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

Forming a Rainbow

• Java Applet

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