
• Crystal orientation and shape determine the type of halo produced
• Minimum deviation angle of 22° creates the common circular halo
• Complex crystal geometries lead to various halo types and optical effects

22-degree halo

• Most common halo type observed around the sun or moon
• Forms a complete circle with an angular radius of approximately 22°
• Inner edge appears reddish while the outer edge appears bluish
• Brightness varies around the halo due to scattering angle differences

Sundogs and parhelia

• Bright spots of light appearing on either side of the sun
• Form when light refracts through horizontally-oriented plate crystals
• Often display prismatic colors with red closest to the sun
• Sundogs can occur with or without a visible 22-degree halo

Circumzenithal arcs

• Appear as upside-down rainbows high in the sky
• Form when light enters the top face of horizontal plate crystals and exits through a side face
• Most vivid when the sun is low on the horizon (elevation < 32°)
• Often mistaken for unusual rainbow phenomena

Atmospheric conditions

• Specific atmospheric conditions influence the formation and appearance of optical phenomena
• Understanding these conditions helps predict and analyze atmospheric optical effects
• Atmospheric Physics examines the relationship between atmospheric properties and observed optical phenomena

Water droplet size

• Affects rainbow brightness color purity and the presence of supernumerary bows
• Smaller droplets (< 0.5 mm) produce broader less vivid rainbows
• Larger droplets (> 1 mm) create narrower more intense rainbows
• Optimal droplet size for vivid rainbows ranges from 0.5 to 1 mm in diameter

Ice crystal shape

• Determines the type and characteristics of halo phenomena
• Hexagonal plates produce sundogs and parhelia
• Hexagonal columns create vertical pillars and tangent arcs
• Complex crystal shapes (bullet rosettes) lead to rare halo types

Sun elevation angle

• Influences rainbow height and arc length
• Lower sun angles produce higher fuller rainbow arcs
• Higher sun angles result in lower flatter rainbow arcs
• Critical angle of 42° determines maximum rainbow visibility

Aerosol effects

• Impact light scattering and absorption in the atmosphere
• High aerosol concentrations can reduce rainbow visibility and color intensity
• Certain aerosols may enhance sky brightness affecting contrast
• Aerosol size distribution influences the appearance of coronas and glories

Observation techniques

• Various methods enable detailed study and analysis of atmospheric optical phenomena
• These techniques provide valuable data for atmospheric research and modeling
• Atmospheric Physics utilizes advanced observation methods to investigate complex optical effects

Photography methods

• High dynamic range (HDR) imaging captures full intensity range of rainbows
• Polarizing filters enhance contrast and reveal polarization effects
• Wide-angle lenses allow capture of full rainbow arcs
• Time-lapse photography records temporal changes in optical phenomena

Spectral analysis

• Spectrometers measure precise wavelength distribution in rainbows and halos
• Hyperspectral imaging provides detailed spatial and spectral information
• Spectral analysis reveals atmospheric composition and particle size distribution
• Raman spectroscopy identifies molecular species in atmospheric particles

Polarimetry measurements

• Polarimeters quantify degree and orientation of light polarization
• Imaging polarimetry maps polarization across entire optical phenomena
• Polarization data provides information on particle shape and orientation
• Helps distinguish between water droplets and ice crystals in mixed-phase clouds

Time-lapse observations

• Record temporal evolution of rainbows halos and related phenomena
• Reveal changes in intensity color and structure over time
• Aid in understanding atmospheric dynamics and particle motion
• Useful for studying short-lived or rapidly changing optical effects

Mathematical modeling

• Mathematical models simulate and predict atmospheric optical phenomena
• These models enhance our understanding of light-matter interactions in the atmosphere
• Atmospheric Physics employs advanced modeling techniques to investigate complex optical effects

Ray tracing algorithms

• Simulate light paths through water droplets and ice crystals
• Account for multiple internal reflections and refractions
• Predict rainbow and halo geometries based on particle properties
• Enable visualization of complex optical paths within atmospheric particles

Mie scattering theory

• Describes light scattering by spherical particles (water droplets)
• Accounts for particle size wavelength and refractive index
• Predicts scattering intensity and angular distribution
• Explains rainbow intensity variations and supernumerary bow formation

Airy function applications

• Models interference patterns in rainbows
• Describes intensity distribution across rainbow arcs
• Predicts spacing and intensity of supernumerary bows
• Accounts for wavelength-dependent diffraction effects

Computational simulations

• Combine multiple physical models for comprehensive predictions
• Incorporate atmospheric conditions particle distributions and light properties
• Enable study of complex phenomena (moonbows fogbows)
• Facilitate comparison between theoretical predictions and observations

Historical and cultural significance

• Rainbows and halos have played important roles in human history and culture
• Understanding their significance provides context for scientific study
• Atmospheric Physics explores the evolution of knowledge about these phenomena

Ancient explanations

• Greek philosophers (Aristotle) attempted to explain rainbow formation
• Native American tribes viewed rainbows as bridges to the spirit world
• Norse mythology depicted rainbows as Bifrost the bridge to Asgard
• Chinese folklore associated rainbows with the union of yin and yang

Artistic representations

• Rainbows frequently appear in paintings (Turner Constable)
• Medieval art often depicted halos around holy figures
• Modern artists use rainbow imagery to symbolize hope and diversity
• Photography captures and preserves ephemeral atmospheric optical phenomena

Scientific discoveries

• Descartes (1637) explained rainbow formation using geometric optics
• Newton (1666) demonstrated dispersion of white light into spectrum
• Young (1803) explained supernumerary bows using wave theory of light
• Airy (1838) developed mathematical description of rainbow intensity

Cultural symbolism

• Rainbows symbolize hope peace and new beginnings in many cultures
• LGBTQ+ community adopted rainbow flag as symbol of pride and diversity
• Some cultures associate rainbows with good fortune or divine messages
• Halos around the sun or moon often interpreted as omens or spiritual signs

Related optical phenomena

• Various atmospheric optical effects share similarities with rainbows and halos
• Studying these phenomena provides a broader understanding of atmospheric optics
• Atmospheric Physics investigates the connections between different optical effects

Glories

• Appear as circular rainbow-like rings around observer's shadow
• Form through backward scattering of light by water droplets
• Often seen from aircraft flying above clouds
• Angular size typically ranges from 5° to 20°

Coronas

• Colorful rings surrounding the sun or moon
• Result from diffraction of light by small water droplets or ice crystals
• Color sequence inverted compared to rainbows (blue on the outside)
• Size of corona inversely related to particle size

Iridescent clouds

• Display vivid pastel colors often in patchy patterns
• Form when sunlight diffracts around small uniform cloud droplets
• Colors can change rapidly as cloud shape evolves
• Most common in altocumulus lenticularis and cirrocumulus clouds

Green flash

• Brief green spot visible above the sun's upper limb at sunset or sunrise
• Caused by atmospheric refraction and dispersion of sunlight
• Requires clear skies and unobstructed view of horizon
• Duration typically less than 2 seconds

Applications and research

• Atmospheric optical phenomena provide valuable tools for scientific research
• Studying these effects contributes to various fields beyond atmospheric science
• Atmospheric Physics applies knowledge of optical phenomena to diverse research areas

Weather prediction indicators

• Rainbow and halo observations can indicate local atmospheric conditions
• Presence of halos may signal approaching warm fronts and precipitation
• Changes in rainbow characteristics can indicate shifts in air mass properties
• Optical phenomena observations complement traditional meteorological data

Remote sensing techniques

• Polarization properties of rainbows used to study aerosol characteristics
• Halo phenomena provide information about cirrus cloud microphysics
• Spectral analysis of optical phenomena reveals atmospheric composition
• Lidar systems utilize similar principles to study atmospheric structure

Climate change studies

• Long-term changes in optical phenomena frequency may indicate climate trends
• Shifts in ice crystal habits could signal changes in upper atmosphere conditions
• Aerosol effects on rainbow properties may reflect air quality changes
• Optical phenomena observations contribute to global radiation budget studies

Exoplanet atmosphere analysis

• Rainbow-like effects (primary rainbow glories) predicted for some exoplanets
• Polarization signatures of rainbows could indicate liquid water on exoplanets
• Halo phenomena may reveal presence of ice crystals in exoplanet atmospheres
• Modeling Earth-based phenomena aids interpretation of exoplanet observations