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Wave Optics
Interference and other Mysteries Explained
Particle or wave?
You Predict
• What happens when a pitcher throws lots of fastballs at two holes?
• What pattern do you see on the wall beyond?
Predict This
• What happens when a beam of light goes through two tiny slits?
• What pattern do you expect on the screen beyond?
Double Slit Interference Applet
• What if light from two slits interferes?• http://www.ece.gatech.edu/research/ccss/ed
ucation/Java/1998.Winter/Projects/pierce-woods/project/bin/projApp.htm
• Experiment performed by Young in 1801• Convincing evidence for wave nature of
light• Another Double Slit Applet
Double Slit Derivation
• http://noether.physics.ubc.ca/Teaching/Physics101/StudySheets/Double.html
Understanding Path Difference
• dsind is the path difference for waves traveling to a given point on the fringe pattern
• If path difference is an integer number of wavelength, interference is constructive
(bright fringe)• If path difference is a half integer number of
wavelengths, interference is destructive
(dark fringe)
Line Spacing
• d sin = m mconstructive
• d sinmmdestructive
• x = LLmd for bright fringes
using sin~ in radians
x
L
d ~ tan = x/L
What Will Happen to the Fringe Spacing…
• x = Lmd• …if the wavelength increases?
• …if the distance to the screen increases?
• …if the slit width increases?
Find
• x = Lmddx/Lm = 6.12 x 10 –7 m = 612 nm
• x = 2.5 mm
• L= 2.6 m
• d = 0.6 mm
x 10 –7 m = 578 nm
Varying the Slit Separation
Courtesy of Siltec Ltd. http://www.infoline.ru/g23/5495/Physics/English/feedback.htm
• x = Lmdxd/L for adjacent fringes= 4x10-3 x 5x10-4
2.6
= 7.7 x 10-7 = 770 nm
Problem
• When white light passes through two slits 0.50mm apart an interference pattern appears on a screen 2.5m away. The fringe separation is 2.5 mm for the violet light. Find the wavelength of this light.
Hint: solve x = Lmd for
L dx/mL = dx/L = 5.0 x 10-7 m = 500nm
Single Slit Interference
• Also called diffraction
• Fringes are larger
• Size of fringes decreases out from center of pattern
• Derivation http://oldsci.eiu.edu/physics/DDavis/1160/Ch25WO/Diff.html
Homework
• Ch 24 Problems
• 3,5,7,9,10(613 nm), 11
More On Single Slit Interference
• Pattern dominated by central maximum
• Called central diffraction maximum
• Width measured from minimum to minimum
• Twice as wide as other fringes
• Much brighter than other fringes
Single Slit Diffraction- Varying the Slit Width
• Fringes get bigger as slit gets smaller
Double Slit vs. Single Slit
• Double• d sin =
mbright• d
sinm Dark modest central
maximum m=0,1,2,etc
• Single• d sin = mdark• d sinm bright• Dominant central
maximum• Fringes usually larger• m=1,2,3, etc
Single Slit Problem
• 500 nm light is incident on a slit of width 0.001 mm which is 1.0 m from a screen. Find the width (2of the central diffraction maximum. (hint: use dsinm
degrees
Dispersion• Spreading of white light into spectrum of
wavelengths
Why Dispersion Occurs
• Index of refraction, n, depends on wavelength
• Typically n decreases as increases
• Exit angle from prism depends on
White light
Diffraction Gratings
• Diffraction Grating has thousands of lines per cm cut into glass plate
• Light from each slit interferes with light from all other slits
• Analysis like Double Slit• Sin = m/d principal maxima (bright)• Lines very close so maxima occur at large angles is maximum possible so only a few
maxima (“orders”)exist
Courtesy http://fermi.bgsu.edu/~stoner/P202/interfere/sld015.htm
Grating Set-Up
Courtesy http://physics.okstate.edu/courses/experiments/o5.html
A. Mercury lamp
B. Spectrometer
C. Gratings
How Grating Works in Practice
• Purpose is to analyze spectrum of light from source such as unknown gas or a star
Spectrum Produced by Grating
Diffraction Grating Problem
• A grating contains 5000 lines per cm– Find the slit separation (d) in meters
• 500 nm light is incident on the grating.– At what angles will the first, second and third
orders be observed? Is there a fourth order?– Hint: use Sin = m/d
2 x 10-6 m
m=1 14.40 ; m=2 300 ; m=3 48.60 ; m=4 900 not visible
= 0.5x10-6m/2x10-6
Thin Film InterferenceLet film thickness = t
Assume no net phase change on reflection
2t = mm
Condition for bright
2t = (m+1/2)
Condition for dark
For one hard reflection 2t =mbecomes condition for dark
Complication #1Soft and Hard Reflections
• SOFT• beam exits higher n
material• No phase shift on
reflection
• HARD• beam enters higher n
material • Phase shift of /2 on
each reflection
Air n=1.0
Coating n=1.38
Glass n=1.52
Complication #2What Wavelength to Use
• Use n = n where n is the index of refraction in the medium where refraction occurs (the film)
• Example: green 500nm light leaves air and enters a thin layer of oil n=1.25 floating on water. What wavelength should be used to find the minimum thickness of oil for the oil to appear green?
n = /1.25 = 500nm/1.25 = 400nm
Oil On Water
Courtesty of http://physics.bu.edu/~duffy/PY106/Diffraction.html
How many hard reflections are there?
What is the total phase shift due to reflections?
What should you use?
1
n =
What Really Happens
This shows why the wavelength must be divided by n in the film – to get the two reflected waves to interfere completely destructively
Anti-reflective Coating
Problem• A coating of MgF on glass has an index of
refraction of 1.38. What is the minimum thickness of this coating to prevent reflection of 550 nm light?
2t =(m+1/2) n
For m = 0 t = n/4
t= t = 100nm
Puzzle
• If the two reflected beams interfere destructively, what happens to their energy?
It is transmitted! That’s the point of an antireflective coating.
Multi Coating
Super-Multi-Coating (SMC) - Pentax's unique seven layer coating applied to each lens element of the lens to increase light transmission, increase color saturation and to help prevent flare.
Polarization
• Intensity varies as polarizer is rotated
Courtesy Siltec Ltd.
Polarization
Courtesy of 3M Corporation
In linear Polarization light vibrations become confined to a single linear plane
Polarization Analogy
Two Polarizers
• What will happen if the polarized beam hits another polarizer rotated 900 from the first?
Propagation of a Linearly Polarized Electromagnetic Wave
Animation Courtesy Siltec Ltd. http://www.infoline.ru/g23/5495/Physics/English/feedback.htm
Courtesy: http://webug.physics.uiuc.edu/courses/phys112/summer97/lectures/lect24/sld014.htm
n = c/v
Link to Interference Applet
• In ripple tank
• link