So far Geometrical Optics Reflection and refraction from
- Slides: 39
So far • Geometrical Optics – – Reflection and refraction from planar and spherical interfaces Imaging condition in the paraxial approximation Apertures & stops Aberrations (violations of the imaging condition due to terms of order higher than paraxial or due to dispersion) • Limits of validity of geometrical optics: features of interest are much bigger than the wavelength λ – Problem: point objects/images are smaller than λ!!! – So light focusing at a single point is an artifact of our approximations – To understand light behavior at scales ~ λ we need to take into account the wave nature of light.
Step #1 towards wave optics: electro-dynamics • Electromagnetic fields (definitions and properties) in vacuo • Electromagnetic fields in matter • Maxwell’s equations – Integral form – Differential form – Energy flux and the Poyntingvector • The electromagnetic wave equation
Electric and magnetic forces
Note the units…
Electric and magnetic fields
Gauss Law: electric fields
Gauss Law: magnetic fields
Faraday’s Law: electromotive force
Ampere’s Law: magnetic induction
Maxwell’s equations (in vacuo)
Electric fields in dielectric media atom under electric field: • charge neutrality is preserved • spatial distribution of chargesbecomes assymetric Spatially variant polarization induces localcharge imbalances (bound charges)
Electric displacement Gauss Law: Electric displacement field: Linear, isotropic polarizability:
General cases of polarization Linear, isotropic polarizability: Linear, anisotropic polarizability: Nonlinear, isotropic polarizability:
Constitutive relationships E: electric field D: electric displacement B: magnetic induction H: magnetic field polarization magnetization
Maxwell’s equations (in matter)
Maxwell’s equations wave equation (in linear, anisotropic, non-magnetic matter, no free charges/currents) matter spatially and temporally invariant electromagnetic wave equation
Maxwell’s equations wave equation (in linear, anisotropic, non-magnetic matter, no free charges/currents)
Light velocity and refractive index cvacuum: speed of light in vacuum 0 n: index of refraction c≡cvacuum/n: speed of light in medium of refr. index n
Simplified (1 D, scalar) wave equation • E is a scalar quantity (e. g. the component Ey of an electric field E) • the geometry is symmetric in x, y⇒the x, yderivatives are zero
Special case: harmonic solution
Complex representation of waves angular frequency wave-number complex representation complex amplitude or " phasor"
Time reversal
Superposition
What is the solution to the wave equation? • In general: the solution is an (arbitrary) superposition of propagating waves • Usually, we have to impose – initial conditions (as in any differential equation) – boundary condition (as in most partial differential equations) Example: initial value problem
What is the solution to the wave equation? • In general: the solution is an (arbitrary) superposition of propagating waves • Usually, we have to impose – initial conditions (as in any differential equation) – boundary condition (as in most partial differential equations) • Boundary conditions: we will not deal much with them in this class, but it is worth noting that physically they explain interesting phenomena such as waveguiding from the wave point of view (we saw already one explanation as TIR).
Elementary waves: plane, spherical
The EM vector wave equation
Harmonic solution in 3 D: plane wave
Plane wave propagating
Complex representation of 3 D waves complex representation complex amplitude or " phasor" " Wavefront"
Plane wave
Plane wave (Cartesian coordinate vector) solves wave equation iff
Plane wave " wavefront": (Cartesian coordinate vector) constant phase condition : wave - front is a plane
Plane wave propagating
Plane wave propagating
Spherical wave equation of wavefront “point” source exponential notation Outgoing rays paraxial approximation
Spherical wave spherical wavefronts exact parabolic wavefronts paraxial approximation/ /Gaussian beams
The role of lenses
The role of lenses
- Geometric optics ppt
- What is optics
- Difference between ray optics and wave optics
- Reflection and refraction venn diagram
- Far point of hyperopic eye
- Rainbow total internal reflection
- Refraction of sound
- Poem reaction
- Partial reflection and refraction examples
- Reflection refraction transmission and absorption of light
- Infrared light is also known as bill nye
- Reflection about invictus
- Why can we represent light rays using a ruler
- Single ray
- Venn diagram of heat and electricity
- Bill nye reflection and refraction
- Reflection and refraction learning task 1
- Refraction vs reflection
- Reflection refraction diffraction interference
- Reflection refraction diffraction
- When a wave strikes an object and bounces off
- Reflection refraction
- For lives that slyly turn
- What plots the map of the slum children
- In a kingdom far far away
- Far far away city
- Geometric symbol
- Meniscus lens ray diagram
- Geometrical isomers
- Geometrical tolerance
- 14 gd&t symbols
- Geometrical
- Geographical data types
- Geometrical representation of complex number
- Curved surface area of a cylinder
- Geometrical spreading
- Geometrical shadow
- Geometrical isomerism
- Physics 241
- Fibre optics disadvantages