PH 103
Dr. Cecilia VogelLecture 8
Review
Outline
diffraction interference
coherence
Diffraction/interference examples double-slit and diffraction grating single slit thin films holograms
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
Two-slit interference Geometry if slits d and << L
difference in distance traveled = dsin or dy/L
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
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
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
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)
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
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
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
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
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
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?
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
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!
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