PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline diffraction interference coherence ...

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PH 103 Dr. Cecilia Vogel Lecture 8

Transcript of PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline diffraction interference coherence ...

Page 1: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

PH 103

Dr. Cecilia VogelLecture 8

Page 2: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Review

Outline

diffraction interference

coherence

Diffraction/interference examples double-slit and diffraction grating single slit thin films holograms

Page 3: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Two-slit interference AKA Young’s experiment Two waves start out in phase, but

one travels farther one wave gets behind (analogy: cars)

Geometry:

slits

Observationscreen

Page 4: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Two-slit interference Geometry if slits d and << L

difference in distance traveled = dsin or dy/L

Page 5: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Two-slit interference Constructive interference if difference

in distance traveled = integer # of wavelengths

dsin = m or dy/L = m

Destructive interference if difference in distance traveled = (integer-1/2)wavelengths

dsin = (m - ½) or dy/L = (m - ½)

Ld

& ifonly

Ld

& ifonly

Page 6: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

How does interference pattern depend onslit separation?

Larger d, smaller y -- fringes closerwavelength?

Longer , larger y -- fringes fartherlonger wavelengths diffract moreinterference can tell yellow from red +green

material? = o/n, shorter

Bright fringes: dy/L = m

distance between fringes:dy/L =

Two-slit interference

Page 7: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Many-slits = diffraction grating

Each pair of slits behaves like double-slit

Constructive interference if dsin = m or dy/L = m

Destructive interference if dsin = (m - ½) or dy/L = (m - ½)

Fringes are in same place as double-slit, but sharper

Page 8: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Many-slits = diffraction grating

How far apart are the slits? Suppose the are 10 lines/cm, then there is one line in

1/10 cm = 0.1 cm the lines are 0.1 cm apart

generally d = 1/(number of lines per unit length)

Page 9: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Single Slit diffraction pattern

Dark Fringes occur at (m =integer again)

So, width of center bright spot, center

How does pattern depend onslit width

narrower slit causes more diffraction & wider pattern

wavelengthlonger wavelengths diffract more

mW sin

Wcenter

2sin

Page 10: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

One-slit/Two-slit Confusion Note: W=slit width, but d=slit separation Is the spot bright or dark?

Single-slit eqn is for dark (destructive interference)

Double-slit eqn is for bright (constructive interference)

What values of m are possible? M = all integers for double slit m = integers except zero for single slit

md sin mW sinSingle-slit Double-slit

Page 11: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Circular opening diffraction pattern

Circular diffraction pattern depends onAperture radius, a

smaller - more diffraction & wider patternwavelength

longer wavelengths diffract more

So two objects separated by ½ that can be resolved as separate bright spots = “Rayleigh Criterion”

acenter 22.1

2

aRayleigh

22.1

Page 12: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Hologram Light wave split in two by half-silvered

mirror One part shines on object, then reflects to film = “

object beam“ one part goes directly to film = “reference beam“

Interference of these two waves depends on how much further one travels than the other

3-D shape of the object recorded as Developed film is like a complicated

grating When light falls on film, reproduces light

from original object

Page 13: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

One more thing about Reflection

Wave will change phase by 180o (i.e. ½) if it reflects from material where the wave goes slower (higher n)

Wave will not change phase if it reflects from material where the wave goes faster (lower n)

Demo

Page 14: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

VERY Thin film When light strikes a thin film at small

incident angle, some reflects from top surface, some from bottom surface.

If the film is very thin, the only difference between the two reflected waves is if one has a phase change when it reflects.

Does each wave experience a phase change?

Page 15: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

VERY Thin Films Constructive interference if both or neither change

phase light comes from the smallest n, film is intermediate or light comes from largest n, film is intermediate

Destructive interference if film is largest n or film is the smallest n

Page 16: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

Thin Films The two waves also differ in distance

traveled by twice the thickness = 2t If difference in distance traveled is integer

number of cycles, then same result as very thin film beware: wavelength within film (use n of film) 2t = m /n

If difference in distance traveled = integer number of cycles + ½ cycle, then

opposite result from very thin film again beware: wavelength within film 2t = (m+½) /n

Must know what happens to very thin film 1st!

Page 17: PH 103 Dr. Cecilia Vogel Lecture 8. Review Outline  diffraction  interference  coherence  Diffraction/interference examples  double - slit and diffraction.

EXAMPLEAntireflective coating:Thin coating of material with n=1.25 on glass

(n=1.55) makes 525-nm green light not reflect. How thick should the coating be?

1st: What happens when light from air hits a very thin film like this? n of film is intermediate, so it would be bright.

2nd: To make it dark instead (opposite), it must travel through a thickness given by:

2t = (m-½) /nt = (m-½) /2n=(½)(525nm)/(2(1.25))

= 105 nm =1050 Å