interference and diffraction - Department of Physics shih/interference and... Interference patterns
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Key to understanding interference:Key to understanding interference: Path difference () phase difference ()
Say total phase difference is
Say total phase difference is From source 1, E1(t) = Eo cos(t) From source 2, E2(t) = Eo cos(t+ )
When = 2m constructive interference When = (2m+1) destructive interference
Interference effect in thin films 1 2
Two contributions to the phase differences
• Interface contribution P th diff t ib ti
• Path difference contribution
Phase change due to reflection at the interfaces
• I = 0 if n1 > n2; • I = if n1
From geometric optics to wave optics!
•In geometric optics: rays. In wave (physical) optics wavefronts!In geometric optics: rays. In wave (physical) optics wavefronts!
•Light does not like to be squeezed it diffracts!
•The stronger it is squeezed, the stronger it diffracts!
•For two coherent light sources, the intensity of the sum can be more than the sum of intensities constructive interference!
•Or less destructive interference!
Light Waves in Interference
Light Waves in Interference
Constructive interference: maxima
Destructive interference: minima
Double Slits Calculate Intensity using phasor diagram
From S1, E1(t) = Eo cos(t) From S2, E2(t) = Eo cos(t+ )
Path difference = dsin. Also when L >> y, sin y/L )()(2 tEEy, y/
Phase change due to the path difference 2
cos(2 tEE otot
(cos4 2max 2
0 1 2‐2 ‐1 )(
(cos 2max 2
max L ydIII
Phasor diagram for three equally spaced slits
Primary maximum secondary maximumminimum
Interference patterns of multiple slits
• Within one period, the # of minima = N‐1 • The intensity ratio of primary and secondary maxima ~ N2 • The width of the primary maxima ~ 1/N in the large N limit • The multiple slit interference pattern is modulated by an envelop function due to diffraction
Diffraction C id i l lit f t idthConsider a single slit of aperture width a.
Hueygens’ principle treat aperture as having N identical point sources The first source and the last source are separated by aThe first source and the last source are separated by a distance of the aperture size a
The phasor diagram is shown below: The vectors from N individual sources form an arc with the phase angle
= 2 asin
individual sources form an arc, with the phase angle difference between the 1st and the Nth sources to be
Note that the arc length is conserved corresponding to the
Note that the arc length is conserved, corresponding to the total E field on the aperture. Let us call this arc length = Eo
Eo = R R
The total field arrive at the observer is Et = 2Rsin(
The intensity observed
The first minimum occurs at (/2) = , i.e. asin=.
This is for single slit diffraction. The For circular aperture, the condition is modified, asin=1.22 The diffraction g
diffraction pattern looks like pattern looks like