Chapter 32: Interference and Diffraction
• Brief review of wave interference (PHY2048)
• Two-slit wave interference
• Diffraction
• Single-slit diffraction
Reading: up to page 575 in the text book (Ch. 32)
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• ;
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EM Wave Interference & Diffraction: Constructive & Destructive, Double-Slit & Single-Slit, Slides of Physics
The concepts of interference and diffraction of electromagnetic waves through mathematical proofs and explanations of constructive and destructive interference, the double-slit experiment, and single-slit diffraction. Students studying physics, particularly phy2048, will benefit from this material as they delve into the wave nature of light and its behavior when interacting with obstacles.
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Chapter 32: Interference and Diffraction
- Brief review of wave interference (PHY2048)
- Two-slit wave interference
- Diffraction
- Single-slit diffraction
Reading: up to page 575 in the text book (Ch. 32)
- ;
Interference of waves
- Suppose two electromagnetic waves with the same frequency,
polarization and amplitude travel in the same direction, such that
E
1
= E
m
sin ( kx!! t )
E
2
= E
m
sin ( kx!! t + !)
- The waves will add.
Interference of waves
- Mathematical proof:
E
1
= E
m
sin ( kx!! t )
E
2
= E
m
sin ( kx!! t + !)
E ' ( x , t ) = E
1
( x , t ) +^ E
2
( x , t )
= E
m
sin ( kx!! t ) + E
m
sin ( kx!! t + !)
Then:
1 1
2 2
But: sin α + sin β = 2sin α + β cos α −β
E ' ( x , t ) = 2 E
m
cos
1
2
sin kx!! t +
1
2
So: ( !)
Amplitude
Wave part
Phase
shift
Interference of waves
E ' (^) ( x , t ) = 2 E m
cos
1
2
sin kx & ' t +
1
2 ( !)
If two electromagnetic waves of the same amplitude,
polarization and frequency travel in the same direction,
they interfere to produce a resultant electromagnetic
wave traveling in the same direction.
- If ϕ = 0, the waves interfere constructively, cos½ ϕ = 1 and the wave
amplitude is 2 E m
.
- If ϕ = π, the waves interfere destructively, cos(π/2) = 0 and the wave
amplitude is 0 , i.e. no wave at all.
- All other cases are intermediate between an amplitude of 0 and 2 E m
.
- Note that the phase of the resultant wave also depends on the
phase difference.
Double-Slit Interference
Double-Slit Interference
Optical path difference between
the two waves:
d sin!
When equal to an integer number of wavelengths,
constructive interference occurs, i.e., bright fringes.
d sin! = m! ( m = 0 , 1 , 2 ,...)
Diffraction
Huygen’s principle: All points on a wavefront act as point sources of
spherically propagating wavelets that travel at the speed of light. A short
time later, the new wavefront is the unique surface tangent to all of the
forward-propagating wavelets.
Slit width >>!
Diffraction
Huygen’s principle: All points on a wavefront act as point sources of
spherically propagating wavelets that travel at the speed of light. A short
time later, the new wavefront is the unique surface tangent to all of the
forward-propagating wavelets.
Slit width <!
Single-Slit Diffraction and Interference
a sin! = m " ( m = 1 , 2 , 3 ,...)
Destructive interference when:
WARNING: This formula looks identical to the two-slit
interference formula; IT IS NOT!! Note that a is the slit
width, d is the slit separation. Furthermore, the above
formula describes destructive interference, whereas the
two-slit formula describes constructive interference.