Feb 2

5.7.1-5  Eyes - microscopes

Concepts

5.7.1 Read at the depth you wish, but focus on:

·        Where is most focusing done:  Cornea as a lens, or the crystalline lens?

·        Different functions of rods vs cones

·        fovea centralis

·        accommodation: relaxed, object is at _______.  Fig 5.82

·        near point

5.7.2 Read at the depth you wish, but focus on:

·        dioptric powers, addition

·        dioptric power of a lens surface

·        fig 5.83, 5.85 correcting near and far sightedness

·        far point

·        astigmatism: eye shape is combination of spherical and cylindrical lenses

5.7.3

·        angular magnification M_a or magnifying power MP

·        magnifying glass: creates virtual magnified image, ideally at the far point.  M_a is defined vs the image at near point.

5.7.4 First two paragraphs only

·        eyepiece: transforms image from optical system into a virtual image at ______ that’s easy for the relaxed eye to see, and is perhaps magnified.

5.7.5 First two paragraphs only

·        Function of objective and eyepiece of a microscope: Fig 5.99. 

·        Angular magnification is product of what two magnifications?

5.7.6 Camera: FYI only

Skills

Sketch microscope diagram and rays

Derivations

Feb 4

In addition to book, read also my Aberration summary of a few common ones.

5.7.7-5.8.1 Telescopes, adaptive

Concepts

Aberrations summary

·        achromatic doublet

·        spherical aberration: source of problem and corrections

·        coma: source of problem

·        See fig 5.104 for examples of how multiple lenses can cancel these aberrations.

5.7.7 through p223

·        Simple telescope fig. 5.106; also notice how same arrangement can expand or shrink a collimated laser beam

·        need for erecting system in terrestrial system

·        advantages of reflecting telescopes

·        Diagram of Newtonian telescope fig 5.111b

5.8.1 Adaptive optics  

·        Wavefront distortion from stars to sealevel: typical sideways distance to move on a snapshot of wavefront before distortion is significant is about 10 ____.

·        How distortion is corrected:

·        How often must the correction be applied to keep up with fluctuations?

Skills

Sketch telescope diagram and rays

Derivations

Angular magnification of infinite conjugate telescope: eq 5.83, from dashed ray in fig 5.106.

Feb 6

Sections 4-6 of PeatrossCh9.4-8 is reading instead of Hecht

Concepts

• during propagation of a ray _____ changes but ____ does not.
• at an interface _____ changes but ____ does not.
• upon reflection, z follows ray
• order of matrices is important: first physical event is the _____ right/left side of product.
• imaging condition puts a constraint on one matrix element.  Know why this is so.
• how normal imaging equation comes from combined matrix including object distance, lens, image distance.
• one element of a combined matrix (including object distance, lens, image distance gives the magnification).  Why?

Skills

make combined  matrices for propagation, reflection, refraction

Derivations

matrix for propagation in air or medium.

matrix for reflection from concave mirror, given figure in lecture

matrix for refraction  from spherical interface, given figure in lecture

Feb 9

Concepts

Peatross 9:7,8

• can reduce any complicated optical system to an effective thin lens as long as the system has the same ______ on both sides
• then we can use the thin lens imaging equation 1/f = 1/i + 1/o as long as object and image distances are measured with respect to the _______  planes
• Condition to find principal planes: (ABCD)’ =(ABCD of physical system plus principal plane distances) must look like a thin lens:  A’= ____  B’ = ____   D’= _____.
• We also get effective focal length from C’ = _____, focal point from principal planes
• Lecture: Ray diagrams into/out of principal planes:  Just like thin lens
• Note: You don’t have to use principal planes for imaging with ABCD.  Can use method of last time with object, image distances and B_total  = 0.
• Laser cavities: ABCD is for one round trip
• Ray height must remain _______  after infinite round trips for a stable cavity
• Lecture: geometric criterion for stable cavity.  

Hecht 6.4

• parabolic index gradient in GRIN lens
• Sinusoidal paths: period
• Fig 6.3 and how imaging can be done with a GRIN lens.  Note  some of the rays entering and exiting the lens are missing refraction bending, but the overall idea is correct.
• Lecture: spherical aberration is essentially eliminated in GRIN lens.

Skills

Find principal planes from ABCD of optical system.  Use for imaging, ray diagrams

Derivations

Determine equations for finding principal planes from the ideas in the line above speaking of (ABCD)’ . Very simple relations. 

Feb 10

7.1-2 Superposition of waves

Concepts

same frequency:

• Result of adding two waves is another wave with different amplitude and phase.
• interference term effect on intensity.
• phase shift due to path differences eq 7.15,16 is k*OPL
• Intensity of addition of N waves eq 7.19: If interference term averages to zero, they are incoherent waves and we add _________ of each.   Or if perfectly coherent,  add ___________ first then square to find _________ .
• Standing waves: opposite traveling waves
• Fig 7.13 partial standing wave from two unequal waves contains traveling part

different frequencies:

• beats
• group and phase velocity.  Changes near absorptive resonances
• superluminal pulses: no violation of causality. Parts of pulses that are already there are either absorbed or amplified, but no information can be transmitted faster than c.
• subliminal and stopped light: FYI only, but pretty interesting:  a way to store  all beam coherence info into coherent atomic excitations, then get it back again.
• Lecture: stimulated emission is handled by the Lorentz model by putting  “positive” friction in the model:  gives energy.   This also modifies n, and gives a negative imaginary part ni.

Skills

Add waves of different intensities, same or different frequencies, either with complex method or graphically.

Predict intensities of incoherent and perfectly coherent waves of the same frequency

Find group velocity and changes in it with changes in n(w).

Derivations

Feb 13  

Change in reading schedule:  Please read: Lec 16 Colors.pdf to prepare for class.

Feb 18  

8.1-2, 8.3.1, 8.4 Polarization and Birefringence

Concepts

• Linearly (plane) polarized light vibrating along any direction written in vector form
• Get circularly polarized light by delaying one component of linearly polarized light by _____ degrees.
• RHcirc:  E rotates CW looking at the source
• Elliptical polarization as general state Fig 8.7.
• eq 8.15 gives angle of either major or minor axis of ellipse vs x.  Lecture: how to determine axes
• Randomly, partially polarized light and superposition of states of polarization
• R and L photons carry angular momentum of amount ___. Linear: each photon is a superposition of  R and L states.
• Malus’ law
• Wire grid polarizers, Polaroid sheets act similarly
• Birefringent crystals: electron cloud has different resonances and for different polarizations:
• optic axis:  symmetry direction in crystal
• ordinary rays: polarization is always ______ to the optic axis.  Obeys all the optics you’re used to.
• extraordinary rays: polarization has component ______ to the optic axis. Dipole induced is no longer parallel to .   is still direction of energy, info, images.  obeys Snell’s law, and gives phase surfaces, but is not  to ; ellipsoidal Huygen’s wavelets.
• Lecture: angle between and .

Skills

Find complete state of polarized light given and delay of y vs x.

Break incoming light at normal incidence into possibly o- and e-rays in a birefringent crystal.  Find directions of S and k.  Find speeds of ellipsoidal wavelets.

Derivations

Feb 20

8.5-8.8 Polarization by scattering; reflection, retarders

Concepts

·           Remember script-P in the book means plane-waye (linearly) polarized light, not p-polarized (vs s-polarized).  It’s a bit of a misnomer because all of the forms of polarization can occur in plane waves:  . See how the phase shift of y vs x appears very simply.

8.5

• Polarization by scattering: dipoles are driven by a given linear polarization but can’t  radiate along that line, so light is most polarized 90 degrees from k direction.  Fig 8.31.  Reason why sky light is most polarized looking 90 degrees from sun’s direction.

8.6: Is mostly a review of how s, p polarizations reflect differently, which can polarize light.  You can just skim it if you're clear on s vs p reflection from earlier Fresnel coefficient section.  

8.7 (Can skip 8.7.2)

·           Waveplates are usually cut with optic axis in the plane of the plate (Fig 8.37). 

·           Phase shifts for ordinary vs extraordinary rays give the various kinds of polarization states we've studied

·           Fast and slow axes are determined by which is greater: no or ne.

·           Half wave plate is used for ________________________

·           Quarter wave plate is used for _______________________

·           To get these effects, have to orient line of linear polarization between fast and slow axis.

• Phase shifts due to total internal reflection depend on angle; glass prisms can make essentially achromatic retarders

Feb 23  8.11.2-3,  8.12,  8.13.2,3 Modulators, LCD  Jones vectors (ignore Mueller method)
 

Concepts

8.11.2-3

·           Electromagnetic modulators:  materials between polarizers can turn light on and off quickly.

·           Faraday modulator uses longitudinal ________ field in a crystal to rotate polarization.

·           Kerr modulator uses transverse ________ field to induce an optic axis in a symmetric material to rotate polarization

·           Pockels modulator uses transverse ________ field to modify n in a uniaxial crystal to change the relative delay of x- and y-components.

·           Lecture: acousto-optic modulator uses ultrasonic waves to induce a dynamic grating in a crystal, which deflects part of the light.

8.12 LCDs

• How are windows prepared to make crystals line up a certain way right at that window?
• When aligned, they form an optic axis  ________ to their length.
• Phase modulator:  OPL of cell can be changed by switching on cell voltage if light E-field is parallel to the ______ fast/slow axis (why this one?).  This can be done for many pixels to change wavefront.
• Intensity modulator: put cell between crossed polarizers
• Twisted nematic cell rotates polarization by  ____ degrees when voltage  is ____ on/off
• LDC display uses twisted cells between two polarizers

8.13.2,3 Jones vectors and matrices (ignore Mueller method)

• Only delay of y vs x components and ratio of the two amplitudes defines the polarization state

Skills

Make a Jones vector for any kind of polarization state.  Manipulate the state with matrices for polarization components. 

Find how to represent a polarization state in terms of superpositions of other polarization states.

Feb 25  9.1-3 Interference

Concepts

9.1

·           Difference between this and ch 7 discussion is that if the polarizations (vector part of E) are not parallel, modify the interference terms by the dot product (eq 9.11).

·           eq 9.14 should make sense in terms of Ch 7 discussion.

·           Two points sources emitting spherical waves give max/mins that are on surfaces which are  _________ of revolution.  Notice that in 9.21 we have our simple relation (phase diff) = k (OPL diff)

·           The last paragraph shows that two slits and two points give essentially the same fringes close to the center line (see fig 9.3b)

9.2

·           In white light different colors/frequencies don’t interfere…only the (very nearly) same colors/frequencies do.

·           Best contrast occurs for nearly _______ amplitudes

·           Temporal coherence.  Coherence time: average time over which the lightwave resembles a _________.   Typical atomic discharge lamps have coherence lengths of a few _____.    This is achieved using a filter that selects a single atomic line.

·           Why is coherence time a measure of spectral purity?

·           Spatial coherence: phase predictability moving sideways across the beam

·           Fig 9.6 on interference for different polarizations.  Look at Fresnel-Arago law #1, which is the only one we will worry about.

9.3   

• Wavefront splitting interferometry:  Different portions of a wavefront are brought to interfere one a screen
• The reason Grimaldi failed to see fringes from sunlight on two pinholes and Young didn’t:
   
• Why fringe visibility vs. slit separation is a test of spatial coherence.
• Why do fringes away from the center disappear for low temporal coherence? (Fig 9.10)
• pg 398-399: know how to sketch one of these examples of wavefront splitting interferometry (names aren't important)

Skills

Derivations

Derive bright and dark fringe locations in q (or y on screen) for two slit (two-point) interference pattern (fig 9.8c).

Derive I(y or q) on the screen given the two waves and the phase shift vs q from the derivation above.

Feb 27  9.4 (Will skip 9.5) Interference amplitude splitting

Concepts

9.4 Can skip pg 403

·            What is meant by amplitude splitting?

·            Lecture: review normal incidence thin film reflectance interference as in Phys 123

·            Thin film reflectance at angle: Eq 9.33 OPL difference L at an angle is ___ less/more than at normal incidence (by factor cosq), due to growth with angle of segment AD in fig 9.17.  

·            ±p  phase shift due to some reflections must be included

·            a fringe of equal inclination:  All along that fringe, the light enters the film the same angle from the normal.

·            a fringe of equal thickness:  the fringe follows contours of constant thickness, usually of a film or gap

·            Why at the very top of a soap film, just before it bursts, there is essentially no reflection as thickness becomes small (black region):

·            wedge fringes shown and Newton’s rings  have the same physics of interference  due to changes in thickness of _____ (what material?).   Details aren’t important if you get the concept you can easily derive the fringe positions.

·            Michelson interferometer: just skim this but be able to sketch the interferometer itself.

Skills

Find interference conditions for thin films and gaps

Derivations

Thin film interference path length difference eq 9.33