Introduction to Light Stolen from Florin Albeanu 2016/07/19

Light as an oscillating electro-magnetic field ELECTRO-MAGNETIC RADIATION:

Light as an oscillating electro-magnetic field direction of propagation Wavelength (λ) Amplitude (A) Intensity I α A 2 z0z0 z t0t0 z0z0 z t1t1 z0z0 z t2t2 0 π/2 π 3π/2 Phase (φ) Light oscillating electric field: E (x,t) = A sin(kx – ωt + ε)k = 2π/λ; ω = 2π*ν; ε initial phase E (x,t) = A e i(kx – ωt + ε) z z0z0 z t3t3 Frequency ν=λ/c

Light as wave 0 π/2 π 3π/2 λ 0-2π λ/2 π λ/4 π/2

Superposition of waves Superposition: point by point addition of amplitude of light waves Superposition of light waves generates interference patterns Relative phases determine whether the interference is constructive vs. destructive 0 π/2 π 3π/2 0-2π π π/2 destructive interference constructive interference intermediate interference 2π2π

Light Wavefront wavefront – all points that have same phase Direction of propagation is orthogonal to the wavefront

Light Wavefront spherical wavefronts turn into planar wavefronts with increasing distance from the source

Huygens Principle The wavefront of a propagating wave of light at any instant conforms to the envelope of spherical wavelets emanating from every point on the wavefront at the prior instant

Reflection and Huygens Principle

Light in vacuum Light (EMR) propagates in vacuum at a speed: c Speed = distance/time = λ / T = λ * ν = 300*10 6 m/s nanometers femtoseconds ~10 15 Hz The speed of EMR is constant in vacuum c … but it decreases when light travels through media

Light in media

n1n1 n2n2 θ1θ1 θ1'θ1' θ 1 = θ 1 ’ Law of reflection: Law of refraction (Snell’a law): n 1 sinθ 1 = n 2 sinθ 2 n 1 = c/v 1, n 2 =c/v 2 θ2θ2 n 2 > n 1 Reflection Refraction Principle of least time – Pierre Fermat

Refraction and Huygens Principle Wavefronts have to be continuous!

Refraction… car in mud analogy

Light in media Frequency stays constant across media Wavelength changes Light slows down in media. How are the frequency and wavelength impacted? Light slows down – less distance traveled per cycle

Light in media - Dispersion Multicolor refraction: dispersion n1n1 n2n2 n 2 > n 1 1 < n red < n green < n blue v blue < v green < v red < c

Light in media – Dispersion through prisms

Diffraction and resolution in microscopy Superposition of two spherical wavefronts

Constructive interference Destructive interference Constructive interference

Optical path difference Assumption holds for L >> d ~θ θ d*sin θ d θ L >> d CONSTRUCTIVE INTERFERENCE: d*sinθ = mλm = 1, 2, 3 … DESTRUCTIVE INTERFERENCE: d*sin θ = (m + 0.5) λ Light waves emitting from the two slits interferes – constructively or destructively depending on the difference in traveled distance

The smaller the distance d between the slits, the bigger the diffraction angle θ Information about the fine spatial detail (small slits) in the sample, is contained in higher diffraction orders – large angles Information about the coarse spatial detail (big slits) in the sample is contained in lower diffraction orders – smaller angles

Objective θiθi θNθN Optical imaging – microscopes, telescopes Devices to steer light to capture diffraction orders

Numerical aperture Relationship between resolution and NA θ focal plane f n D pupil plane D = 2 f NA = 2 f n sin θ d = λ / sin θ R min(x,y) ~ λ / NA

Polarization of light

LINEAR POLARIZATIONCIRCULAR POLARIZATIONELLIPTICAL POLARIZATION DIFFERENT TYPES OF POLARIZATION

Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light.

λ/2 and λ/4 waveplates

Is light really a wave? Intensity (J/m 2 ) ~ amplitude of the light electric field Energy (J) ~ frequency of the light electro-magnetic field PHOTOELECTRIC EFFECT e e e METAL Classical wave theory of light: increasing either the frequency or the intensity of light would increase electron emission rate BUT Frequency threshold : below this threshold, no electrons are emitted, even if intensity is increased Light propagates as discrete packets of energy called PHOTONS: Energy = hν h: Plank’s constant Light oscillating electric field: E (x,t) = A sin(kx – ωt + ε) k = 2π/λ; ω = 2π*ν; ε initial phase

ELECTRO-MAGNETIC WAVE AS STATISTICAL DISTRIBUTION OF PHOTONS Wave - particle duality of light Interference (laser light through a double slit) Photon counting WAVE! PARTICLES!

Diffraction pattern of a laser beam through a pinhole Laser light through a double slit WAVE PARTICLES Sequence of images acquired with a position sensitive photo-multiplier tube illuminated by an image of a bar chart (exposure times at 8, 125, 1000, ms) "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. (…) We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do" Wave - particle duality of light