Atoms & Light Emission & absorption of radiant energy depends on electrons in atoms Recall: Ground and excited states – moving e between energy levels (valence e) These transitions are quantized Excitations are short lived ~ ns Loss of energy either light of thermal agitation For light E = h f There are specific transitions, and therefore frequencies These are resonant frequencies – an atom efficiently absorbs and emits energy

Scattering and Absorption The process of absorbing a photon and emitting another photon Incident photons on a substance can either: be absorbed (and “lost”)or be scattered If the photons energy (frequency) matches one of the excited states of the atom, the atom absorbs it The energy is transferred via collisions to random K (rather than reemitted) The photon vanishes, its energy converted to heat Most things have the colors they do because of absorption (dissipative)

Nonresonant Scattering Suppose photons of light have frequencies too small to cause e to move to a higher energy level The EM field can cause e cloud into oscillation at the same frequency The atom remains in ground state This causes e to accelerate, creating photons This scattered photon moves in same direction as original photon Causing material to be transparent

Light passing through space has nothing to interact with and moves in a straight line at c The beam cannot be seen from the side

When atom and molecules are very far apart, the scattered photons do not interfere in a substantial way Commonly referred to as Rayleigh scattering Since air molecules have electron resonance in UV, the closer the visible light is to UV, the greater the scattering (violet) Why sky is blue Other colors interact less often and pass through

Refraction A change in wave direction when passing to different medium Incident wave: some energy reflected & some transmitted Transmitted light direction is different, it is “bent” The wave speed is material dependent

As wave fronts pass into material, the speed changes, therefore the λ changes v 1 = f λ 1 & v 2 = f λ 2 Index of refraction, n Ratio of speed of light in vacuum per speed of light in medium  n = c / v Leads to Snell’s Law  n 1 sin θ 1 = n 2 sin θ 2

Where n 1 = leaving medium & n 2 = entering medium When n 2 > n 1 refracted ray is bent towards normal line Each ray is reversible The > the change in index, the > change in direction Light along normal is not deflected

Applications Pencils appear to be “bent” in water Objects in water appear closer to surface than they actually are

Dispersion & the Rainbow Index of refraction is frequency dependent Glass is opaque to ultraviolet – the atoms resonate in those frequencies The closer EM radiation is to resonance, the slower it travels Therefore, the higher f, higher n Violet “bends” more than red White light spreads out by refraction - dispersion

Dispersion of white light due to drops of rain causes rainbows As sunlight enters drop: it refracted (& dispersed) internally reflected off the back of drop Refracted again(& dispersed) as the light leaves the drop Light must come from behind viewer Why most often viewed at sunset

Rainbow is top half of a cone between 40 & 42 degrees

Double rainbows have two internal reflections The order of colors is reversed Range of 50 to 53 degrees Fainter than primary due to larger area encompassed and wider band of bow