Optics

1. Geometrical Optics — Reflection and Refraction

• Law of reflection: angle of incidence = angle of reflection (both measured from the normal, the line perpendicular to the surface).
• Snell's Law (refraction): n₁·sin(θ₁) = n₂·sin(θ₂), where n is the refractive index of each medium and θ is measured from the normal.
• Light bends toward the normal when entering a denser medium (higher n), and away from the normal when entering a less dense medium.
• Total internal reflection: occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle θc, where sin(θc) = n₂/n₁ (n₁ > n₂). Beyond this angle, no light refracts out — it all reflects back.

Common mistakes: measuring angles from the surface instead of from the normal (a very common setup error); forgetting total internal reflection only happens going from denser to less-dense medium, never the other way.

2. Physical Optics — Interference and Diffraction

• Interference: when two coherent light waves overlap, they combine according to their path difference. Constructive interference (bright) occurs when the path difference is a whole number of wavelengths (Δ = mλ); destructive interference (dark) occurs at half-integer wavelengths (Δ = (m+½)λ).
• Diffraction: the bending/spreading of waves around obstacles or through narrow openings (slits). More pronounced when the opening size is comparable to the wavelength.

Common mistakes: confusing constructive interference (path difference = whole wavelengths) with destructive (half-wavelengths) — easy to swap by mistake; assuming diffraction requires a very large slit — actually the opposite, diffraction is more noticeable through SMALL openings.