Optics: Questions Flashcards
What is light?
Light is both a particle (photon) and an electromagnetic wave that has a given energy, wavelength, and frequency.
What are the wavelengths of visible light?
400 - 700 nm
What are the frequencies of visible light?
10¹⁴ - 10¹⁵ Hz
What is Maxwell’s equation for the (charged) source of an electric field in a vacuum?
∇ = del operator
E = electric field
What is Maxwell’s equation for the (charged) source of a magnetic field in a vacuum?
∇ = del operator
B = magnetic field
What is Maxwell’s equation for electromagnetic induction (Faraday’s Law)?
∇ = del operator
E = electric field
B = magnetic field
What is Maxwell’s equation for Ampere’s Law?
∇ = del operator
B = magnetic field
E = electric field
ε₀ = dielectric constant in a vacuum
µ₀ = permeability in a vacuum
c = speed of light
How can the wave equation for an electric field in a vacuum be derived using Maxwell’s equations?
1) Apply ∇ x to Faraday’s Law.
2) Use the identity ∇ x (∇ x A) = ∇ (∇ . A) - ∇² A for the LHS of this equation.
3) Knowing that ∇ . E = 0 and using Maxwell’s equation for Ampere’s Law, the wave equation can be found.
What is the wave equation for an electric field?
∇ = del operator
E = electric field
c = speed of light
How can the wave equation for a magnetic field in a vacuum be derived using Maxwell’s equations?
1) Apply ∇ x to Ampere’s Law.
2) Use the identity ∇ x (∇ x A) = ∇ (∇ . A) - ∇² A for the LHS of this equation.
3) Knowing that ∇ . B = 0 and using Maxwell’s equation for Faraday’s Law, the wave equation can be found.
What is the wave equation for a magnetic field?
∇ = del operator
B = magnetic field
c = speed of light
What is the speed of light in a vacuum?
c₀ = speed of light in a vacuum
What is the equation for the wavelength in a vacuum?
λ₀ = wavelength in a vacuum
c₀ = speed of light in a vacuum
ν = frequency
What is the equation for the wavelength in a medium?
λ’ = wavelength in a medium
c’ = speed of light in a medium
ν = frequency
What is the solution to the wave equation in one dimension?
E₀ = amplitude (could also be B₀ for a magnetic wave)
k = wavenumber = 2π/λ
ω = angular frequency = 2πν
What is the solution to the wave equation in three dimensions?
E₀ = amplitude
k = wave vector
ω = angular frequency = 2πν
What is the solution of the wave equation for a plane wave?
E₀ = amplitude
r = (x, y, z)
k = wave vector
ω = angular frequency = 2πν
c.c = complex conjugate
What is the solution of the wave equation for a spherical wave?
E₀ = amplitude
r = |r| = √(x² + y² + z²)
k = wave vector
ω = angular frequency = 2πν
c.c = complex conjugate
Plane waves have planes of _______ phase. The wave moves ____________ to these planes.
Constant
Orthogonally
Define the Poynting vector
A vector that describes the flow of energy. It is orthogonal to the electric and magnetic fields in an EM wave and points in the direction of travel of the wave.
What is the equation for the Poynting vector?
S = Poynting vector
E = electric field
B = magnetic field
µ₀ = permeability in a vacuum
Define the index of refraction
The ratio between the speed of light in a vacuum and the speed of light in a medium.
What is the equation for the index of refraction?
c = speed of light in a vacuum
c’ = speed of light in a medium
εᵣ = ε/ε₀ = dielectric constant in the medium
µᵣ = µ/µ₀ = permeability of the medium
What is Huygen’s Principle?
Each point on a wavefront is a source for a secondary, spherical wave. Cumulatively, the waves produced from these sources will form an envelope and produce a new wavefront.