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Atmospheric Optics: Sky Color, Rainbows, Halos, and Mirages

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optics scattering rainbow halo mirage rayleigh-scattering

Core Idea

Many sights in the sky come from three things light can do in the atmosphere: scatter off molecules and particles, refract and reflect inside water drops and ice crystals, and bend through layers of air at different temperatures. Air molecules scatter short (blue) wavelengths much more strongly than long (red) ones, which makes the sky blue and sunsets red. Raindrops refract and reflect sunlight into rainbows, and six-sided ice crystals refract it into halos and sun dogs. Air layers of different density bend light into mirages.

How It's Best Learned

Use a glass of water or a glass sphere and a flashlight to show light bending and reflecting inside a "drop." Then go outside: stand with your back to the Sun and spray a fine mist to make a rainbow, and measure its angle with an outstretched hand. Have students sketch the path of light for each effect and name the process involved: scattering, refraction, reflection, or diffraction.

Common Misconceptions

Explainer

You already know that light bends, or refracts, when it passes from one medium to another, and that the amount of bending depends slightly on wavelength. That is why a prism spreads white light into colors. The atmosphere is full of natural prisms, mirrors, and scatterers, and the results are some of the most familiar sights in the sky.

Scattering explains sky color. Air molecules are far smaller than the wavelength of visible light. This kind of scattering, called Rayleigh scattering, is much stronger for short wavelengths, varying roughly as one over the wavelength to the fourth power. Blue light is therefore scattered across the sky far more than red light, and the sky looks blue from every direction. At sunset, sunlight travels through a much longer path of air. So much blue is scattered out of the direct beam that the Sun and nearby clouds look orange and red. Cloud droplets are much larger than light waves. They scatter all colors about equally, so clouds look white, or gray when they are thick enough to block light.

Rainbows need sunlight behind you and falling drops in front of you. Light enters a drop, refracts, reflects off the back, and refracts again as it leaves. The light comes back most strongly at about 42° from the antisolar point, the point directly opposite the Sun. Red bends least and appears on the outside of the bow. Some light reflects twice inside the drop and forms a fainter secondary bow at about 51°, with colors reversed.

Halos come from ice. In thin cirrostratus clouds, six-sided ice crystals bend light by at least about 22°, so a bright ring appears 22° from the Sun or Moon. When flat plate crystals float with their faces horizontal, bright spots called sun dogs appear about 22° to each side of the Sun.

Mirages come from air layers of different temperature. Over a hot road, the air near the surface is hot and less dense. Light from the sky bends upward as it passes through this layer, so you see an image of the sky on the road that looks like water. Over very cold surfaces, the bending goes the other way, and distant objects can appear raised above the horizon.

Practice Questions 4 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Combining Small Groups Within 5 → Number Bonds Within 5 → Number Bonds to 10 → Tens and Ones Place Value → Reading and Writing Three-Digit Numbers → Comparing Three-Digit Numbers → Comparing and Ordering Three-Digit Quantities → Comparing and Ordering Whole Numbers → Comparing Numbers 1 to 20 → Ordering Numbers to 20 → Number Line 0 to 20 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Opposites and Additive Inverses → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Multiplying Binomials (FOIL) → Factoring Trinomials → Factoring Completely → Introduction to Rational Expressions → Simplifying Radical Expressions → Segments and Distance → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Similar Right Triangles and the Geometric Mean → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Special Right Triangles: 30-60-90 → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Green's Theorem and Its Applications → Divergence Theorem: Flux and Outflow → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Parallel Plate Capacitor Geometry and Field → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → Resonance Structures and Delocalized Electrons → Resonance and Formal Charge → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Dry Adiabatic Lapse Rate → Environmental Lapse Rate → Atmospheric Temperature Inversion → Atmospheric Optics: Sky Color, Rainbows, Halos, and Mirages

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