Lecture 16 Interference

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Lecture 16Interference
Chapter 24.1 ? 24.4
Outline

• Conditions for Interference
• Experiments Showing Interference
• Interference in Thin Films

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Wave Optics
Geometric optics considers light as rays. Wave
optics applies to wave properties of light.
Interference is a superposition of two or more
waves. It can be constructive or destructive.
Interference Demonstration

• Conditions for interference
• The waves must maintain a constant phase shift
  between them (coherency)
• The wave must have identical wavelengths

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Youngs Double Slit Experiment
Demonstration
Double slit interference
Assumption The two waves travel in parallel
lines (the wave source at infinity).
Constructive interference the path difference is
an integer multiple of the wavelength d sin ?
m ?. Destructive interference, the path
difference is an odd multiple of ?/2 d sin ?
(m1/2) ?.
d ? distance between the slits, m ? the order
number, ? ? angle between the slit line and the
wave direction, ? ? wavelength.
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Wavelength Measurement
The double slit experiment allows to measure ?.
Assumption ? is small, so sin ? ? tan ?
L is the distance between the slits and the
screen, y is the distance between the normal to
the screen and the image position.
?L y ? m d
y L tan ? ? L sin ?
For bright fringes
d sin ? m ?
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Problem with Double Slit
Problem The double slit is at 0.80 m from the
screen. If the distance between alternating
bright fringes is 0.95 cm and ? 580 nm, what is
the slit separation (d)?
1 nm 10?9 m L 80 cm dy 0.95 cm
?L yb ? m d
?L dy ? d
?L d ? dy
?
d 4.9 10?5 m 49 microns (?m)
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Interference from Reflection
Interference can be produced by reflection
Lloyds mirror. One wave goes directly to the
viewing point, while the other one is reflected
off a mirror. Reflection produces a 180o phase
shift.
Result the positions of the bright and dark
fringes are reversed compared to the double slit
interference.
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Interference in Thin Films
Thin films have two surfaces, producing
reflection and causing interference.
Consider a film of uniform thickness d and index
of refraction n.
Definitions if a EM wave travels from a medium
with index of refraction n1 to that of n2 and n2
gt n1, it undergoes a 180o phase change. No phase
change in the reflected wave if n2 lt n1. Also, ?n
?/n.
Constructive interference 2nd (m1/2) ?,
m0,1,2
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Newton Rings
Newton rings are circular interference fringes
observed through a planoconvex lens.
The film in this case is air ? n 1.
Radii of the dark fringes (rings) rd ?
?(m?R) Radii of the bright rings rb???(2m1)R?/2?
R is the radius of curvature, m is any integer
number including 0, ? is wavelength.
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Summary

• Interference is one of the wave-like properties
  of EM waves.
• Interference can be constructive or destructive.
• Reflection in a material with a higher index of
  refraction inserts a 180o phase change in the
  reflected wave.