Questions: Rayleigh Scattering and the Color of the Sky

Question 1

By about what factor is 450 nm blue light scattered more strongly than 700 nm red light by air molecules?

• A. About 1.6
• B. About 2.4
• C. About 5.9
• D. About 24

Answer: (C)

Intensity scales as 1/λ⁴. (700/450)⁴ = (1.556)⁴ ≈ 5.9.

Question 2

Skylight seen at 90° from the direction of the Sun is strongly linearly polarized.

• T. True
• F. False

Answer: True

The induced dipoles oscillate perpendicular to the incoming sunlight. Viewed at 90°, only the component of oscillation perpendicular to your line of sight radiates toward you, so the scattered light is largely polarized.

Question 3

Why does the Sun look red or orange near sunset?

• A. The Sun's surface cools in the evening
• B. Sunlight crosses much more air, and blue light is scattered out of the direct beam along the way
• C. Red light is created by the atmosphere at low angles
• D. The atmosphere reflects red light from the ground

Answer: (B)

Near the horizon the path through the atmosphere is many times longer. Short wavelengths are scattered out of the beam, so the light that reaches you directly is depleted in blue.

Question 4

Starting from the fact that a dipole of amplitude p₀ oscillating at angular frequency ω radiates power P ∝ p₀²ω⁴, explain why the scattered intensity varies as 1/λ⁴ for molecules.

Model answer: For light far below the molecule's resonant frequencies, the induced dipole p₀ is proportional to the field and nearly independent of frequency, so P ∝ ω⁴ ∝ 1/λ⁴.

Electrons in air molecules have resonances in the ultraviolet. Visible light drives them well below resonance, where the response is nearly constant. The ω⁴ factor from radiation then sets the wavelength dependence.