Lecture 5 Lens Equation White LED Interference...
Transcript of 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
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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
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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
Lab demos - Dr. Janet Pan
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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)
Lab demos - Dr. Janet Pan
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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
Lab demos - Dr. Janet Pan
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Large Area Laser Interference Lithography
National Institute of Standards and Technology (NIST) Actinix 197nm UV Laser
Lab demos - Dr. Janet Pan
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
http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html
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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
http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html