1. Interference and Diffraction
Chapter 37 2 8 2

2. Combination of Waves + =
In general, when we combine two waves to form a composite wave,
the composite wave is the algebraic sum of the two original waves,
point by point in space [Superposition Principle].
When we add the two waves we need to take into account their:
Direction
Amplitude
Phase + =

3. The combining of two waves to form a composite wave is called:
Combination of Waves
The combining of two waves to form a composite wave is called:
Interference + =
Constructive interference
(Waves almost in phase)
The interference is constructive
if the waves reinforce each other.

4. The combining of two waves to form a composite wave is called:
Combination of Waves
The combining of two waves to form a composite wave is called:
Interference + =
(Close to p out of phase)
(Waves almost cancel.)
Destructive interference
The interference is destructive
if the waves tend to cancel each other.

5. Interference of Waves + + = Constructive interference = (Waves cancel)
(In phase) + =
( p out of phase)
(Waves cancel)
Destructive interference 20 20 10

6. * Interference of Waves + = When light waves travel different paths,
and are then recombined, they interfere.
Mirror 1 2 *
Each wave has an electric field whose amplitude goes like:
E(s,t) = E0 sin(ks-t) î
Here s measures the distance
traveled along each wave’s path. + =
Constructive interference results when light paths differ
by an integer multiple of the wavelength: s = m  20 20 11

7. * Interference of Waves + = When light waves travel different paths,
and are then recombined, they interfere.
Mirror 1 2 *
Each wave has an electric field whose amplitude goes like:
E(s,t) = E0 sin(ks-t) î
Here s measures the distance
traveled along each wave’s path. + =
Destructive interference results when light paths differ
by an odd multiple of a half wavelength: s = (2m+1) /2

8. Interference of Waves
Coherence: Most light will only have interference for small optical path differences (a few wavelengths), because the phase is not well defined over a long distance. That’s because most light comes in many short bursts strung together.
Incoherent light: (light bulb)
random phase “jumps” 20 20 12

9. Interference of Waves
Coherence: Most light will only have interference for small optical path differences (a few wavelengths), because the phase is not well defined over a long distance. That’s because most light comes in many short bursts strung together.
Incoherent light: (light bulb)
Laser light is an exception: Coherent Light: (laser)
random phase “jumps” 20 20 13

10. Thin Film Interference
We have all seen the effect of colored reflections
from thin oil films, or from soap bubbles.
Film; e.g. oil on water 20 20 14

11. Thin Film Interference
We have all seen the effect of colored reflections
from thin oil films, or from soap bubbles.
Rays reflected off the lower
surface travel a longer
optical path than rays
reflected off upper surface.
Film; e.g. oil on water

12. Thin Film Interference
We have all seen the effect of colored reflections
from thin oil films, or from soap bubbles.
Rays reflected off the lower
surface travel a longer
optical path than rays
reflected off upper surface.
Film; e.g. oil on water
If the optical paths differ by
a multiple of , the reflected
waves add.
If the paths cause a phase difference , reflected waves cancel out. 20 15 20

13. Thin Film Interference
Ray 1 has a phase change of  upon reflection
Ray 2 travels an extra distance 2t (normal incidence approximation) 1 t 2
oil on water
optical film on glass
soap bubble
n = 1
n > 1
Constructive interference: rays 1 and 2 are in phase
 2 t = m n + ½ n  2 n t = (m + ½)  [n = /n]
Destructive interference: rays 1 and 2 are  out of phase
 2 t = m n  2 n t = m  20 16 20

14. Thin Film Interference
When ray 2 is in phase with ray 1, they add up constructively
and we see a bright region.
Different wavelengths will tend to add constructively at different angles, and we see bands of different colors. 1 t 2
oil on water
optical film on glass
soap bubble
n = 1
n > 1
Thin films work with even low
coherence light, as paths are short
When ray 2 is  out of phase, the rays interfere destructively.
This is how anti-reflection coatings work. 20 20 18

15. Michelson Interferometer
A Michelson interferometer uses a beam splitter to create two
different optical paths. This can be used for optical testing.
Input
Mirrors
Beam-splitter
Output
What is the output? 20 20 20

16. Michelson Interferometer
A Michelson interferometer uses a beam splitter to create two
different optical paths. This can be used for optical testing.
Input
Mirrors
Beam-splitter
Output
What is the output?
- If the output beams are perfectly aligned, they will
interfere uniformly, giving either a bright or dark
output, depending on their relative phase. 20 21 20

17. Michelson Interferometer
But usually the beams will be a little misaligned:
Input
Output
Interference of misaligned beams: 20 20 22

18. Michelson Interferometer
But usually, the beams will be a little misaligned:
Input
Output
Interference of misaligned beams: (the lines represent maxima) 20 23 20

19. Michelson Interferometer
But usually, the beams will be a little misaligned:
Input
Output
Interference of misaligned beams: (the lines represent maxima) 20 20 24

20. Michelson Interferometer
But usually, the beams will be a little misaligned:
Input
Output
Interference of misaligned beams: (the lines represent maxima)
Regions of high
intensity 20 25 20

21. Michelson Interferometer
But usually, the beams will be a little misaligned:
Input
Output
Regions of high
intensity S
Interference of misaligned beams: (lines = maxima)
“Fringes” 20 20 26

22. Optical Testing With a Michelson Interferometer
A Michelson interferometer uses a beam splitter to create two
different optical paths. This can be used for optical testing.
Optical
window to
be tested
Input
Mirrors
Output 20 20 27

23. Optical Testing With a Michelson Interferometer
A Michelson interferometer uses a beam splitter to create two
different optical paths. This can be used for optical testing.
Optical
window to
be tested
Input
Mirrors
Output
If the window distorts the
waves, this will show up
in the interference fringes:
Good window. 20 20 28

24. Optical Testing With a Michelson Interferometer
A Michelson interferometer uses a beam splitter to create two
different optical paths. This can be used for optical testing.
Optical
window to
be tested
Input
Mirrors
Output
If the window distorts the
waves, this will show up
in the interference “fringes”:
Good window Bad window 20 20 29