Sky Optics Lab — which phenomenon makes each optical effect?

Answer:  P→5, Q→4, R→1, S→3

1. (P) Aurora borealis → (5). Charged particles from the Sun are guided down the Earth's magnetic field near the poles. They excite oxygen and nitrogen in the upper atmosphere, and the atoms emit light at fixed wavelengths: green 557.7 nm and red 630.0 nm from oxygen, violet 427.8 nm from N₂⁺. A spectrometer sees separate bright lines. Scattered sunlight is a smooth continuum strongest in the violet, so it cannot make a green or red sky.
2. (Q) Partially polarized sunlight → (4). Air molecules scatter sunlight. A scattering molecule cannot radiate along its own oscillation, so light scattered at angle θ from the Sun has degree of polarization P = sin²θ/(1 + cos²θ): zero looking at the Sun, partial in between, largest at 90°. Total internal reflection reflects both polarizations completely (|r_s| = |r_p| = 1), so it cannot polarize the light.
3. (R) Rainbow → (1). Sunlight enters a raindrop, is refracted, reflects once from the back, and refracts out. Because n depends on wavelength (1.331 red, 1.343 violet), the minimum deviation differs by colour: the bow is at 42.4° (red) and 40.6° (violet) from the point opposite the Sun. That is dispersion and reflection. The reflection is not total: the ray meets the back at about 40°, below the critical angle of 48.7°, so most light leaves the drop. Option (2) is the trap.
4. (S) Dark and bright fringes → (3). Light of one colour passing a narrow opening spreads, and its parts superpose. A single slit of width a is dark where a sin θ = mλ. This is diffraction. Dispersion and reflection cannot make dark fringes in light of a single colour.
5. That is P→5, Q→4, R→1, S→3: option (A). Option (D) fails on S, (B) on P and Q, and (C) on P, Q and R.

Understand the concept

Key takeaways

• The aurora is emission (atomic lines), not scattering. The blue sky is scattering.
• Skylight is partially polarized by molecular scattering, most strongly at 90° from the Sun.
• A rainbow needs dispersion and one internal reflection. That reflection is partial, not total.
• Fringes behind a slit or edge are diffraction: dark where a sin θ = mλ.

Verification: an independent derivation for each effect; the aurora wavelengths from atomic energy levels (λ = hc/ΔE) against the smooth scattered-sky spectrum; the polarization of dipole scattering summed numerically and in sympy, and Fresnel's equations for total internal reflection; the rainbow ray traced through a drop by coordinates and by Descartes' condition, with the internal angle checked against the critical angle; the single slit summed as Huygens phasors; every option audited; and the page's own engine, run by tests/verify_p1phyq14.py. The MathonGo solution was read first only for the intended approach; the official key (A), read last, and MathonGo (A) agree. Status: script-verified by the PrayogX simulation factory; no review by a person has been recorded.