Test 4 Optics

2- Polarization

Maximum E vector is the amplitude

Orientation of E field is polarization

E field parallel to dipole

Plane polarized – all E vectors in one plane

Methods of polarization

Polarization by anisotropic substances

Birefringence (double refraction)

Birefringent crystals

Optic axis and polarization

E and O rays

Dichroism – birefringence plus selective absorption of certain E vector orientations

Polaroid sheets – orientation of molecules vs pass axis

Crossed polarizers

Polarizer and analyzer

Law of Malus

Ix = Ip cos2 θ

Liquid Crystal Displays (LCDs)

Polarization by reflection

Brewster’s angle

tan iB = n2

tan iB = n2/n1 if n1 does not equal 1.00 (air).

E vectors of polarized light from reflection

Polarization by scatter

Rayleigh scattering

Rayleigh scattering: the intensity of scatter (Is) is inversely proportional to λ4

Mie scattering: particles are larger than the wavelength of the incident light

Rayleigh produces polarized light, Mie does not

Sunglasses and pass axis

Stereopsis tests

Suppression testing

Hiadinger’s brush

Spectacle tempering and birefringence

Half wave plate: recombining exiting wave is linearly polarized 90° to the entering orientation

Quarter wave plate: E vector of the exiting wave rotates around the axis of the light ray as circularly

polarized light .

Right and left circular polarizers

Circular polarization reverses on reflectionOptical activity

positive and negative optical activity

Molecule asymmetry and optical activity

Symmetric molecules but asymmetric crystal lattice and optical activity

3 – The Summation of Waves

Periodic motion

Amplitude

Period

Frequency

Wavelength

Velocity

V = λ/T

c = 3.00x105 km/sec, 3.00x108 m/s, or 3.00x1010 cm/sec

When monochromatic light passes into and through a medium, the frequency will remain the same.

The wavelength and velocity will change depending on the refractive index of the medium.

Radians and degrees

Simple harmonic motion

Phasors

Phase diagram

Reference circle

Phase angle

θ = 360(t/T)

y = a sin θ

y = a sin(θ) = a sin (360

λ) ∶ particle displacement over distance

θ = 360

phase difference

δ = θ2− θ1

Addition of SHM waves

Principle of superposition

If wavelengths are equal between waves, sine wave results: SHM

If wavelengths unequal, more complex waves: no SHM

Phase difference and wave summation

Fourier analysis: breaks non sine waves down into sine wave components

Phasor determination of A1+2 and θA for summed waves

Intensity of a light wave vs amplitude

Wave coherence

Coherent light: same phase and wavelength

Incoherent light: different wavelength or different distance to summation

Summated amplitude for coherence vs incoherent waves of equal I4 - Interference

Interference basics

Division of Amplitude

Division of Wavefront

Path length difference

ΔD = D2 – D1

Constructive interference

Destructive interference

Thin film interference

Soap bubbles and oil slicks

Phase shift on reflection when n2>n1

t = m (λ n2

⁄

2 ) for destructive interference when i = 0°

t = m ( λ n2

⁄

2 cos 𝑟) (For destructive interference when i ≠ 0

Fiseau fringes and Newton’s rings

t = m (λ

2) (For destructive interference when i = 0°

t(≡s) = h2/2r (sagittal formula)

Antireflection coatings

t =

4 ( λ

n2) and if i > 0, t =

4 (λ n2

⁄

cos r)

n2 = √n3n1 (= √n3 if n1 is air for index of ideal antireflection coating)

Intensity of reflection

= (n2−n1

n2+n1)2

(II = incident I; IR = reflected I).

Amplitude of reflection

AR1

= (n2− n1

n2 + n1)

Michelson interferometer

d = m(λ/2)

Interference by division of wavefront

Young’s experiment

x =

mλ

d D (bright fringes) , where m = 0, 1, 2, etc. And:

θrad = x/D = mλ/d (bright fringes).

Fringe contrast

M =

Imax− Imin

Imax + Imin

Fresnel’s biprism

Fresnel’s mirrors

Lloyd’s mirror

Coherence length5- Diffraction

Young’s double slit vs diffraction

Huygen’s principle

Wavelets

The pinhole effect

Narrow vs wide slits

Diffraction pattern

Fraunhofer diffraction

Intensity profile of a single slit diffraction pattern

Phasor arrows as distance from Po increases

θh(rad)=

f for single slit

h =

f for single slit

Circular apertures

Airy disk

h = 1.22 λ

f for circular aperture

θh(rad)= 1.22 λ/a for circular aperture

Resolving power

Rayleigh’s criterion

Mnecessary

Mnecessary =

RP eye

RP instrument

Empty magnification

numerical aperture and how to modify it

Single slit vs double slit diffraction

Increasing d with constant a

Diffraction gratings

x =

mλ

d D

Diffraction gratings vs double slit diffraction

Relationship between d and x

Diffraction grating vs prism

Converting between slits/cm and cm/slit

θh(rad)=

mλ

transmission vs reflection diffraction gratings6- Fresnel Diffraction

Fresnel vs Fraunhofer diffraction

Fresnel diffraction and shadows

Fresnel diffraction from circular apertures

Wavefronts with Fresnel diffraction

Half period zones

Obliquity effect

ATOT = a1/2 for full wavefront

Wavefront and circular apertures

Poisson Spot with opaque disk

Zone plate

Phase plate

Cornu’s spiral

Blazed phase plate

Huygen’s principle and how a lens focuses light

How a mirror reflects light