lecture 5 lens equation white led interference...

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UCSD COSMOS Cluster 5

Lecture 5

Lens Equation White LED

Interference & Holography

Moire Pattern & Lithography (Dr. Janet Pan) Particle-Wave Duality

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Anatomy of a Lens

http://www.physicsclassroom.com/class/refrn/Lesson-5/The-Anatomy-of-a-Lens

Positive Lens Negative Lens

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Derivation of Lens Equation

Measurements start at lens and point outward. Left is negative. Right is positive.

OA = Object distance = o; OA’ = Image distance = i, OF2 = focal length = f

ΔOAB and ΔOA’B’ are similar à A’B’/AB = OA’/OA

C

ΔOCF2 and ΔF2A’B’ are similar à A’B’/OC = F2A’/OF2 = A’B’/AB = OA’/OA

(OA’ – OF2)/OF2 = OA’/OA à (i – f)/f = i/(-o) à -io + fo = if

Divide by iof à -1/f + 1/i = 1/o à 1/f = 1/i – 1/o

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If the focal length of the lens, f, is 1 cm, the object distance o is 1.25 cm to the left from the lens, what is the magnification? A.  -4 B. -2 C. 2 D. 4

Measurements start at lens and point outward. Left is negative. Right is positive.

o

i

f

hi

ho

1 f o i

= - 1 1 _ _ _

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What About Negative Lenses?

f f

If the focal length of the lens, f, is -1 cm, the object distance o is 2 cm to the left from the lens, what is the magnification? A.  - 3 B. – 1/3 C. 1/3 D. 3

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Multi-Lens Imaging

1 f o i

= - 1 1 _ _ _ The imaging equation still works

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3

2

-5

What is the magnification A . 5

B. 3 C. -1 D. -3 E. -5

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Multi-Lens Imaging

The imaging equation still works 6

3

2

-5

1st image: i1 = (1/3 + 1/(-6))-1 = 6; m = -1

2nd object distance: 6 - 2 = 4

2nd image: i2 = (1/(-5) + 1/4)-1 = 20; m = 20/4 = 5

mtot = -1 x 5 = -5

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Minimum Focal Spot Size or Best Resolution

Diffraction Limit

f

focal length

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Depth of field

F

Dia

met

er D

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Phosphor-Converted White Light

http://www.rpi.edu/~schubert//Light-Emitting-Diodes-dot-org/chap11/chap11.htm

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Approaches to White Light

Mixing Optics

RYGB LEDs

RYGB White

Color Mixing

RYG Phosphors

Blue LED

RYGB White Phosphor Down- Conversion

Tri-color phosphor Fluorescent Lamp Spectrum

Adding Yellow to make the white light warmer

13 http://energy.sandia.gov/energy/energy-efficiency/solid-state-lighting-2/overview/beyond-2d-3/

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Progress to Date

http://energy.sandia.gov/energy/energy-efficiency/solid-state-lighting-2/overview/brief-history-of-solid-state-lighting-technology/

PC-White: Phosphor-converted white

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Photolithography

15 4:35

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Waves: Plane and Spherical

Plane Wave

Spherical Wave

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Phase of a Wave

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/interf.html#c3

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Constructive and Destructive Interference

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/interf.html#c3

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Interference

http://members.ozemail.com.au/~rdunlop/public_html/CoplandMain/Phys12_07/InterfYoungs/WavesDiffractInterfLG_09.htm

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Incoherent and Coherent Wave

http://www.physicsforums.com/showthread.php?t=182755

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Interference of Two Coherent Beams

http://scienceblogs.com/builtonfacts/2012/12/12/interference-on-the-moon/

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Interference at Different Angles

http://scienceblogs.com/builtonfacts/2012/12/12/interference-on-the-moon/

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Interference

http://www.efunda.com/designstandards/sensors/laser_doppler/laser_doppler_flow_theory.cfm

δ = λ/( 2 sin(θ/2))

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Holography?

•  Allows the light scattered from an object to be recorded and later reconstructed

•  Optically stores, retrieves, and processes information

•  Preserves the 3D information of a holographed subject

25 http://www.slideshare.net/abin2892/3-d-holographic-projection-technology-27587990?utm_source=slideshow02&utm_medium=ssemail&utm_campaign=share_slideshow_loggedout

1971 Nobel Prize in Physics

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Transmission Hologram

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Photography vs. Holography Photography Holography

Depth 2D 3D

Light Incoherent Coherent (Usually)

Records Energy (Power x Time)

Amplitude + Phase

Medium Silver-Halide CCD

Film & Other

Lens No lens

Line of sight Interference

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Rainbow Hologram •  Viewable under white light

illumination •  Horizontal slit used to

eliminate vertical parallax •  Changing spectral color

rather than vertical perspectives

•  Reflection hologram: Object and reference beams are incident on the plate from opposite sides of the plate.

•  Viewed from the side of the reconstructed beam

–  Credit card

Object and reference laser beams not shown

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Are these “Holograms”?

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Apple A7 Processor iPhone 5S, iPad Air, iPad Mini 2, iPad Mini 3

Lab demos - Dr. Janet Pan

●  Over 1 billion transistors in 102 mm2 die

●  10 million transistors per square mm

●  Minimum feature size 28nm

●  Blue wavelength is 400nm ●  How to make contact to

1billion transistors with 28nm accuracy?

●  Electron beam lithography (concept similar to optical lithography)

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Moire Pattern Aligning of Photolithographic Mask

Bell Labs US Patent 3,690,881 Filed Sept 28, 1970


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Moire Patterns

Spatial Beat = cos((K1-K2).r)

2cos(K1.r)cos(K2.r) = cos((K1-K2).r) + cos((K1+K2).r)

Beat = (K1-K2)

K2

K1

Beat Wavelength = 2 / (K1-K2)


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Beat = (K1-K2)

K2

Moire Patterns

Spatial Beat = cos((K1-K2).r)

2cos(K1.r)cos(K2.r) = cos((K1-K2).r) + cos((K1+K2).r)

K1


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Large Area Laser Interference Lithography

National Institute of Standards and Technology (NIST) Actinix 197nm UV Laser


2011Interna+onalSymposiumonLithographyExtensions,Miami,October20-21,2011

InterferencepaAernatedgeoffield

InterferencepaAernatcenteroffield

Moire Interferometry ● Laser interference pattern

projected on the wafer reference grating.

● ±1 diffraction orders in vertical direction for both beams imaged on CCD cameras.

● Moire pattern gives deviation from perfect alignment of the laser interference pattern with the wafer reference grating.

● Perfect alignment achieved when the Moire pattern is eliminated thru: stage rotation, stage translation, wavelength control, and adaptive optics.

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Photoelectric Effect

If shining the metal with a certain wavelength of light produces photoelectrons, increasing the intensity of light A. increases the electron kinetic energy B. has no effect on the electron kinetic energy C. decreases the electron kinetic energy

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html

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Photoelectric Effect Red light will not cause the ejection of electrons, no matter what the intensity! A weak violet light will eject only a few electrons, but their maximum kinetic energies are A.  greater than B.  the same as C.  smaller than

those for intense light of longer wavelengths


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Photoelectric Effect

Electron energy = hν – constant à Whatever knocking the electrons out

has an energy proportional to light frequency

The ejected electron energy is independent of the total energy of illumination à The interaction must be like that of a particle which gives all of its energy to the electron

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Wave-Particle Duality of Light


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