interference applications physics 202 professor lee carkner lecture 25
Post on 18-Dec-2015
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PAL #23 Interference
Light with = 400 nm passing through n=1.6 and n=1.5 material N = (L/)(n) L = N/n = (5.75)(400)/(0.1) =
Compare to L = 2.6X10-5 m N = (2.6X10-5)(0.1)/(400X10-9) = 6.5
Orders
At the center is the 0th order maxima, flanked by the 0th order minima, next is the 1st order maxima etc.
The intensity varies sinusoidally between minima and maxima
Intensity of Interference Patterns How bright are the fringes?
The phase difference is related to the path length difference and the wavelength and is given by:
= (2d sin ) /
is in radians
Intensity The intensity can be found from the electric
field vector E:
I = 4 I0 cos2 (½ )
For any given point on the screen we can find the intensity if we know ,d, and I0 The average intensity is 2I0 with a maximum and
minimum of 4I0 and 0
Thin Film Interference
Camera lenses often look bluish
Light that is reflected from both the front and the back of the film has a path length difference and thus may also have a phase difference and show interference
Reflection Phase Shifts In addition to the path length shift there can also be
a phase shift due to reflection
If light is incident on a material with lower n, the phase shift is 0 wavelength Example:
If light is incident on a material with higher n, the phase shift is 0.5 wavelength Example:
The total phase shift is the sum of reflection and path length shifts
Reflection and Thin Films If the thin film covers glass, both reflection
phase shifts will be 0.5
Interference is due only to path length difference Example:
If the thin film is in air, the first shift is 0.5 and the second is zero
Have to add 0.5 wavelength shift to effects of path length difference Example:
Path Length and Thin Films
What is the path length difference between the two reflected rays?
Don’t forget to include reflection shifts
Reflection and Interference What kind of interference will we get for a particular
thickness?
The wavelength of light in the film is equal to:
For an anti-reflective coating (no net reflection shift), the two reflected rays are in phase and they will produce destructive interference if 2L is equal to 1/2 a wavelength
2L = (m + ½) (/n2) -- The two rays will produce constructive interference if 2L is
equal to a wavelength2L = m (/n2) --
Interference Dependencies
For a film in air (soap bubble) the equations are reversed
Soap film can appear bright or dark depending on the thickness
Since the interference depends also on soap films of a particular thickness can produce strong constructive interference at a particular
Color of Film What color does a soap film (n=1.33) appear to be
if it is 500 nm thick? We need to find the wavelength of the maxima:
= (2Ln) / (m + ½)
= 1330 nm / (m + ½)
= Only 532 nm is in the visible region and is green
Interference: Summary Interference occurs when light beams
that are out of phase combine The interference can be constructive or
destructive, producing bright or dark regions
The type of interference can depend on the wavelength, the path length difference, or the index of refraction What types of interference are there?
Reflection
Depends on: n Example: thin films Equations:
• n1 > n2 -- phase shift = 0• antireflective coating
• n1 < n2 -- phase shift = 0.5• soap bubble
Path Length Difference
Depends on: L and Example: double slit interference Equations:
d sin = m -- maxima d sin = (m + ½) -- minima